;lMrl lili!i!ii!i';;i '!l''' pi; UNIVERriTY of CALIFORNIA i .. i. L(/S A .CEl.ES LixJiviiiv 1 THE NEW RATIONALISM THE DEVELOPMENT OF A CONSTRUCTIVE REALISM UPON THE BASIS OF MODERN LOGIC AND SCIENCE, AND THROUGH THE CRITICISM OF OPPOSED PHILOSOPHICAL SYSTEMS BY EDWARD GLEASON SPAULDING Professor of Philosophy in Princetoo Uciversity NEW YORK HENRY HOLT AND COMPANY r*. "- (^ (\ O C^ D V-'' *>•■> ^ COPTKIQHT, 1918, BY HENRY HOLT AND COMPANY PubliBhed May, 1918 THE QUINN « BODCN 00. Mill HAHWAY, N. J. i ^3 3 Cop,( PREFACE As I send this manuscript to the publishers, I am keenly aware of how far the results that it presents fall short of attaining that ideal both of method and of accomplishment which has been before me during the period of composition, and which I have explained in Chapters I. and III. Yet coinci- dentally with the closing of my labors I find that I am con- vinced more strongly than ever that, although there are many other ways, of undoubted value, in which to study philosophy, nevertheless the point of view and the method of treating problems which this book presents offer one way or mode of approach that has thus far been of much too infrequent use in philosophical investigation. For it has been my experience, especially during a number of years of teaching at Princeton University, as well as of presenting philosophical problems to the scientific workers of the Marine Biological Laboratory at Woods Hole, Mass., that there is, at present at least, a much deeper interest in a systematic than in a historical treatment of philosophy. An opportunity to satisfy such an interest would be presented to a far greater extent than it now is, if only the effort were made in philosophy, as it is in science, not to em- phasize history, but to investigate problems of fact, and finally to obtain such a fairly extensive body of knowledge as will receive general acceptance and be recognized as meaning a well- defined advance and progress. The present tendency in philosophy, at least in our educa- tional institutions, is, however, directly opposed to such a pro- cedure, for it is to the almost exclusive study of the history of philosophy that both student and general reader are urged and directed. The result is that the average student of philosophy is left so perplexed through, e.g., the multiplicity of systems which his study discloses to him, that his dissatisfaction usually far exceeds his satisfaction with the outcome of his intellectual efforts. But even if this is not true of the student, it most vi PREFACE certainly is the case with the scientist, who is thereby frequently moved not only to the sharpest criticism of all philosophy what- soever, but also to the total neglect of philosophical considera- tions where these cannot well be neglected. This book, therefore, represents the results of departing abruptly from the historical method, and of endeavoring to ascertain both what those postulates are from which each philo- sophical system is logically derivable, and also, whether there is, finally, one body of principles that is common to all systems, and logically presupposed by them. It is my conviction both that there is such a single "doc- trine," difficult though it may be to discover what it is, and also that this doctrine in its fundamentals is logically present in every effort to philosophize rationally. It is for these reasons, therefore, that I have chosen the title, The New Rationalism, for a position which also becomes, as a developed theory, a Neo-realism of ideals that are discovered by reason, as well as of those reals that are disclosed to the senses and that form what we call nature. A further constant stimulus to my efforts has been the con- viction, also, that, if it is to be admitted that philosophy is of direct and far-reaching effect on life — and what more convincing demonstration of such an effect could there be than the origins of the present world-crisis? — then that philosophy which the world needs to accept and to act upon at the present time, is one that holds to the actuality of ideals, discovered by reason, rather than one that justifies our living only in accordance with our biological nature. For it is such a naturalistic philosophy and ethics that, it seems to me, has not only actuated the present attack on civilization, but is also persistently used to justify this attack. There is need, therefore, not only of combating by physical force those physical forces to the use of which such a naturalistic philosophy has led, but also of combating and refuting by argument and by philosophical investigation that philosophy which is used to justify such a physical attack — if only such a refutation can be found. For if such a refutation cannot be found, then intellectually our attitude should be one of calm acceptance of the outcome, whatever it may be. PREFACE vii It is a most important problem, then, to ascertain whether or not there is possible a philosophical refutation of this nat- uralism that is challenging the world to the very foundations of its civilization, and, if there is such a refutation, to ascertain vJiat it is, or where its means can be found. » Such means are, however, surely not those of merely dog- matically denying the truth of Naturalism, nor of studying its history or development as a philosophy, nor, seemingly, of appealing to the opposed system of Idealism, which in the face of the present horrors that afflict humanity seems to have suf- fered collapse in its basic doctrine that "all's well with the A\orld." But, if the refutation of Naturalism is not possible by such means, then it would seem to me that it is possible only by a philosophy which can demonstrate that, while some "things" evolve, not all "things" are subject to the principle of evolution; that, while a ruthless struggle for existence may be one condition for progress, cooperation is another and, per- haps, more important condition ; that, while the best may survive (and may not), the mere fact of survival is itself not identical with heing the best; that, while justice may be useful to him who survives, there are, nevertheless, other reasons for the practice of justice than its usefulness; and, finally, that, al- though nature is undeniably fact, not all fact is identical with ruthlessly combating, slowly evolving, strongest-surviving na- ture, but that there are some realities which are beyond nature, and which, though they cannot be seen by the eye of the body, are nevertheless revealed to reason. The only philosophy, however, which can demonstrate these things, — i.e., which can refute and not merely deny Naturalism — is one that, in fearlessly submitting all "things" to reason's testings, includes among these "things" the very means either of defense or of refutation, namely, reason itself. And the only outcome at which such a rational "criticism" of reason itself can consistently arrive is one that justifies its own pro- cedure, and, therefore, any rational procedure whatsoever, as such. But such an outcome means the frank recognition that there are not only facts of the senses, but also facts of the reason, and that not all fact is part of nature or of evolution. Such a philosophy is, however, Rationalism. Viii PREFACE It is, therefore, both for the student and for the general reader who are interested, first, in problems that concern fact rather than history, and, secondly, in the more specijfic prob- lem, What is the correct philosophy, Naturalism, or some other opposed system? that this book is written. It is, also, for such readers, in case they are not familiar with psychology and logic, that I have presented certain questions, such as the Problems of Method of Part I., Section III., that are not usually offered in an ' ' Introduction. ' ' These Chapters may be omitted by one who is conversant with their contents, as may also Chapters II., XXII., XXIV., XLIII., vii.-x., if they are found too difficult. In conclusion I desire to express my appreciation of the sym- pathy and inspiration that I have received from my friends, Professors E. B. Holt, W. T. Marvin, W. P. Montague, R. B. Perry and W. B. Pitkin in the development of a point of view, a method, and, finally, a positive philosophy. The present volume is not cooperative, as was The New Realism in which my five friends and myself collaborated, but it is, nevertheless, in part an outgrowth of frequent discussions with these friends, and of definite attempts to cooperate. My thanks are also due my friend, Mr. Henry Lane Eno, who, in thorough sympathy with the general character of my endeavor, has kindly read the greater part of the manuscript. I also desire to acknowledge my obligation to my friend and colleague, Professor H. C. Longwell, for his careful reading of the proofs. Finally, I should explain, that the bibliographical references are intended, not to be complete, but only to indicate either the more important literature on a topic under discussion, or those places where the correctness of my assignment of certain specific positions to certain writers may be confirmed. Princeton, October 10, 1917. CONTENTS PART I PAQE Introduction xv SECTION I THE PROBLEM OF THE POINT OF VIEW CHAPTER I Postulates and Assumptions 3 II Realism and Logic 12 III The Old and the New Logic 25 I Introductory 25 II The Origins of the Traditional Logic ... 29 ni The Formulation and the Criticism of the Tradi- tional Logic 35 SECTION II THE HISTORICAL PROBLEMS OF PHILOSOPHY IV Introductory 44 V The Ontological Problem 51 VI The Cosmological Problem 64 VII The Teleological Problem ....... 57 VIII The Theological Problem 62 IX The Problem of Values 66 X The Epistemological Problem 71 XI The Psychological Problem and the Nature op Con- sciousness .88 SECTION III METHODS AND PROBLEMS OF METHOD I THINKING XII Reasoning by Words and the Psychology of Thinking 95 I Introductory 95 n The Thinking Situation 95 m The Psychology of Thinking; Symbols ... 96 IV Grammar 99 X CONTENTS CHAPTEB PAGE XIII The Logical Aspects of Thinking: Interpretations OF the Nature of Logic 99 I The Realistic View of Logic 100 II The " Psychologizing " Tendency .... 105 III The Pragmatic Tendency 109 II the traditional technical methods of reasoning XIV The Categorical Syllogism Ill XV The Truth of Premises 119 I The Regress of Premises 119 II Common Sense and the Social Tradition . . . 120 HI Induction 121 rv How Facts Are Given 122 1 Sense Experience 123 2 Intuition, Feeling, and Emotion . . . 124 3 Memory 126 4 Imagination 126 5 Self-Evidence 129 6 The Inconceivability of the Opposite . , 130 7 Presupposition by Denial 132 XVI The Nature of Contradiction 136 XVII The Disjunctive Syllogism 141 XVIII The Hypothetical Syllogism 144 XIX The Dilemma 148 XX Analogy 152 III analysis and the new logic XXI Further Implicative Situations and New Methods of Establishing Premises 155 XXII Analysis 158 XXIII Analysis by Incorrect Principles 160 XXIV Misinterpretations of Correct Analysis . . . 170 XXV The Methods of the New Logic: Summary . . . 173 IV theories of relations XXVI The Theories of External and Internal Relations 176 I The Formulation of the Theories .... 176 II The Proofs or Arguments for the Theories of Re- lations 178 1 The Theory of External Relations . .178 2 The " Modification " Theory of Relations . 182 3 The Underlying or Transcendent Reality Theory of Relations: Criticism of the Argu- ment 185 CONTENTS XI CHAPTER XXVII PAGE Types of Relations, of Wholes, and of Unities . . 190 I Types of Relations 190 II Types of Wholes 292 ni Types of Unity 197 IV Theories of Relations and Types of Logic . . 198 V Material Principles of Proof 200 PART II SECTION I INTRODUCTORY XXVIII The Problem about Problems 203 I The Epistemological Problem 203 II The Value-Centric Predicament 206 ni The Solution of the Ego-Centric Predicament , . 208 SECTION II CAUSATION PHILOSOPHIES XXIX Phenomenalism 216 I The Logical Derivation of Phenomenalism . . 216 II Phenomenalism's Solution of Problems . . . 224 in Criticism of Phenomenalism 230 XXX Subjective Idealism 233 I Logical Derivation 233 n Subjectivism's Solution of Problems: Criticism . 237 XXXI Positivism 041 I Derivation 241 II Criticism 251 XXXII Naturalism 257 I Detailed Naturalism 259 II Materialism, Psychism and Dualism: Materialism 262 m Universal Dualism or Parallelism . . . .264 IV Psychism : Criticism of Naturalistic Theories . . 268 XXXIII Pragmatism 273 I Pragmatism's Anti-Substance Doctrine . . . 273 n Pragmatism's Anti-Intellectualism .... 274 m Pragmatism's Evolutionism 283 1 Criticism: Truth and Falsity for Pragmatism 288 2 The Degrees of Pragmatism's Evolutionism . 295 IV General Criticism of Pragmatism .... 299 V Conclusion 3q1 xii CONTENTS SECTION III SUBSTANCE PHILOSOPHIES: OBJECTIVE IDEALISM CHAPTER PAGE XXXIV INTEODUCTORT 308 I Objective, Subjective, and Platonic Idealism . . 308 II The Historical Development of Objective Idealism out of Phenomenalism 311 XXXV The Logical Derivation of Objective Idealism: Criti- cism 317 XXXVI Developments of Objective Idealism .... 328 I Theism and Pantheism 328 II Panlogism and Ethical Idealism .... 329 XXXVII Further Developments of Objective Idealism . . 335 I Voluntarism 335 II Vitalistic and Romantic Idealism .... 342 XXXVIII Conclusion 345 I Monism's Solution of Philosophical Problems: Criticism 345 II What can the Absolute One be? . . . . 354 SECTION IV REALISM: FUNCTION PHILOSOPHIES I the central doctrine of realism XXXIX The Solution of the Eqo-Centric and Value-Centric Predicaments . 364 XL Realism's Hypotheses 372 I Knowing and Known Object may be Qualitatively Different 373 II Illusory Objects are Objective 374 in 1 Objects may be Genuinely Known . . . 378 2 They may Become Known and Cease to be Known 378 3 Not All Objects are Known . . . .378 IV Other Instances of External Relations. The Free- dom of Reason 382 V Philosophical Problems not Generated by their History 396 VI Truth an External and Non-causal Relation . . 396 VII Analysis does not Alter the " Thing " Analyzed 396 Vin Individualism and Skepticism are Logically False Positions 402 jx Analysis reveals Facts, and Mysticism is False . 402 CONTENTS l^iij C5APTEE PAGE XLI The Principles of Realism 408 I There are Propositions , 409 II There are Terms aud Relations .... 409 ni There is the Relation of Implication . . . 412 IV There is the Relation of Contradiction . . 414 V There is Consistency 418 VI There is a System of Propositions . . .421 VII There are Specific Processes called Knowing, and There is Knowledge 423 VIII There is Truth 423 IX Truth is Distinct from Certainty .... 424 X The Nature of Truth is not the Same as the Outcome of Knowledge, i.e., of its Successful and Satisfactory Working 425 XI Truth is Independent of its Proof and Tests . 426 XII Analysis is Possible 426 xni Reason is Free to Follow the Implicative Struc- ture of Reality 427 XIV An Analysis of the Knowing Situation is Pos- sible 427 XV Truth is not a Completely Implicative System of Truths 427 XVI There is a System of Ideal Truth .... 428 XVII Knowing and Known Object may be Both Quali- tatively and Numerically Distinct . . . 428 XVIII Particular Existent Entities are not the Only Objects that can be Known .... 429 XIX There are Two Types of Knowing, namely, (a) by Specification, (b) by Type .... 429 XX " Unknown " is not the Same as " Unknowable " 429 XXI Error is a Fact that can be Explained . . 429 XXII There are Certain Entities that are Related by Logical Priority 429 xxin Relations are Themselves not Causally Related 429 n CONSTRUCTIVE AND DETAILED REALISM XLII The Ontological Problem as Solved by Realism . . 430 I Introductory 430 n Realism's Solution of the Ontological Problem 432 XLIII Realism's Solution of the Cosmological Problem . 437 I Normal Objects, ii Error, and ill The Nature of Consciousness 437 IV Complex Entities; v Creative Synthesis; vi Freedom 444 VII and VIII Space and Time as Part of the Cosmos : Infinity and Continuity 451 XIV CONTENTS OHAPTEB PAGE IX Number 455 X Motion, Qualitative Change, and Evolution . 464 XI Consciousness as a Dimension and a Variable . 470 XLIV Epistemoloqy and Psychology as Pabt of Cosmoloqy 486 XLV The Realistic Doctrine of Values 496 ^LVI Realism's Teleology and Theology 607 INTRODUCTION The reader familiar with philosophical literature will find in this book a not inconsiderable departure from the usual presenta- tion and treatment of the problems, methods, and systems of philosophy. Such a departure, however, has been deliberately adopted by the author, not out of any mere desire to be ex- ceptional, but because of a philosophical and scientific point of view of the correctness of which he is deeply convinced. Some of the most notable features of this point of view and of the departure that proceeds from it are, briefly, as follows: — I. Genuine philosophical problems are regarded as being independent of their historical origin, setting, and develop- ment. This, of course, does not imply that these problems and the systems of philosophy which are sets of solutions of them, have not had a history. But, if the problems are real, and not false, it means that, while the consciousness of the problems has had a history, the problems themselves are not necessarily historical in character, nor conditioned by the development of the consciousness of them. Not all problems can be admitted to be historical or genetic, since, if history itself presents real problems, there may be other problems of fact that, as such, are not conditioned by their history and development. II. Each of the several great systems of philosophy is re- garded as a set of solutions (of philosophical problems) that are obtained by the use of certain methods and presuppositions which are in most cases otily assumed, either tacitly or explicitly, but not established and proved. These methods and presup- positions, moreover, have been regarded and employed in the past as absolute and self-evident, chiefly because of the influence of tradition on individual philosophers. They now, however, can be restated in a purely logical and disinterested manner, and subjected to examination and criticism by a method quite analogous to that strictlj^ scientific procedure which has recently xvl INTRODUCTION been adopted in the examination of the several geometrical sys- tems, namely, the Euclidean, Lobatchewskian, and Riemannian, not, of course, in reference to their history, but to their self- consistency, their basic postulates or so-called axioms, and their logical structure. III. The position is taken and developed at length, that most great philosophical systems have been worked out under the domination of a logic and of certain philosophical concepts that have come down in the tradition whicli emanated from Aris- totle. This tradition is one that uecognizes chiefly only a lim- ited number of relations between rentities, such as the relations of similarity and difference, as well as a limited number of philosophical concepts, such as cause and substance, so that it is limited as an organon, or method. IV. Historical study reveals the domination of this Aris- totelian tradition in its several phases, but does not so readily disclose its origin. However, this difficulty is to be expected if the character of the tradition is due to the unconscious influ- ence of certain entities on its initiators. But that hypothesis which accounts both for the specific character of the logic and for the concepts ivhich have dominated most traditional phil- osophical thinking is, that the physical thing, conceived as identical ivith a substratum in which qualities inhere, occupied the attention of the great philosophical pioneers more than did relations and events. This being the case, one should expect a logic of a specific kind, namely, a logic that is modeled after the most patent relations among physical things, and these are: — (1) independence of order, or mere additiveness, along with (2) resemblance and (3) difference, by virtue of which there are classes, and (4) the inclusion of one class in another, either completely, or partially-, or negatively. Furthermore, one should expect philosophies that are based either on the view that all entities are (5) in causal interaction with one another, or on the view that entitii^ are (6) substances or substrata in which attributes (7) inhere, or, (8) in some cases, on both views combined. } These expectations a e fully confirmed by the character of the greater part of pft.losophical development, in which there have appeared a seri28 both of causation-philosophies and of INTRODUCTION xvii substance-philosophies, though with neither of these fully ex- cluding the other in any one instance. We may therefore say, if a homely, but most expressive term may be coined, that philosophy has largely been "thingized" throughout its entire history. V. At the same time that philosophy has been, throughout most of its history, under the domination of the Aristotelian tradition, an independ'^it development has been taking place in science, especially for the last four hundred years. In this development a logic has Ix-^n used that is radically different from the logic of the traditic i, while the concepts of "relation" and of "event" or "happening" have played the dominant role as philosophical principles of thinking, rather than the concepts of substance and cause. This "new" logic and these principles have only recently come to full consciousness and received careful and accurate formulation. The logic is not limited to the logic of classes and, therefore, to such relations as similarity and inclusion, but is essentially the "science of order" — a principle which, as identical with the non-additive relationship of parts to form a whole, allows of the appearance and subsistence in the whole of qualities that are lacking to the parts. It fully recognizes also (1) the functional relation- ship as opposed to the causal, and (2) those asymmetrical and transitive relations that are present in series, such as the series of positive integers in order of magnitude. A pivotal point, also, in this new logic is the discovery (3) of the complete com- patihility of relatedness and independence, as instanced in a number of respects in the functional relation. VI. From the point of view and by the method which this new and non-Aristotelian logic furnishes, a number of im- portant philosophical positions ai i found both to be logically- justified and to receive empirical confirmation. One of the most important of these positions is, that the relationship between knowing and T -t which is known, what- ever that object may be, is but anothe ■ instance of entities that are related and yet independent, whic^i means, of course, that knowing does not create nor even affect that which is (to be) known, in contradistinction from the ri lit which is obtained if the problem of knowing is "solved" by the Aristotelian logic xvi'ii INTRODUCTION and by the principles of cause and substance. This episte- mological position is both Rationalism and Realism. Another position or result is, that the entities which can be known {in this way) are not limited to those of the physical and mental "worlds," but include, as well, universals and such ideals as perfect justice, which, though they may never "exist," are nevertheless facts. It is also found that recent attacks on intellectual analysis are really baseless because arbitrarily and unjustifiably they limit intellect to the use of a logic and of methods that are Aristotelian, and so seem to be able to demonstrate its failure; whereas, if in place of this traditional logic and method, the principles of the new logic be granted to intellect, it can be shown as inevitably to succeed. PART I PROBLEMS AND METHODS SECTION I THE PROBLEM OF THE POINT OF VIEW CHAPTER I POSTULATES AND ASSUMPTIONS In presenting an examination and analysis of the several great philosophical systems, not historically, but according to their success or failure in the solution of philosophical problems, and their logical dependence upon one or another set of initial assumptions, the writer has no intention to minimize the interest and importance of that study of philosophy which concerns its development. The literature of philosophy, however, is already full of both books and articles that are historical. There is opportunity, then, for a volume which has resulted from the conviction that, although philosophical problems and their mani- fold solutions have both had a history, nevertheless these prob- lems are not in every instance generated by their history, any more than are the problems of the science of history itself. This statement requires, perhaps, some elucidation, since the term history is somewhat ambiguous. It may be used to desig- nate the actual development, throughout one time period or another, of human thought, ideas, and institutions, or of the structure and functions of living organisms, or the evolution of chemical elements, or planets and suns. For the modem view is that all these evolve and have a history. The term may also be used to mean the scientific, or at least the systematic study of this development and evolution in any specific instance. Sometimes, however, the term is so employed that it seems to have both meanings at once, whereupon confusion arises. In this volume, however, it is the first meaning that concerns us most. Therefore, unless otherwise indicated, the term will be 3 4 THE PROBLEM OF THE POINT OF VIEW used to identify history with development and evolution. When used in the second sense we shall refer specifically to history as a science. With these distinctions made, the statement is clear, that history as a science has itself had a history or development. When this specific development is studied, as it is, e.g., in investigating the progress in historical methods and canons, we have the history of history. We may conclude, then, that history as development, history as a science, and the history of history itself are three different "things," and that the distinction between them is essential. It is important next to note that history as a science does not generate its own problems — at least, not all of them. The most it can do is to focus the attention of historians upon one kind of problem rather than upon another, as, e.g., upon that branch of history which concerns itself with the rule of kings rather than with the aspirations and deeds of the people ruled. As a science history is selective, not generative of its own prob- lems, unless these problems be false ones, — which is not beyond the range of possibilities. That history as a science must always be rewritten from the point of view of the present, is a dictum both frequently re- peated and widely accepted. But the reinvestigation of that which is past fails of its purpose, unless there are 7iew methods and points of view which themselves reveal facts and truths that are not historical. Indeed it may be that it is only by such truths and facts, and by such methods and points of view, now to be regarded as correct, that the real character of the past, oftentimes in its falsity of hypothesis and of problem, can ever become known. In other fields, e.g., in biology, the situation is quite similar. There has been a development of biological science, and there is a history of this development ; but biology as a science is little concerned with the study of this specific development, and is certainly not identical with the history of itself. A similar condition holds of many other sciences, such as logic, mathematics, mechanics, physics, chemistry, and astron- omy. Indeed one can say of these sciences that they themselves would not have had a development and a history, had there not POSTULATES AND ASSUMPTIONS 5 been problems which are themselves not developmental or his- torical. Philosophy presents no exception to these principles. It is admittedly a fact of compelling interest and importance that there has been a long and extensive development of human thought and knowledge, especially among European peoples, which because of its character and influence is called philo- sophical. For philosophy means love of knowledge. It is to be admitted, too, that this great ''stream of thought" has touched, or included in itself, to some degree at least, perhaps every phase of human activity, more especially religion, science, art, and politics. But the great vis a tergo in the onward sweep of its currents has been the conviction that there are problems of fact which have not been conditioned by their own develop- ment. Indeed, the consciousness that there are problems of development has itself been almost entirely absent throughout the greater part of history, as is witnessed by the comparatively recent origin of history, and especially evolution as sciences. It is the writer's intention, therefore, to present in this non- historical way the several great philosophical systems of the past in respect to their problems, their methods and their solu- tions of problems (whether these be true or false), and thus to review the comparative anatomy and morphology, as it were, of these systems, not as they have grown up in a maze of surroundings and of antecedent historical causes, but as each may be regarded today as a set of possibly genuine solutions of problems. As systems that have this character, they are open to examination and analysis as to their logical structure, their presuppositions, their self-consistency, their implications, and their agreement with facts, quite as much as they are in respect to their historical setting. And an investigation of this character also serves the purpose of presenting to the reader, whether he has a knowledge of the history of philosophy or not, the various systems of philosophy as they may solve or fail to solve problems that concern facts. Such a program, moreover, is not different from that of the scientist, e.g., of the student of geometry, who elucidates the older geometries in the light of present geometrical science, and who examines and develops in a purely logical manner the THE PROBLEM OF THE POINT OF VIEW possible geometrical systems, of which it is now well known there are several. Indeed, the character and purpose of this volume may be further made clear by the statement, that the writer has long been convinced of the close resemblance between the situations in geometrical science a7id in philosophy. This resemblance, while it is important, is, however, not complete. The several geometries, e.g., the Euclidian, the Lobatchewskian, and the Eiemannian, are each self-consistent and free from internal contradiction,^ This, however, cannot be said of the several philosophical systems, some of which are very evidently self- contradictory and self-refuting at critical points. Of this, Phenomenalism is a good example in its denial, on the one hand, of the possibility of knowing "things-in-themselves" {i.e., things as they really are), and in its assertion, on the other hand, that this is the real "state of affairs" concerning know- ing.^ But geometrical and philosophical systems both seem to agree in this, that there issues from them that which is put into them by way of initial postidation or assumption, be this taciti or explicit. In geometry it is usually explicit or conscious, while in philosophy it is, more frequently than not, almost entirely tacit or unconscious. The study of the psychological influences on the philosopher, both past and present, demon- strates this quite convincingly. The procedure of explicit postulation is commonly recognized to be the correct one in geometrical science today, though the history of geometry shows that it has not always been so. For not until Bolyai, in 1832, and Lobatchewsky, in 1835, inde- pendently found it possible to develop a consistent system of geometry by denying the Euclidean axiom of parallels, was there known a non-Euclidean system. This denial was made by postulating what amounted to the proposition, that through a given point not on a given line there are an infinite number of lines parallel to this given line. The non-Euclidean system that results is self-consistent and quite as applicable to our space as the traditional Euclidean geometry, as far as empirical measure- ment can determine. ' See the bibliography at the end of this chapter. "See Chap. XXIX. POSTULATES AND ASSUMPTIONS 7 Today, however, still other geometrical systems are known, of which the same assertion can also be made as regards their internal consistency and their application to the space in which we measure angles, distances, and the like. Among these sys- tems there is the Riemannian, which is based on the postulate, among others, that through a given point not on a given line no lines pass that are parallel to this line. Each of these geometries is a consistent body of propositions that are implied or generated by the original propositions which, as not derived from other propositions still "further back," are freely postulated or assumed. The process of discovering or deriving these later propositions chat are implied by these initial ones is deduction. This process, so far as it is correct, follows, as it were, the thread-like network of implications that already subsist or are facts. Each system is said to apply to a manifold of such entities, whether these be points, lines, sur- faces, or spheres, or something else, as can be "exhibited" to be in "consistent standing" with the propositions asserted about them. Thus a line, or a space of one dimension is found to be the field of entities, called "points," that are related in a very definite and specific manner, namely, by an asymmetrical and transitive relation.^ But emphasis is placed upon the rela- tions rather than upon the specific character of the entities that are related. In this way the necessity of making a defini- tion, e.g., of a point, is avoided, other than to assert that, e.g., a point is such an entity as is "consistent with what is said about it." The test of the consistency of a system of initial postulates and implied propositions is the "exhibition" of a class of entities of which the system holds. It is to be emphasized, however, that the geometer discovers a certain freedom to postulate * one set of initial propositions (axioms?) or another, so that, by taking advantage of this freedom, the several extant systems of geometry are developed. But it is further discovered that, although the Euclidean geom- etry historically preceded the other systems, nevertheless all the geometries are open to an examination and criticism • See Chap. XXVII. *Cf. articles by H. C. Brown and Karl Schmidt in the general bibli- ography at the end of the chapter. 8 THE PROBLEM OF THE POINT OF VIEW that is quite independent of the temporal order of their appearance. The writer of this book is convinced that a situation very similar to that which exists among the various geometries is to be found among the several great philosophical systems, not- withstanding certain obvious points of difference. In phi- losophy, as in geometry, there are fundamental divergences between the respective sets of propositions which constitute the different systems, and also between the respective manifolds of entities to which these propositions apply. Also, these differ- ences result from initial postulates. However, unlike the results in geometry, in philosophy not all systems are found by em- pirical tests to apply equally well to the universe. Further, not all systems are self-consistent and free from self-contradic- tion, and finally, the right or the freedom to postulate is not recognized. Rather, in philosophy the making of postulates that condition the remaining whole structure of a system, is found, in many instances to have been determined either by the emo- tional disposition of the individual philosopher, or, very fre- quently, by tradition, or by both together. Because of either of these two influences, or of both combined, fundamental philo- sophical assumptions are made unconsciously, or uncritically, and quite tacitly, and oftentimes with the support of the con- viction that they are necessarily true, either because they are self-evident, or because their opposite is inconceivahle, or both.^ However, tests or evidence of this kind are found, on the one hand, to be generated by the influence of tradition and author- ity, and, on the other hand, — which is not surprising — to be thoroughly unreliable as criteria of that which they are held to reveal, namely, absolute truth. That which is self-evident or inconceivable to one person, or to one generation, is not to another; and it is certainly not self-evident, that that which is self-evident, or whose opposite is inconceivable, must be true, and could not be false. That it might be false, is itself not inconceivable. But to become thus aware that it has been, not the unbiased investigation of facts, but rather the influence of tradition and authority that has led many of the great philosophers to develop ° Cf. the examination of these tests in Chap. XV. POSTULATES AND ASSUMPTIONS 9 their specific systems, is itself one of the first steps in freeing oneself from this very influence, and in establishing a firm foundation for further examination and criticism. On this basis one not only can discover that there have been great historical tendencies or postulates in philosophy, but also can critically restate these postulates, much as this is done in geometry, i.e., both the postulates themselves and the philo- sophical systems that result from them can be restated logically and quite apart from their historical setting, and both postulates and systems can be examined for their self -consistency and com- pared with one another. As a result it is found, not only that not all systems are self-consistent, but that some of them, and indeed perhaps all of them, presuppose one system. This system, since it is 0710 among systems, must, then, presuppose itself, and in this respect be self -consistent. This self-consistent and basic system, in the form in which it appears to the writer in respect to both its fundamental princi- ples and its detailed structure, is philosophical Kealism, the exposition and defense of which is here conducted by examining other, opposed systems as to their logical structure of primary postulates and derivative propositions, and not in their his- torical setting and development. The opposed systems, of which this system is critical, and which are found to presuppose it, and, possibly, also to be self- contradictory, are classified, contrary to the usual more elaborate classifications, as fundamentally only two, and even these two can be shown to arise from a common source and tradition. These two systems are a causation-philosophy, represented by Phenomenalism, and a "substance" and monistic philosophy, which usually takes the form of Objective Idealism. The common source is the Aristotelian tradition, with its logic of classes, and its dominant concepts of cause and substance. Other systems of philosophy, as they are usually classified, e.g., as Subjective Idealism, Positivism, Naturalism, and Prag- matism, and as Voluntarism, Pan-logism,® and the like, are but • See Wm. James, The Problems of Philosophy, for the types of phil- osophical systems; also L. Stein, Philosophische Stromungen der Gegen- tcart. 10 THE PROBLEM OF THE POINT OF VIEW specific modifications of these two more fundamental phi- losophies. These more specific systems thus fall together under two great heads because each is a product of one or the other of two great tendencies, which, on the one hand, have produced a rather definite historical succession of systems, and, on the other hand, are each identical logically with the tacit presup- position of a very definite set of metaphysical presuppositions. Thus, Subjective Idealism, Positivism, Naturalism, and Prag- matism (Naturalism up-to-date) present an historical sequence of systems which have resulted from the metaphysical assump- tion that all things causally affect one another^ On the other hand, the monistic systems of such philosophers as Spinoza, Fichte, Schelling, Hegel, Bradley and others have resulted from the assumption that a numerically single, suh stance-like, under- lying entity is necessary in order to mediate the relationships^ which are universal among all "things." ^ In the last analysis, however, even these two basic logical and metaphysical doctrines are traceable to a common source, namely, the Aristotelian phi- losophy and logic, especially as each of these has come down in the tradition. It is because of the influence of this tradition, not only that these metaphysical principles have been postulated unconsciously and uncritically, but that they have been in many instances accepted as self-evident and their opposite regarded as inconceivable. The metaphysics of cause and substratum (substance) and the logic of classes, since these together form the core of the Aristotelian tradition, constitute, then, that philosophy from which later systems have diverged as branch- ing genera and species from an ancestral tree.^ The Realism which is accepted, defended, and explained in this book is one that is based on logical and metaphysical doc- trines that are directly opposed to the logic and metaphysics of the Aristotelian tradition. The logic is one that has long been used in the development of modern science, but that has only recently been formulated as the logic of series, or as the ^ See Chap. XXVI. on the modification theory of relations, and Chaps. XXIX.-XXXIII. on the systems that are developed from this. " See Chap. XXVI. on the underlying-reality theory of relations, and Chaps. XXXIV.-XXXVIII. on the systems that are developed from this. " Bee Chap. III. for the expansion of this hypothesis. POSTULATES AND ASSUMPTIONS n science of order, and that can be designated broadly as non- Aristotelian.^o The metaphysics is one that denies the uni- versality of causation and of substance, and that emphasizes relations. On this basis it is found that the knowing situation is of such a character that the knowing process neither causally affects, modifies, or creates that which is known, nor demands an underlying entity to mediate the relationship between know- ing and its object. For this reason the position is called Realism. It is that position which results from discovering such empirical evidence, including non-Aristotelian logical principles, as allows for a knowledge of all entities in their genuine character. One of these entities is that very ''state of affairs" which the position itself asserts to be true concerning the knowing situation. Cer- tain other systems are not thus self -consistent. This Realism is, however, not one that limits the realm of entities that are knowable in their true character to the objects and relations of the physical universe, and to conscious proc- esses. Bather, it is a Realism which insists also on the factuality and knowableness of entities that are neither physical nor mental, nor "individual" in the usual sense of this term as meaning spatially and temporally particularized. All such entities may be called " subsistents" to distinguish them from the temporally and perhaps also spatially particularized ex- istents. They include what are frequently called " universals, " and also "ideals" such as justice, and still other entities, such as numbers, and the ideal systems of mechanics. This Realism is one which holds that the realm of such subsistents, as entities that are both knowaUe and yet independent of being known, is even more varied and extensive than the realm of existential entities." Indeed, as an important demonstration in the closing chapters of this book, it is shown that such worths and values, typified by justice and beauty, although they are ideals which are never completely attained, are, nevertheless, realities, BIBLIOGRAPHY Concerning the actual development of non-Euclidean svBtems, aa well aa the use of the method of postulation in other fields, see H. C. Brown in li^asays Philosophical and Psychological in Honor of William James, 1908. "Bee Char'xSv'^^^" ^^^^' '' ^°^ "' ^' ^°^ ^^^P' ^^"- 12 THE PROBLEM OF THE POINT OF VIEW pp. 425-459, and Karl Schmidt, Studies in the Structure of Systems, 4, " The Generating I'roblem," Jour, of Phil., Psych, and Scientific Methods, Vol. X., pp. 64-75, especially p. 73 on the freedom to postulate, etc.; also " Critique of Cognition and its Principles," Jour, of Phil., Psych, and Scientific Methods, Vol. VI., p. 281 ff. Concerning (1) the method of postulation in geometry, or (2) the actual systems that result, see J. Bolyai, The Science Absolute of Space, trans, by G. G. Halsted, 1896; original edition in Latin, Editio Nova, by the Hungarian Academy of Science, Teubner, 1903; K. Bonola, Non- Euclidean Geometry, trans, by H. S. Carslaw, 1912; B. Erdmann, Die Axiome der Geometric; D. Hilbert, Foundations of Geometry, trans, by E. J. Townsend; E. Husserl, Logische Untersuchungen; E. V. Huntington, Sets of Independent Postulates for the Algebra of Logic, trans, of the American Math. Society, 1904, Vol. V.; Wm. James, A Pluralistic Uni- verse, Lecture I.; Lobatschewsky, Geometrical Researches on the Theory of Parallels, trans, by G. B. Halsted; R. H. Nunn, Aims and Achievements of Scientific Method, Chap. V.; H. Poincare, Science and Hypothesis, 1905, Chap. Ill, on Non-Euclidean Geometries; B. Russell, Foundations^ of Geometry, 1897, and Principles of Mathematics, 1903; B. Riemann, f/fter die Uypothesen welche die Geometric zu Grunde liegen, 1868, Abh. Ges. Gottingen, 1868; also in Gesam. Werke, 1892; F. C. S. Schiller, Axioms as Postulates, in Personal Idealism; O. Veblen, A System of Axioms for Geometry, trans. Am. Math. Soc, 1904, Vol. V.; J. W. Withers, Euclid's Parallel Postulate, 1908; F. S. Woods, Non-Euclidean Geometry, in Monographs on Topics of Modern Mathematics, ed. by J. W. A. Young, 1911; A. N. Whitehead and B. Russell, Principia Mathematica, 3 vole.. Vol. I., Introduction; A. N. Whitehead, Axioms of Projective Geometry, 1906, and Axioms of Descriptive Geometry, 1907; J. W. Young, Ftmda- mental Concepts of Algebra and Geometry, 1911. CHAPTER II REALISM AND LOGIC ^ That ultimately a realistic position is taken in philosophy, even when one attempts the opposite,' and that this Realism is not limited to the acceptance alone of an existential world of physical and mental entities, has been, in the author's opinion, exceedingly well shown by Professor Josiah Royce in his Essay, "The Principles of Logic," in the volume entitled. The En- cyclopedia of the Philosophical Sciences, Logic, 1913. Pro- * This chapter was originally published under the title of " Realistic As- pects of Royce's Philosophy," in the Philosophical Review, Vol. XXV., No. 3, in the number in honor of Professor Royce. ' Uf. the criticism, throughout Fart II., of systems opposed to realism. REALISM AND LOGIC 13 fessor Royce probably would not have accepted this judgment as to the outcome of his demonstrations, but that the judgment is correct I shall endeavor to show by quoting^ and discussing certain paragraphs of the essay. Professor Royce 's essay will be examined in this way, both because it is a most timely and excellent presentation of recent results in the field of modern logic, and because of what seems to be its bearing on philo- sophical problems and their solution. The essay is divided into three sections. The last two, making up its greater part, are (p. 67) "devoted to indicating, very summarily, the nature of a doctrine of which the traditional General or Formal Logic is but a part, and, in fact, a very subordinate part. To this doctrine the name 'The Science of Order' may be given. It is a science which is indeed inci- dentally concerned with the norms of the thinking process. But its character as a normative doctrine is wholly subordinate to other features which make it of the mos*t fundamental im- portance for philosophy. It is today in a very progressive con- dition. It is in some notable respects new. It offers inex- haustible opportunities for future progress.' Defining Applied Logic, or Methodology, as that "special and very extended" part of "Logic as a Normative Science" "which deals with the norms of thought in their application to the methods used in various special sciences," Professor Royce says (p. 69) : "Methodology, taken in its usual sense as a study of the norms and methods of thought used in the various arts and sciences, is the mother of Logic taken in the other sense hereafter to be expounded. For the undertakings of Methodo- logy lead to certain special problems, such as Plato and Aristotle already began to study, and such as recent inquiry makes more and more manifold and important." "They are problems regarding, 7iot the methods by which the thinker succeeds, nor yet the norms of correct thinking viewed as norms, but rather the Forms, the Categories, the Types of Order, which characterize any realm of objects which a thinker has actually succeeded in mastering, or can possibly succeed in mastering, by his methods." • The meaning of the passages quoted is not altered by removal from their context. 14 THE PROBLEM OF THE POINT OF VIEW Discussing some of the solutions of the problems of method as they have occurred in the development of philosophy, he cites (p. 71) the view of Plato, that (1) "The realm of the Universals or 'Ideas' is essentially a System, whose unity and, order are of the first importance for the philosopher; (2) /n- ference is possible because truths have momentous objective Rela- tions, definable precisely in so far as the process of inference is definable; (3) The 'Order and Connection' of our rational proc- esses, when we follow right methods, is a sort of copy of an order and connectio^i which the individual thinker finds, but does not make. One thus sets out to formulate the right method. One discovers, through this very effort, a new realm — a realm of types, of forms, of relations. All these appear to be at least as real as the facts of the physical world. And in Plato's indi- vidual opinion they are far more real than the latter." Professor Royce then says (p. 72) : "We are not in the least concerned to estimate in this discussion the correctness or even the historical significance of the Platonic Metaphysic, — a doc- trine thus merely suggested. It is enough to note, however, that even if one sets aside as false or as irrelevant all the principal metaphysical conclusions of Plato, one sees that in any case the Methodology of the logician, even in this early stage of the doctrine, inevitably gives rise to the problem as to the relatively objective order and system of those objects of thought to which the methodologist appeals when he formulates his procedure. The Platonic theory of Ideas, Aristotle's later theory of Forms, the innumerable variations of the Platonic tradition which the subsequent history of thought contains — all these may or may not be of use in formulating a sound metaphysic. But in any case this comes to light : If a logician can indeed formulate any sound method at all, in any generally valid way, he can do so only because certain objects which he considers when he thinks, — be these objects definitions, classes, types, relations, proposi- tions, inferences, numbers, or other 'principles,' — form a more or less orderly system, or group of systems, whose constitution predetermines the methods that he must use when he thinks.* This system, or these systems, and their constitution, are in some sense more or less objective. That is: What constitutes order, * Italics mine. REALISM AND LOGIC 15 and what makes orderly method possible, is not the product of the thinker's personal and private caprice. Nor can he 'by- taking thought' wilfully alter the most essential facts and rela- tions upon which his methods depend. If any orderly classifica- tion of a general class of objects is possible, then, however sub- jective the choice of one's principles of classification may be, there is something about the general nature of any such order and system of genera and of species, — something which is the same for all thinkers, and which outlasts private caprices and changing selections of objects and of modes of classification." And again Professor Royce says to the same point (p. 73), "Order is order. System is system. Amidst all the variations of systems and of orders, certain general types and character- istic relations can be traced. If, then, the methodologist attempts to conduct thinking processes in an orderly way, he inevitably depends upon finding in the objects about which he thinks those features, relations, orderly characters, upon which the very possibility of definite methods depends. Whatever one's meta- physic may be, one must therefore recognize that there is some- thing objective about the order both of our thoughts and of the things concerning which we think; and one must admit that every successful methodologist depends upon grasping and fol- lowing some of the traits of this orderly constitution of a realm that is certainly a realm of facts." In all th^se quoted statements Professor Royce seems to accept very directly and unconditionally the objectivity not only of entities that are ideal and general and abstract, but also of those that are logical. Thus he opposes the dominant and tradi- tional view that logic is "subjective," and is, in this sense, the "art of thinking," and that the "laws of thought" are laws of a psychical process.* From the quotations given it would appear that all logic, including the traditional, narrow logic of classes and of the syllogism, is objective, and is only one of the several types of order. There follows, in Professor Royce 's essay, an exposition of some of the most important features of The New Logic, espe- cially as this includes "Order-types." In these sections such « Of. Chap. XUI. 16 THE PROBLEM OF THE POINT OF VIEW ' subjects as Relations and their "logical properties," Classes, Series, the Correlation of Series, Functions, and, finally, "The Logical Genesis of the Types of Order," are presented in con- siderable detail, and the following interesting statements, bear- ing upon specific points, are made (p. 97) : "Relations are of such importance as they are for the theory of order, mainly because, in certain cases, they are subject to exact laws which permit of a wide range of deductive inference. To some of these laws attention must be at once directed. They enable us to classify relations according to various logical properties. Upon such properties of relations all deductive science depends. The doctrine of the Norms of deductive reasoning is simply the doctrine of these relational properties when they are viewed as lawful characteristics of relations which can guide us in making inferences, and thus Logic as the 'Normative Science' of the deductive inference is merely an incidental part of the Theory of Order." Thus the implicative relation, the progressive dis- covery or guidance of which is identical with or accompanies our correct reasoning processes, is held to be objective. Rea- soning, as defined in this manner, has its conditions. Did these conditions not subsist, there might still be a "world," and this "world" might be knowable, but we could not reason about it. For, says Professor Royce (p. 107), "Without objects con- ceived as unique individuals, we can have no Classes. Without classes we can, as we have seen, define wo Relations, without relations we can have no Order. But to he reasonable is to con- ceive of order-systems, real or ideal. Therefore, we have an absolute logical need to conceive of individual objects as the elements of our ideal order-systems." With all this, excepting only a seemingly implied dependence of the individuality of "individuals" upon their being conceived as such, one can agree. But at this point, as in other places, Professor Royce seems to retract his earlier introductory asser- tions of the objectivity of the logical situation, and to color these now with an idealistic tinge. He introduces the thin edge of a wedge for his idealism even more noticeably, but quite as unnecessarily, in the statement (p. 108), that "Apart from some classifying will, our world contains no classes." One may very well ask. then: How about the class of ivilh that classify? Is REALISM AND LOGIC 17 this, as a class of individual wills or ^vill-ads that are related and so ordered in a certain way, itself dependent upon a classi- fying will? And, if not, may not other classes, and the indi- viduals, the relations, and the order, by virtue of which they subsist as classes, be equally independent of a classifying will, although related to it ? Professor Royee's "proof" or demonstration that Individual, Relation, and Class are "the Forms," or "Categories" that "characterize any realm of objects which a thinker has actually succeeded in mastering, or can possibly succeed in mastering," is contained in the Section on "The Logical Genesis of the Types of Order." His proof is the familiar one of finding cer- tain propositions that are "presupposed by their own denial." ° But in applying this test or criterion he again seems to pass from the earlier acknowledged objectivity of logical entities to a somewhat surreptitious introduction of an idealism that does away with this. Professor Royce's demonstration and the prin- ciple on the basis of which he makes it can be granted in the specific instance chosen. But one cannot allow either the limitation of the principle to this instance, or the conclusions which he draws from this specific demonstration. Some of the main points of his demonstration are as follows (p. 131) : — "(1) To any 'mode of action,' such as 'to sing' or 'singing' (expressed in English either by the infinitive or by the present participle of the verb) there corresponds a mode of action, which is the contradictory of the first, for example 'not to sing' or 'not singing.' Thus, in this realm, to every x there corresponds one, and essentially only one, x." "(2) Any pair of modes of action, such for instance as 'singing' and 'dancing,' have their 'logical product,' precisely as classes have a product, and their 'logical sum,' again, pre- cisely as the classes possess a sum. Thus the 'mode of action' expressed by the phrase: 'To sing and to dance' is the logical product of the 'modes of action' 'to sing' and 'to dance.' The mode of action expressed by the phrase, 'Either to sing or to dance,* is the logical sum of 'to sing' and 'to dance.' These logical operations of addition and multiplication depend upon triadic relations of modes of action, precisely analogous to the • See Chap. XV., rv, 18 THE PROBLEM OF THE POINT OF VIEW triadic relation of classes. So then, to any x and y, in this realm, there correspond xy and x + y." "(3) Between any two modes of action a certain dyadic, transitive and not totally non-symmetrical relation may either obtain or not obtain. This relation may be expressed by the verb 'implies.' It has precisely the same relational properties as the relation — -< of one class or proposition to another. Thus the mode of action expressed by the phrase, 'to sing and to dance,' implies the mode of action expressed by the phrase 'to sing.' In other words 'singing and dancing' implies 'singing.' " " (4) There is a mode of action which may be symbolized by a 0. This mode of action may be expressed in language by the phrase, 'to do nothing,' or 'doing nothing.' There is another mode of action which may be symbolized by 1. This is the mode of action expressed in language by the phrase 'to do some- thing,' that is, to act positively in any way whatever which involves 'not doing nothing.' The modes of action and 1 are contradictories each of the other." Professor Royce finds further (p. 134) : — " (1) That the members, elements, or 'modes of action' which constitute this logically necessary system 2 exist in sets both finite and infinite in number, and both in 'dense' series, in 'con- tinuous' series, and in fact in all possible serial types." " (2) That such systems as the whole number series, the series of the rational numbers, the real numbers, etc., consequently enter into the constitution of this system. The arithmetical continuum, for instance, is a part of the system ^." " "(3) That this system also includes in its complexities all the types of order which appear to be required by the at present recognized geometrical theories, projective and metrical." In conclusion. Professor Royce arrives at a position which, he calls Absolute Pragmatism, and which he holds "differs from that of the pragmatists now most in vogue." He says (p. 121), "There are some truths that are known to us not by virtue of the special successes which this or that hypothesis obtains in particular instances, but by virtue of the fact that there are certain modes of activity, certain laws of the rational world, ' Uf. for (1) and (2) Chaps. XXI.-XXV. and XLIII., vu., vni., ix., x. REALISM AND LOGIC 19 which we reinstate and verify, through the very act of attempt- ing to presuppose that these modes of activity do not exist, or that these laivs are not valid. Thus, whoever says that there are no classes whatever in his world, inevitably classifies. Who- ever asserts that for him there are no real relations, and that, in particular, the logical relation between affirmation and denial does not exist, so that for him yes means the same as no, — on the one hand himself asserts and denies, and so makes the difference between yes and no, and, on the other hand, asserts the existence of a relational sameness even in denying the dif- ference between yes and no." "In brief, whatever actions are such, whatever types of actions are such, whatever residts of activity, whatever con- ceptual constructions are such, that the very act of getting rid of them, or of thinking them away, logically implies their pres- ence, are known to us indeed both empirically and prag- matically; hut they are also absolute. And any account which succeeds in telling what they are has absolute truth J Such truth is a 'construction' or 'creation,' for activity determines its nature. It is 'found' for ive observe it when we act." With the general tenor of Professor Royce's essay I am in closest sympathy, and it is only to certain restrictions and con- clusions that exception must be taken. One can accept even the specific instance which the application of "proof by denial" furnishes, namely, that the "modes of action," "to assert" and "to deny," are themselves instances which conform to and pre- suppose the logic of classes, of relatio7is, of logical products, and of series. However, this is not proof for the idealistically tinged conclusion, that this logic is in some way created by "will," e.g., by the "will to assert" and "to deny," or that individuals, classes, relations, order, and the like are in some way dependent on "will." This idealistic tendency is exhibited in the statement, previously quoted, that "Apart from some classifying will, our world contains no classes." Modes of action such as those of willing, of affirming and denying, — and especially of finding that denial presupposes the very thing denied, may indeed present a specific existential case ' Cf. the criticisms of systems opposed to realism all through Part II. 20 THE PROBLEM OF THE POINT OF VIEW of entities that are individual, are similar, form classes with sub-classes, have logical products, and form series that are infinite, and, also, either discontinuous, dense, or continuous. But this does not imply that any of these generic entities as such, or that any instance of them, such as, e.g., the real num- bers, points, and physical objects, is created hy ''will," or dependent on it. The ground for this assertion is the generally recognized principle, accepted by Professor Royce himself, that, if there is one "instance," it is always a permissible hypothesis that there are others. Perhaps, indeed, "instance" means or implies just this possibility. It follows, that, if there is one "instance," namely, of acts of ''will" which form classes, series, etc., the possibilities cannot be denied (1) that there are other instances of these generic entities, class, series, etc., and (2) that these generic entities themselves also are, i.e., have being. However, if there are these possibilities, there are also the further ones, (3) not only that these other instances of individuals, classes, and series may be independent of that particular series which is identical with acts of will, but also (4) that the generic en- tities, class, series, and the like, may be similarly independent.^ In fact, this independence of "other instances" is itself identical with that of these generic entities. But in any case, even with only the possibility implied, that there are other instances of series than the will-series, it is logically prohibited to infer the dependence, either of these other instances, or of the generic entities, on the will-series itself. The opportunity for their inde- pendence is quite as good as for the opposite. Such an inde- pendence is quite compatible with a relatedness of both the specific and the generic entities to will, to reasoning, or to know- ing, and means the objectivity both of the generic logical entities, class, individual, series, and of all instances of these entities. However not only can one thus find that this hypothesis of the objectivity of logical entities and principles is permissible, and that it is confirmed by empirical investigation," but also one can show that Professor Royce himself really presents no obstacles to its acceptance as confirmed. For the very logical » Cf. Cliap. XLIV. ' Cf. Chap. XXVI., ii., 1. REALISM AND LOGIC 21 principles which our author himself elucidates and accepts, if they are applied to the specific situation under discussion, them- selves demand this conclusion. This can be demonstrated as follows : — Professor Royce makes a number of statements to the effect that "rational will," ''modes of action," "reasoning," "the making of conceptual constructions," and "the getting rid of them," and the like, each "presupposes" or "logically" implies that logic which is identical with classes of individuals that stand in one or another, or in many, of several relationships, and that form one of the several kinds of series. Although neither "presuppose" nor "imply" is defined by Professor Royce, each of these "entities" is by his own logic (at least) a relation. This is the case, first, because the distinc- tion is made between the act of "rational activity" (the \n\l to reason) and that which this activity presupposes or logically implies, namely, individuals, classes, and series. "Presupposer" and "presupposed" are, therefore, at least two. But, secondly, a relation is defined (p. 96) as "a character that an object pos- sesses as a member of a collection (a pair, a triad, etc.), and that would not belong to that object, were it not such a mem- ber." We must conclude that, since "presupposer" and "pre- supposed" are two, they are related, and that "presuppose," or "imply," is the relation present between them. The next important question is, Can that which is presup- posed or implied be related to, and yet be independent of the "presupposer" or "implier"? And again Professor Royce gives us the materials for an answer. In his presentation of the several classes of relations as dyadic, triadic, symmetrical and non-symmetrical, transitive and intransitive,^" he says (p. 99), ''Transitivity and symmetry are mutually independent rela- tional characters." This independence is then exhibited by finding instances of the one character without the other. Thus the relation of "greater than," symbolized by >, is transitive, since, il A > B and B > C, A > C; but it is totally non- symmetrical, since, ii A>B, this precludes B > A. Likewise the relation "father of" {A is "father of* B) is also non- symmetrical, yet it is non-transitive, since, if A is father of B, " See Chap. XXVIl. 22 THE PROBLEM OF THE POINT OF VIEW and B is father of C, A is precluded from being father of C: the relation '' father of" does not "go" from A to C. "An- cestor of" is, however, both non-symmetrical and transitive. Thus are symmetry and transitivity demonstrated to be, in Professor Royee's own words, '^ independent relational char- acters." But, in any case, by the principles previously stated, since these characters are two, i.e., a pair, they are related. Therefore it follows, in at least one case, that relatedness and independence are quite consistent, and 'cosuhsist.' '^^ Here again it must be said, that, if there is one instance of such compatibility, there may be others, and, further, that in no case does relatedness merely of itself imply, necessitate, or carry with it, dependence; nor independence, non-r elatedness. Just such another instance, however, may be the important relation, just discussed, of "presupposition" or "implication." That which is presupposed or implied, namely, the logic of order, may be related to and yet be independent of that which pre- supposes (or implies) it, namely, that very rational activity which Professor Royce emphasizes so much. With this the case, one certainly cannot justifiably assert that (p. 109) "our world contains classes" only because there is the will to classify. One cannot in this manner logically maintain a "synthetic union" of "creation" and "discovery." However, in order to confirm empirically this hypothesis, that independence and relatedness are quite compatible. Professor Royce himself need only have found, if possible, another class and series of individuals that bear the same relation (that of being "reviewed") to his own investigating mind as do his own rational modes of action. He discovers among or in these last, quite as Descartes found that either to deny or to assert con- sciousness is to presuppose it, a relation that generates a series. Thus he finds that to review a mode of action is itself a mode of action that implies its own possible reviewal in another mode of action, and so on, in an infinite series. Further, this series is found to be generated by an asymmetrical transitive relation, and is either discontinuous, dense, or continuous.^- However, each member of the series is, as Professor Royce himself admits " See Chap. XXVI., n., 1. ^= Cf. Chap. XLIII., vn.-x. REALISM AND LOGIC S8 (p. 153), "distinct," and sooner or later there is that member of the series which discovers, or is identical with ihe discovery of, the serial character of the whole. It is shown by the subse- quent study of this series, that, if any specific member drop out, especially any so-called first or last member, the series is no less serial or ordered. The series is, therefore, both related to, and yet independent of any member that can thus "drop out." Thus that very serial character of the "modes of action," which Professor Royce, in order to support his Idealism, would show is created by and depends upon the "will to act," is implied by his own logic to be independent of that individual act or member in which it is discovered. This is Realism. But further, that there are other series than the series of the modes of action called "reviewing," "noting," and the like, is also admitted, at least tacitly. For our author accepts and explains at some length the correlation of series and the func-/ tional relationship.^^ Then, at least, there must be series (at least two) to be correlated, say, by a one-one relation,^* and each series is distinct from the other. But, though thus related, they are also in their distinctness, or bare "twoness," inde- pendent. For. if there must be at least two entities as the con- dition for a relation, then this relation cannot in turn generate or condition this minimum of diversity. We thus reach, finally, an important conclusion of direct bearing on the problem of the character of the relationship between "knowing process" and "entity known," whether this be existential or subsistential, generic or specific, physical or mental. First, there are other manifolds than that of the series of rational will-acts. This is implied by the possibility of series being correlated, for correlation demands at least two series. But the manifold of will-acts is a series. Then there must be other series with which this is in correlation. Accordingly we must include (1) that other manifolds are, or have being; (2) that these other manifolds involve one, some, or all of the logical principles that the series of rational will-acts itself involves; (3) that, as "other than" and numerically distinct from this series, these other series are both independent of and " Cf. Chap. XLIII., VU.-X. " See Chap. XXVII. 24 THE PROBLEM OF THE POINT OF VIEW yet related to it, just as the series of one's own rational "modes of action" (e.g., Professor Eoyce's) are both related to and independent of that specific mode which is the act of discovery; ^^ and (4) that there is at least the possibility that all of these ordered manifolds should be related to, and yet be distinct from, not indentieal with, and independent of one another. This four-fold conclusion presents one of the most important parts of that modern logical doctrine which is called Logical Pluralism. It is the direct opposite of that tendency which Professor Royce supports, at least towards the close of his essay, namely. Logical Monism. These two positions together center on what is perhaps the most important prohlem in philo- sophical methodology, that, namely, of the compatibility of independence and r elatedness. ^^ The one answer to this problem, Logical Monism, has, whether it be true or false, conditioned logically the majority of the great orthodox philosophical sys- tems down to the present. It is an answer that is itself con- ditioned historically and psychologically in the Aristotelian tradition. The other answer, Logical Pluralism, has also had its foreshadowings now and then throughout philosophical devel- opment, but its roots strike deepest into that fertile soil for logical research which is furnished by the relatively recent de- velopment of the empirical sciences, including mathematics. Only of late has this tradition and tendency come, as it were, to self-consciousness, and its logic been formulated. Professor Royce 's essay forms a notable contribution to the formulation and emphasis of the importance of this new logic or "science of order," as it may be called. Indeed this long discussion of the essay has been undertaken because of its recognition of "the inexhaustible opportunities for future progress," both in philosophy and in science, through investigations in this new field. Not so much along the line of continuing to use the traditional logic as in philosophizing in accordance with the new logic, is there the possibility of philosophical advance in the future; not so much by studying substance and causation, mere classes, and the relations of exclusion and inclusion, will real problems be solved, as by examinmg the various types and " See Chap. XXVI., ii., 1. " Ihid. THE OLD AND THE NEW LOGIC 25 the properties of relations and series {as well as mere classes), the correlations of series {e.g., functions), and the nature of implication and presupposition. The one procedure would seem to have exhausted its possibilities : the other is full of promise. CHAPTER III THE OLD AND THE NEW LOGIC I. INTRODUCTORY A SURVEY of the general situation in modern philosophy dis- closes three dominant features. One of these features is the ascendancy of the epistemological problem over all other prob- lems. Thus from the time of Descartes (1596-1G50), of Locke (1632-1704), and of Kant (1724-1804) to the present, there has been sought either an absolutely certain basis for (absolute) knowledge, or a knowledge of how we know, or both, before philosophers have gone ahead and known, as, in contrast, the scientists have gone ahead. Secondly, there has been the almost exclusive influence both of a method or logic and of a set of fundamental premises, often called necessary truths, that may be grouped together under the caption of Aristotelian logic. The third dominant feature is one of omission, but it is the correlative of the other two. Philosophers have proceeded largely in ignorance of the actual practice of, and, in many cases, of the results obtained by the scientists, who have in- creased human knowledge without prior investigation of the problem of knowing. Thus, e.g., philosophy has largely been ignorant, until rather recently, of a logic that is radically dif- ferent from the Aristotelian. Now, as has been suggested in the preceding chapter, the demonstration that there is one philosophical position tvhich is presupposed by others, and that this position is Realism, is obtained by examining the "knowing situation" in the light of ^6 THE PROBLEM OF THE POINT OF VIEW the principles of this neiv logic. The general epistemological problem includes a number of more specific problems, such, e.g., as those of the origin of knowing, the nature of truth and its tests, the limits of knowledge, and the like. But ivhatever posi- tion is taken in the solution of these problems, and whether this position be Skepticism, Individualism, Pragmatism, Naturalism, Positivism, Idealism, or Phenomenalism, it is presupposed that the knowing process and the ''state of affairs"'^ known and asserted in the position taken, are both independent and related. This presupposition, however, is the very essence of Epistemo- logical Realism. In other words, whoever asserts or advances as true a position that is opposed to Realism, of necessity takes a realistic position toward that very ''state of affairs" which this opposed position describes. For, if one arrive at any conclusion at all in solution of the epistemological problem, then some position is asserted, as true in some sense, and this position is descriptive of that "state of affairs," regarding the knowing situation, which includes the relation of knowing to the entities known,, whether these entities be simple or complex. But it is there- with presupposed, that, although this (true) "state of affairs" is known by him who asserts it as true, and is therefore related to this specific knowing, nevertheless it is, as a genuine "state of affairs," not created, altered, or ynodified by virtue of this relation. This, however, is a clear case of asserting and of pre- supposing, at least tacitly, that rclatedness and independence are, in one instance at least, quite compatible. From this it follows, in this specific instance, that one, at least, of the two entities, knowing and entity known, could be without the other. But that this is the fact, is, again, one of the basic contentions of Realism. This discovery of the compatibility of relatedness and inde- pendence in the instance of the knowing situation, and in other cases as well, has extremely important consequences. Indeed this compatibility is a fundamental logical principle that leads to the development both of more specific logical doctrines and of a detailed Realism. One of the most important implications of the principle is, ' E. L. Thorndike, Elements of Psychology, p. 71 et passim, also uses this phrase. THE OLD AND THE NEW LOGIC 27 e.g., that it permits of the validity of analysis. For, iy it, the "thing" analyzed, though related to the act of analysis, can be independent of this. But, if it is thus independent, then the analyzed entity is not created, altered, or modified by the analysis. This principle of the consistency of relatedness and independence that is itself discovered by analysis, thus logically supports the validity of the very method of its own discovery. But, further, the principle implies that those constituent parts of which analysis discloses certain wholes to be made up, are to be accepted as entities that are not thereby created, but that are discovered. For, if entities can be both related and independent, then such constituent entities do not of necessity causally affect, modify, alter, or create one another. They can, therefore, either be removed experimentally without being changed, or, if an experimental removal is impossible, they, or at least certain classes of them, can be selected and isolated in the attention field, while others are ignored. This is analysis in situ - — a method that has been most productive, all through the history of modern science, of the discovery of the details of those complex entities that cannot be experimentally rent asunder. It is also a method of virtual ^ elimination, since, if one class of entities is independent, in the sense defined, of another class, then the one can he studied as if the other were not present. In the results and methods of the more exact sciences, espe- cially mathematics, and the new logic, which is largely the formulation of such methods, any number of instances of re- latedness and independence, of analysis in situ, and of virtual elimination are present. These are found, e.g., among func- tional relations, which subsist between variables; among abso- lutely simple entities, such as points and instants, both in the case of the relations of the individuals of each of these classes among themselves and to those of the other class; and among * Analysis situs is the term that is used in mathematics. But the phrase here used also has recognition; e.g., see Cajori, History of Mathematics, p. 226. Cf. Russell, Principles of Mathematics, pp 141, 466. It is here used with a broader meaning than it has in the technical analysis situs. * Cf . the definition of " virtual " as " existing in effect, but not actually," given by Mach, Science of Mechanics, p. 49, in his footnote concerning The Principle of Virtual Velocities. 28 THE PROBLEM OF THE POINT OF VIEW relations, such as 'cosubsisting' asymmetrical and transitive rela- tions, as we found in the preceding chapter.* If, now, it were not possible to discover in a direct manner, that the knowing situation demands the compatibility of re- latedness and independence and the possibility of an analysis which always leaves the knowing in situ in any situation where something is known, this might he discovered by first forming our hypothesis in accordance with those principles that are recognized in the new logic. Conversely, if these principles had not been already obtained from other sources, then the first sug- gestion of them as well as direct evidence for them could well come from an analysis of the knowing situation itself. Either order of procedure is thoroughly empirical, and the outcome in the two cases is the same. On the one hand it is, that the * ' state of affairs" in the "knowing situation" is one that demands, if no other instance does, those principles which are recognized in the new logic, while, on the other hand, it is, that for these principles there is one more opportunity for "application" in the particular instance of the knowing situation. An analogous statement with reference to the traditional, old logic, especially those doctrines which concern the concepts of substance and of cause, meets, however, with a different fate. First, the result of the empirical study of the knowing situation directly invalidates at least the universality of these two con- cepts. For it is found that the knowing situation is one that makes it impossible for the knowing or the ego to be a sub- stance, or to have a modifying, causal effect on the entity known, on pain of the attempt genuinely to know defeating itself. Or, secondly, if one endeavor, conversely, as it were, to "apply" these concepts of substance and cause, then they fail to account for the facts of the knowing situation, namely, that there is always something that is genuinely known. And yet it is just these traditional principles and concepts that have been applied, in one form or another, again and again, in the orthodox en- deavors to solve the epistemological problem, until, with per- haps every variation tried and a philosophical impasse reached, one must seek success by a radically different procedure. The necessity of thus adopting a new and radical point o^ * Pp. 21-22. THE OLD AND THE NEW LOGIC 29 vietv may indeed be forced upon us even by the mere manifold- ness of systems that result from the application of the tradi- tional doctrines. But, even if this were not so, the discovery of the self-contradictory character of at least some of these systems, and of the presupposition by all of them of the prin- ciples of the new logic, would compel our recognition. II. THE ORIGINS OF THE TRxiDITIONAL LOGIC The modern view is that logic is an empirical science. One accepts various types of relations, of classes, of series, and of functions because one finds that there are these entities. One proceeds here much as he does in physics, chemistry, and biology, namely, by induction. In induction one generalizes from those cases that are regarded as typical and are taken at random. The inductive procedure, further, may be used either quite unconsciously and uncritically, as it often is, indeed, in common sense affairs, or with full knowledge and control of it as a method, as it is in science. This modern view, although one not held by all logicians, as to what logic is, and as to what constitutes logic, results from the use of the general inductive method as it is used in science, namely, consciously. But the use of induction in the historical development of logic has 7iot been of this kind. For, if we investigate the heginnings of logic among the Greeks, we find much evidence for the conclusion, that these founders of logic were unconsciously dominated, in respect to the typical cases which they selected for inductive examination, by physical things. However, that this should have been the case, is, per- haps, not surprising. For psychology shows that, out of all the variety of the realm of entities with which we are acquainted, it is physical things that most extensively and intensively attract the attention of both the individual and the nation that is im- mature. But both psychology and the history of human thought show, also, that the physical thing, when this thus becomes the model for thinking, is itself conceived of as a complex of quali- ties that inhere in a suhstance-like substratum or core, the thing, i.e., the qualities and the substratum together, being "particu- larized" as here or there in space, and as now or then in time. It is the physical thing, therefore, as defined in this way, that 30 THE PROBLEM OF THE POINT OF VIEW was the model after which the Greek philosophers, though uncon- sciously, perhaps, patterned their thinking and formulated the "laws of thought," ^ these laws being called logic. Accordingly, " In the very nature of the case it is difficult to get certain evidence that Aristotle and his predecessors in Greek thought were predominantly influenced by the particular physical thing as the model after which they patterned their thinking, i.e., both their logic and philosophy. For such an influence would, in the circumstances, be exercised without at least the full awareness, criticism, and consciousness of those whom it affected. Therefore we must not expect to find an explicit recognition and formula- tion of this influence in the philosophical writings of the Greeks, but we must, rather, look for such an influence " between the lines," and beneath the surface. If, e.g., Aristotle's Metaphysics is examined in this way, it will be found that, by and large, the whole work, and especially Book V., is couched in terms of the particular thing. That to which Aristotle directs his thought, and from which he derives the rest of his philosophy is a concrete somewhat ( rdde ri ) , an individual thing. This concrete somewhat is a subject {v^roKeifievov) with qualities, quantities, and relations. These latter are the predicates of the former (vnoKelfievov ) , while the former, the subject, does not stand in the relation of predicate to the latter or to anything else. As examples of statements that confirm this whole view one finds in the Metaphysics the following definitions: Book V. (A), Chap. I., "'Be- ginning ' means that from which a thing arises, e.g., as the foundation of a house." Chap. IV., " ' Nature ' means the genesis of growing things." Chap, v., "'The necessary' means that without which, as a condition, o thing cannot live, e.g., breathing and food are necessary for an animal." Chap. VI., b, " Things are called one — because the substratum does not difl'er in kind." Chap. VIII., " ' Substance ' means the simple bodies, i.e., the earth and fire and water and everything of the sort, and, in general, bodies and the things composed of them, both animals and divine beings and the parts of these. All these are called substances because they are not predicate of a subject, but everything else is a predicate of them." In agreement with the view of the writer, that the particular physical thing was the point of departure for Aristotle, we have also the statement of Grote, Aristotle, 2nd ed., 1880, p. 97, that Aristotle " was, as far as we can see, original in taking as the point of departure for his theory the individual man, horse, or other perceivable object; in laying down this concrete particular with all its outfit of details, as the type of Ens proper, complete and primary; and in arranging into classes the various secondary modes of Ens according to their different relations to the primary type and the mode in which they contribute to make up its completeness." Also, ibid., pp. 69 and 79. A. W. Benn in his Greek Philosophers, 1914, and R. Adamson, in hia Development of Oreek Philosophy, 1008, also agree with my view. See the latter author, op cit., pp. 153-154 and 180-182. Also E. Cassirer, Substanzbegriff und Funktionsbe griff, 1910, Chap. IV., v., concurs in my views, not only as to the origin, but also as to the character of the Aristotelian tradition. On the Aristotelian tradition see de Wulf, History of Mediceval Phi- losophy, 1900, trans, by Coffee, and Scholasticism, Old and Neiv ; H. O. Taylor, The Classical Heritage of the Middle A (jes, and The Media vol Mind; and Adams, Civilization during the Middle Ages, Cambridge Mediaeval History. A good systematic account of the general character of this development in its divergencies, with names, dates, bibliographies. THE OLD AND THE NEW LOGIC 31 it is not surprising that not only in the logic and thinking of these Greek philosophers, but also in the whole long tradition which has developed from them, one should find philosophy to be dominated by the * ^ thing-concept,' ^ and by those further con- cepts that are derivable from this, namely, the concepts of sub- stance and of cause.^ etc., will be found in F. H. Thilly'a History of Philosophy, 1914, pp. 120- 227. Cf. with this, Boutroux, Historical Studies in Philosophy, trans, by F. Rothwell, pp. 74-169, especially pp. 156-162. For the continuation of the tradition in modern philosophy see The Life of Ren6 Descartes, by E. S Haldane, 1905. Evidence that the concrete particular thing was the model for earlier thinkers as well as for Aristotle, is found in Plato in the Cratyhis, the Vhcexlo, and the Parmenides. Plato's logic is presented in the Cratylus, the Phcedo, and the Thecetetus. * As illustrating the character of the tradition, and also as confirmatory of my main hypothesis, I may quote a modern scholastic, P. Coffee, Ontology, pp. 216-217. " First, as regards our knowledge of the existence of substances, and the manner in which we obtain our concept of substance. We get this concept from corporeal substances, and afterwards apply it to spiritual substances; so that our knowledge of the former is 'immediate' only in the relative sense of being prior to the latter, not in the sense that it is a direct intuition of the natures of corporeal substances. We have no such direct insight into their natures. But our concept of them as actually existing is also immediate in the sense that at first we spontaneously conceive every object which comes before our consciousness as something existing in itself. The child apprehends each separate stimulant of its sense perception — resistance, color, sound, etc., — as a ' this ' or a ' that,' i.e., as a separate stimulant in itself; in other words, it apprehends all realities as substances: not, of course, that the child has yet any reflective knowledge of what a substance is, but unknowingly it applies to all realities at first the concept which it undoubtedly possesses of ' something existing in itself.' It likewise apprehends each such reality as ' one ' or ' undivided in itself,' and as ' distinct from other things.' Such is the child's immediate, direct, and implicit idea of substance. But if we are to believe Hume, what is true of the child remains true of the man: for the latter, too, ' every perception is a substance, and every distinct part of a perception a distinct substance.' Nothing, however, could bo more manifestly at variance with the facts. For as reason is developed and reflective analysis proceeds, the child most undoubtedly realizes that not everything that falls within its experience has the character of ' a something existing in itself and distinct from other things.' ' Walking,' ' talking,' and ' actions ' generally, it apprehends as realities, — as reali- ties which, however, do not ' exist in themselves,' but in other beings, in the beings that ' walk ' and ' talk ' and ' act.' And these latter beings it still apprehends as ' existing in themselves,' and as thus differing from the former, which ' exist not in themselves but in other things.' Thus the child comes into possession of the notion of ' accident,' and of the further notion of ' substance ' as something which not only exists in itself (bvaia,] ens in se subsistens) but which is also a support or subject of accidents {vnoKeifjevov, suhstans, suhstare) . Nor, indeed, need the child's reason be very highly developed in order to realize that if experi- ence furniBhes it with 'beings that do not exist in themselves'; that if 32 THE PROBLEM OF THE POINT OF VIEW Such is the conclusion to which the study of the history of philosophy brings us, as is shown by the fact that the dominant concepts in philosophy throughout the middle ages and, indeed, in the greater part of modern philosophy, e.g., in the systems of Descartes, Spinoza, Berkeley, Kant, and Hegel, have been: (1) substance, in the sense of a substratum in which (2) quali- ties seem to inhere'' — as in a physical thing; (3) causation, in the sense in which one physical thing seems to affect another physical thing, namely, by producing an effect which is a new quality that inheres in the substance of the thing affected ; (4) the relations of similarity and dissimilarity, by virtue of which "things" form classes; (5) the fact of class and the relation of inclusion by virtue of which an individual "thing" is included in a class, or one class is included in another class,^ completely, partially, or negatively; (6) and finally, the additive relation by virtue of which, whether it exists alone or together with similarity, parts form a whole that is not ordered or serial in character, and that has only the same characteristics that the parts have. That philosophy and even science, somewhat, should have been dominated by these concepts, is, however, readily understood, if one inquires, What would most probably be the derivative con- cepts if the particular physical thing were unconsciously made the model not only for the formulation of logic but for "actual" thinking and reasoning? "Would it not then have seemed to the ' accidents ' exist at all, it would be unintelligible and self -contradictory to deny the existence of ' substances.' " Hence, in tlie order of our experience the first, implicit notion of sub- stance is that of ' something existing in itself ' ( Svoia ) ; the first explicit notion of it, however, is that by which it is apprehended as ' a subject or support of accidents' (vTroKeifjnov, suhstare, substantia) ; then by reflec- tion we go back to the explicit notion of it as ' something existing in itself.' In the real or ontological order the perfection of ' existing in itself ' is manifestly more fundamental than that of ' supporting accidents.' " 'Aristotle distinguished four causes. Tims he says: "The same thing may have all the kinds of causes, e.g., the moving cause of a house is the art or the builder, the final cause is the function it fulfils, the matter is earth and stones, and the form is the definitory formula." — Metaphysics, translated by \V. D. Ross, Bk. III., Chap. II., p. 990''. These four causes are usually called the efficient, the final, the material, and the foi'mal, respectively. They are in turn " reduced " to two, the material and the formal. * Aristotle's doctrine of the syllogism, contained in the Prior Analytics, the Posterior Analytics, and the Topics. THE OLD AND THE NEW LOGIC 33 uncritical mind, even as it does today, that a thing is not the mere aggregate of its qualities, but that it includes a suhstratum in which these attributes inhere? For, if there are qualities, are they not qualities of something, and so dependent? And do they not, therefore, imply something that, ultimately, is not dependent on anything else, on pain of this again being a quality and so in turn demanding a substratum? With this the case, would it be surprising if, further, the concept of a substance- like unitary ego" had resulted from "thinking" a human being after the analogy of a physical thing, with only the difference that the substratum here is regarded as spiritual instead of as "material"? And would it be a step far removed from this also to conceive of the manifold parts of the universe as inhering in one universal substratum, be this spiritual or material or even "unknowable"? To these inquiries the history of philosophy gives innumerable affirmative answers in, e.g., the doctrines of rational psychology and the modern ontological monistic systems of materialism and spiritualism. But further, with the physical thing made, unconsci'^asly, perhaps, the model for thinking, would it not also seem to the uncritical and naive mind that things woidd affect one another, so as to produce either modifications in old qualities, or quite new ones, yet in both cases without prejudice to the self-ideyitity of the substance-like substratum that is the "core" of each? And also, if all the entities of the universe were conceived of as "things" of this kind, and so in causal interaction, would not each "thing," in respect to its qualities, be infinitely complex by virtue of being affected by everything else? Indeed, would not each complex of qualities depend on all other "things'* to a greater or less degree, so that the universe would be like an organism? And finally, would not the soul, or the knowing ego, or whatever it may be called, be in interaction with other "things," both material and spiritual, so as loth to affect and * The Platonic doctrine of the unity of the soul, presented in the Phcedo, the Thewtetus, and the Parmenides is an excellent example of the trans- ference, to the human personality, of the model of the concrete particular thing defined as a unitary substratum with a manifold of qualities. Further references: C. M. Bakewell, Source Book in Ancient PhUosophij, 1909; Burnett, Greek Philosophy, Part I., Thales to Plato; Gomperz, Greek Thinkers, trans, by G. G. Berry, 1912; Lutoslawski, The Origin and Growth of Plato's Logic, 1905, 34 THE PROBLEM OF THE POINT OF VIEW he affected hy themf Then would not the very act of knowing, as the act of a thing-like-ego, causally affect the object {to be) known, with the result that all genuine knowing would h^ rendered impossible? ^'^ Again do our inquiries receive affirmative answer in some of the great systems of philosophical history. Thus there is phe- nomenalism, holding that things-in-themselves are unknowable, and not merely unknown, because the "structure" of the know- ing ego in its inherent qualities affects the "thing" known, thus to condition the character of all that filters through. Thus it conditions the tvorld that we live in as the only world that we know. Of necessity it follows from this that, ivere knowing eliminable, it could not be removed without altering "things" as we know them. But there are also panzoism, maintaining that the universe is a living being and has a soul, and anti-intellectu- alism, holding that genuine intellectual analysis is impossible, both because each thing is infinitely complex and because the removal of a part alters its causal context." Finally, we may complete our inquiries by asking: If the physical thing is the model after which the naive mind strongly tends both to conceive the entities that it thinks about and also to formulate its logic, then what kind of a logic will this bef Will it not be one that rests on the most patent relations among *' things," in addition to that of causation? And are not these the relations of similarity and of difference, and of mere "to- getherness" or additiveness ? But "things'' in that they are merely additively related form only a plurality or manifold or collection that is quite inde- pendent of order, while, as both similar and dissimilar, they form distinct classes. Patterned on the physical thing as a model, logic thus becomes essentially a system of classes that are either included in or excluded from each other, partially or com- pletely. But, if this is the logic of the naive mind, Greek or other, then, with a tradition based upon it, would there not develop philosophies which, because of the lack of the proper methods of analysis, become involved in unsuccessful struggles to solve such problems as those of infinity and continuity, calling •'Kant's phenomenalistic position: Bee Chap. XXIX. " See Chap. XXXIII. THE OLD AND THE NEW LOGIC 35 the results of these vain attempts "antinomies,"" as Kant does? Would there not also be systems which, because they insist that parts can be only additively related to form a whole, can conceive of 7iotliing new appearing in this world-process? Would they not thus be forced to deny all genuine evolution? And finally, would there not be systems that would be con- spicuous for their ignorance of those entities and relations which science discovers, such as (1) limits, (2) relations that generate series and correlations hetiveen these (some of which are called functions) , and, lastly, many other wholes that have properties which are very different from those of their parts f Historical inquiry shows that nearly all of the great philo- sophical systems, especially those of the last three hundred years, have one or more of the characteristics above mentioned. Yet that this should be the case is not surprising to him who looks sufficiently beneath the surface to discover the influences that have determined both problems and methods and solutions. One may conclude, indeed, that throughout its entire history phi- losophy has been for the most part "thingized," if the term is allowable. The one great postulate from which deductions as to both problems and methods and solutions have been made, is, that entities are "things" which (1) consist of a suhstance- like substratum in which qualities inhere, and (2) are related causally, additively, and by similarity and difference. in. THE FORMULATION AND THE CRITICISM OP THE TRADITIONAL LOGIC At the present time, however, in both philosophical and sci- entific circles there is a fairly general recognition of the necessity of some criticism of the Aristotelian traditional logic and of what it has produced. This criticism, however, is participated in by two schools. The one, attempting to criticize, is nevertheless, with the irony of fate, itself caught up in the onward sweep of the tradition. Even now it can discern no other methods and concepts for intellect to use than the Aristotelian. And since it discovers that, with these, intellect fails to solve certain prob- lems, this school takes refuge in a philosophy of emotionalism, " See Chaps. XXIII., XXIV., and XXIX. 36 THE PROBLEM OF THE POINT OF VIEW of intuition, and of direct experience. A much discussed repre- sentative of this anti-intellectualism, emotionalism, and prag- matism, is the French philosopher, Bergson. In criticism of this school it is perhaps but fair to admit that it is guilty only of an unconscious ignoring of those other methods and principles to which intellect may turn if it does not succeed by the use of the Aristotelian methods and principles. The other school of criticism frankly recognizes these other methods and principles, and, in the knowledge and use of them, not only discovers the reason for the failures of the past, but also solves problems and gains the promise of future advance. Those who thus criticize are, many of them, scientists, but, mostly, philosophers who keep their weather-eye on the methods, the results, and the logic of modern analysis. It is in the light of these methods and results that it is possible to reformulate, in terms of logical theory, the major postulates of the great historical systems of philosophy. The new logic, especially through its principle of the consistency of relatedness and independence, and its denial of universal causation, itself logically justifies the presentation of the "comparative anat- omy" of systems independently of their historical environment and causes. Even the Aristotelian logic in its several aspects receives reformulation and proper placing in a broader realm. Thus the Aristotelian doctrine of the syllogism is found to be but a special instance of the "science of order." An ordered series is generated by some asymmetrical and transitive relation, such as "precedes" or "less than" or "ancestor of," and the relationship of inclusion is only one of a number of such specific relations. Any asymmetrical transitive relation, e.g., "less than," supposing it to be symbolized by the sign <, is of such a character, that, if x — . — ', the meaning of which is evident. X, y, and R symbolize respectively the two related terms and the relation, and U the numerically single, metaphysical reality that medi- ates this. Objective Idealism is an example of a system that is logically derivable from the postulation of this theory as applied to all entities, i.e., to the universe.^^ The logical arguments for both of these aspects of the theory of internal relations will be given in a later chapter.^'^ In direct opposition to this twofold theory of internal rela- tions stands the theory of external relations. A convenient sym- bolism for this is x\R\y, or merely xRy. By this it is in- tended to express (1) the fact of the mere relatedness of the terms by virtue of the relation; (2) the absence of any causal action of either term on the other; (3) the absence of any com- plexity as produced by causal action; (4) the possible absolute, numerical simplicity of either term; (5) the absence of any entity to mediate the relationship, or to relate the relation to the terms; (6) the independence of the terms side by side with the fact of their relatedness. The central question for which each of these theories of rela- tions is asserted by its advocates to be an answer, is, How does a relation relate? The answer of one party is, that a relation relates by carrying with it, or by transmitting, a ca^isal effect from one entity to another ; of another party it is, that a relation relates through the agency of another, a third and underlying entity. Each of these answers is conditioned, at least psycho- " Chaps. XXXIV.-XXXVIII. " Chap. XXVI. THE OLD AND THE NEW LOGIC 39 logically, by the influence of the physical thing as the model for all thinking. The answer of a third party is that a relation just relates, with no causal effect, no dependence, no "under- lying entity." For the third theory, that of external relations, direct and convincing evidence is found throughout a broad field of scien- tific, logical, and philosophical investigation.^® A most impor- tant instance is the functional relationship — between variables, particularly in the case of "one-valued" functions, in which there is a one-one correspondence between two series. Each series is, of course, a manifold and a complex, but it is also an ordered whole; and, in the case of one-valued functions, each individual of the one series is related in a one-one manner to, or is in one-one correspondence with, one and only one specific individual of the other series. A simple illustration of such one-valued functions is presented in the case of the uniform motion of a body. Here the distance traveled is a function of the time required ; i.e., each point of the path or space-series is related in a one-one manner to one, and only one, specific instant of the time-series ; each of these correlatioyis is, therefore, itself a complex, but its constituent parts, namely, a point and an instant, are, not complex, hut simple; they are, therefore, hoth related and independent, since each would be "the same entity," if it were out of the relation, that it is in the relation. The motion itself is the series of these complexes, as these are related asymmetrically and transitively." Another instance of one-valued functions is the relation be- tween the uniform acceleration of a falling body, and the specific time-period required for this change. Acceleration is not mo- tion, but it is change of velocity. It is, therefore, a series of velocities that are correlated with the instants of the specific time series of which it is the function. Each specific velocity is a complex that is correlated in a one-one manner with one and only one instant of this time-series, and this correlation is in turn another complex. But no individual velocity is complex " See G. A. Bliss, "The Function Concept and the Fundamental Notions of the Calculus," in Monographs ov Topics of Modern Mathematics, ed. by J. W. A. Youno:; also A. N. Whitehead, Introduction to Mathematics, 1911, Chaps. 1., II., v., and VI. "See Chap. XLIII., x. 40 THE PROBLEM OF THE POINT OF VIEW by virtue of this particular one-one correlation, since, were there no accelerated motion, there could still be (motion of uniform) velocity. In other words, there could still be that complex, point-correlated-with-instant, which is the constituent term of uniform motion, even if there were not that further correlation of this complex with an instant, which further relational com- plex is the constituent term of acceleration. The brief analysis of these two examples shows that at least certain types of the functional relationship present a number of instances of entities, both simple and complex, that are related externally, as this term has been previously defined. Such in- stances are (1) an ordered series of points, and (2) of instants; (3) in the case of motion, the correlation of a point with an instant, and (4) the ordered series of these complexes as "form- ing" motion. Indeed it may be said, in general, of the func- tional complexes in their several aspects of simple and complex individuals that form series through asymmetrical and transitive relations, and of complexes that are formed by one-one relations, and the like, that a consistent explanation of them is possible only on the basis of the theory of external relations. Further evidence for the theory of external relations from the fields of both science and logic will be presented in the later chapters of this volume. At this point, however, we may note the important fact, that, while philosophy has remained for the most part under the influence of the Aristotelian tradition, scientific development has been, from the time of Galileo (1564- 1641), especially in the mathematical sciences, largely identical with the discovery of functional relationships and of what is involved in them. The expression of these relationships in brief formulae is indeed the symbolic form that is taken by the ma- jority of precise scientific laws. That which these laws express is, in a large number of instances, the correlation of variables, and this correlation is the functional relation.^ ^ Science at the present time distinguishes a number of different kinds of func- tions, and it is remotely possible that some of these do not allow of the "cosubsistence" of independence and relatedness. But the majority of them do, and indeed, in some such manner as •'Whitehead, op. cit.; Eoyce, Essay on "The Principles of Logic" in the Encyclopedia of the Philosophical Sciences. THE OLD AND THE NEW LOGIC 41 our specific examples show. The functional relation at any rate, therefore, involves in a number of ways relations that are external. For this reason, but also to employ a term which will perhaps be more familiar to the reader than "external relation," and which will suggest the sources of the evidence from which this theory is obtained, I shall frequently use "functional" as inter- changeable with "external." This can be done advantageously except in cases where more precise distinctions are necessary. As concerns the relation between the two, it may be said that the theory of external relations is the formulation of that con- sistency of independence and relatedness of which the functional relationship is, in its several aspects, a most important example. As other systems result logically from postulating one or the other aspect of the theory of internal relations for certain situa- tions, so Realism is that theory ivhich is, in general, consisten with the theory of external relations, particularly as "holding for the knowing situation. But there is a radical difference in the two cases. In the one case there may be said to have been a genuine application that was forced on philosophers ty his- torical causes. The systems that result are not only self-refuting, but lack empirical confirmation. In the other ease, that of Realism, the specific theory of external relations is found to be applicable. In other words, the investigation of the conditions under which genuine knowing is alone possible discloses these to be of such a character as to demand the "external" or "func- tional" theory. They are shown to be but another instance of the generic theory of two entities being both related and inde- pendent. For example. Phenomenalism, Subjectivism, Natural- ism and Pragmatism, and Objective Idealism, whatever else they may be, are asserted to be, if not explanatory, then at least descriptive of a "state of affairs" that is known, and that is true. Yet the sole condition on which, in each instance, this specific knowing can really be what it is at least tacitly assumed to be, namely, genuine knowing, is that of the cosuhsistent relatedness and independence of the knowing process and the state of affairs known. But this condition, as a proposition, is precisely what these systems explicitly deny. Therein lies one aspect of their inconsistent and self-contradictory character. i- 42 THE PROBLEM OF THE POINT OF VIEW Genuine knowing, and a cosubsistent relatedness and inde- pendence between the object known and the knowing, are erc- cluded, if the knowing is in any sense a substance after the analogy of a physical thing. For, if it is this, then the knowing process affects the object, and is self-defeating. From this the conclusion is clear, that, if genuine knowing is to be accounted for, and if knowing is to be regarded as a typical conscious process, one hypothesis as to its nature, and that the great his- torical one, is to be excluded. This hrjpothesis is, that knounng and consciousness are substances. Whatever else these entities may be, they cannot be this. They may be specific relations, or specific events, one or both, or even specific disembodied qualities that do not inhere in any substance. All of these classes of entities are shown by modern logical analysis to be quite con- sistent; for an event is a relational whole, and one specific event is qualitatively different from others. All of these classes of entities allow also for a cosubsistent relatedness and inde- pendence. But further, if the "substance view" is found impossible of acceptance in explanation of the nature of knowing and of con- sciousness in general, the suggestion lies near, that it must also be given up as a means of explaining the physical thing. This suggestion is confirmed by physical science. A physical thing is now regarded in physics, not as a substratum in which quali- ties inhere, but as a complex of mere qualities that are related in various specific ways. It is a whole that is the 7ion-additive result of its constituent parts, these parts seeming to be identical with different energy-forms. But even energy, although it is conserved, is not a substratum-like substance. Rather, it is at once a relational whole, a process, and a specifically distinct qualitative constituent of the universe. The "relational view of consciousness" is, then, that one which the writer finds himself compelled to support. Somewhat paradoxical though this view is in the light of tradition, and incomplete though it now is in many details, it is, nevertheless, that view which seems to be forced upon us by the logic of facts. It appears, however, as only one part of a much more extensive position that may be well called the relational view of the uni- verse, and that stands in strong opposition to the substance and THE OLD AND THE NEW LOGIC 4>S the causal views. This position may, however, receive other names. It may be called Ontological Pluralism from the fact that there are found any number of instances of entities, both simple and complex, that are related externally and functionally. No empirical evidence is discovered either for the universality of causation, or for one suhstratum, whether this be mind, matter, or an "unknowable," The position may also be called Realism, since, among the entities that are related externally to other entities, are knowing and consciousness. Objects known are neither modified nor created by the act of knowing, and no underlying reality is required to mediate the knowing. Finally the position may be called The New Rationalism to indicate that there are new methods of rational analysis which make it possible to solve problems where old methods fail. One is not justified in betaking himself to an anti-intellectualism and emotionalism on the ground that intellect fails, unless he has first granted to intellect the freedom to use all possible methods. Recent attacks on analysis '^^ have ignored those new logical methods and principles that come from science, and have assigned to intellect only those methods that are imbedded in the Aristotelian tradition. Intellect, if limited to these, does fail to solve many problems. But such attacks on intellect can have only a seeming success, for there are other methods, as we have seen. These new methods lead both to Logical Pluralism and to Realism. For this reason the name The New Rationalism is perhaps the most suitable for a volume that is a defense and an exposition of a position the character of which is well indicated by any of the three titles suggested. BIBLIOGRAPHY For a discussion of the problems of philosophy and the types of philosophical thinking see J. G. Hibben, The Problems of Philosophy ; W'm. James, A Pluralistic Universe; H. Hoffding, Problems of Philosophy ; A. Key, La Philosophie Moderne; R. Eucken, Main Currents of Modern Thought; VV. Windelband, Philosophische Richtungen der Oegenwart. ^^ E.g. by Bergson in Creative Evolution. SECTION II THE HISTORICAL PEOBLEMS OF PHILOSOPHY CHAPTER IV INTRODUCTORY Having outlined, in some detail, the point of view and also the departure from the more usual methods tvhich that point of view represents, we may now undertake the task of examining in further detail philosophical problems, methods, and solutions of problems. The problems of philosophy will be considered first, since so to proceed is to follow a certain natural order of relationship, whether this be logical, psychological, or historical, or all of these together. For it is clear, that, if there were no philosophical problems, there would be no occasion to apply methods of solution, even if these were ready at hand, and also, that, if there were no problems to be solved, there would be no solutions. To present, first, problems, then methods, and finally solutions, is, therefore, to follow a specific order of relationship between the three main divisions of all philosophical thought and development. However, in carrying out this program, the attempt will not be made to discover a definition of philosophy that will separate its problems from those of science, art, and religion. Rather, without any such definition, reliance will be placed upon the designation, both in the past and at present, of certain problems as philosophical. Thus to recognize the historical point of view is quite in agreement with the position, accepted in Chapter I., that, while history is not the only source of facts and of prob- lems, it is nevertheless one source, and that although many of the historical problems of philosophy may be genuine, many also may be false. But problems that are false logically may 44 INTRODUCTORY 45 psychologically be very serious and real, and should, therefore, in a general list of philosophical problems be included with those problems that are logically and factually genuine. Although the problems of philosophy will, then, be presented in this very general sense, nevertheless they will be limited very largely to that philosophy which has appeared in European intellectual development. This limitation is made with the ex- plicit recognition that very distinctive and interesting phi- losophies have developed in other civilizations, notably in those of India, of China, and perhaps of Japan.^ Indeed, for these, especially for the first, much preeminence in both insight and liberality is claimed by their occasional occidental adherents. It may also be found that these philosophies are adapted to their environment as beliefs to live hy, and that they are poetic in form and suggestive of realities which are mysterious and strange to the European mind; but, since it is also the fact that they have developed in a social environment from which there is absent much both of the knowledge of science and of the logic that is involved in science, we are relieved of the necessity of examining these systems in our present endeavor. With our program thus limited, it is advantageous to remind ourselves of that environment in which the problems, the meth- ods, and the systems of European philosophy have arisen. This environment consists of the realms of common sense, of conduct, of religion, of politics, of science, and of creative art and literature, each in a greater or lesser degree of development. Each of these realms influences the others and is influenced by them, and each contains certain elements which come to be recognized and formulated as philosophical. It is thus that philosophy arises and develops. Philosophy in turn is re- absorbed into each of these realms, to influence them, and again to help form a new environment, out of which, together with its own tradition, there develop new problems, new methods, and new solutions. However, of the parts played by these several realms in containing, in influencing and in being influ- enced by philosophy, it is the parts of religion and science that are most important. Each of these realms has furnished prob- ' See, e.g., P. Deussen, The Philosophy of the Upanishads, trana. by Geden, 1906; and lloyce, World aiul Individual, Chiijis. II. and IV. 46 HISTORICAL PROBLEMS OF PHILOSOPHY lems, methods, and solutions to philosophy, and each has, during certain periods of history, been the dominant motive and source for all philosophizing. Religion played this role, especially from the second and third centuries A.D., down to the seventeenth century, and has recur- rently done so ever sinee.^ But for the last four hundred years, while the problems that come from religion have not been excluded, it is science or at least the scientific impulse that has been the most active stimulus for philosophy.^ Also in the period of the bloom of the Greek civilization it was the scientific and not the religious impulse that was in most intimate inter- action with philosophy. Indeed it is important to note that in their beginnings in that period both science and philosophy arose from a common source, which was the conviction not only that there is absolute truth, but also that the attainment of truth is worth while both for itself and as a means to practical ends. However, since at the present time it is not religion, nor art, nor common sense, but science that is most intimately related to philosophy and that furnishes it with most of its problems and also with its methods, it is interesting to note hoiv this relation- ship has been interpreted in certain specific historical instances. First we may note the historical fact, that many hypotheses, theories, and laws that now are scientific in the strict sense of this term, e.g., the atomic theory, have had their origin in the tendency of men to reflect, to speculate, and to seek for con- sistent descriptions and explanations of the "things" that sur- round them. This specific relationship between science and philosophy, this origin of problems and solutions, is in large part identical with the development of thought among the Greeks, from its beginnings in the sixth century B.C. to its climax in Plato and Aristotle. A second and more sophisticated view is, that philosophy is the queen that reigns over the sciences, possibly in all justice and kindness, yet nevertheless to say them "nay" and to say them "aye," prohibiting and permitting, and passing judgment on the validity of their efforts. In this relationship philosophy " Much philosophy has been and still is apologetics. " iJ.g., with Descartes, Locke, tSpinoza, Comte, ISpencer, Mill, Mach, Avenarius, the Neo-Realists, and probably with the Pragmatists. INTRODUCTORY 47 would assume for herself the role of a science, yet one in which she would be not only distinct from other sciences in respect both of subject-matter and of method, hut also supreme over them. Her oivn distinct method would be that of criticism; her subject-matter, the methods and the results of the other sciences. Such an interpretation of the relationship between philosophy and science is the position of Kant and of the Kantian tradition, and persists even to the present. Thirdly, and in distinction from the relationship just pre- sented, it is also an historical fact, that, while to philosophy there has been assigned both a method and a subject-matter that are special, yet to her the right and the possibility of criticizing has been denied. By this view philosophy is a constructive science, along with other sciences, with her function neither that of destructive criticism nor of sitting in judgment over other sciences. This is a position of ancient lineage, since it is found among the Greeks. It also precedes Kant in the philosophy of Spinoza and of Leibniz, and follows Kant in Hegel and in the Hegelian school. Fourthly, still another interpretation and development, both historical and recent, denies to philosophy not only all right to criticize, both also all specific problems and methods. In this view philosophy is held to be but the sum total, or, perhaps, the organized and consistent unity of the whole group of the special sciences. But the special sciences selected and em- phasized are the group of so-called "natural sciences." Nothing is admitted to be fact except what is recognized by these sciences, and some sciences, such as mathematics, are denied their purity, and wholly identified with their application to natural "things." The whole realm of fact is thus held to be included in, and ex- hausted by Physics, Chemistry, Physiology, Biology, Astronomy, Psychology, and Sociology. This view has become especially prominent during the last hundred years, because of the great expansion of the natural sciences, and especially through the influence of such great empirical generalizations as Evolution and the Conservation of Energy. It is identical with Positivism and Naturalism, and is the position held by such philosophers as Comte, Spencer, and Ostwald, and by the majority of natural scientists. Pragmatism is in large part its latest phase. 48 HISTORICAL PROBLEMS OF PHILOSOPHY Fifthly, — though perhaps this does not exhaust the list of possibilities — there is the tendency of interpretation which grants to philosophy a special field of research, but assigns to her only those methods that have appeared and been tested in the development of science. But in this case, as concerns results, much, if not all, depends upon the view that is taken as to what these scientific methods are. If these are selected as being limited to the formal principles of the Aristotelian logic and the concepts of substance and cause, as is more frequently the case than not, then philosophical systems of a very limited type result.* On the other hand, if recognition and use are made of the modern scientific methods of the *' science of order" in its several branches of analysis in situ, and of discovering func- tional relations, series and their limits, and the various types of non-additive relations, and the like, then there result radically different, new, and satisfactory solutions of those problems that are left for philosophical investigation only because the special sciences omit to consider them. Aside from this, these problems are quite as scientific as they are philosophical, and whether they are referred to by the one name or the other is a matter of complete indifference. That philosophy which results from these liberal scientific methods as applied to the solution of specific problems, may be called Rationalism, or Intellectualism, or Neo-Realism. The general question as to the character of the problems of philosophy in their relation to science may perhaps be still more sharply focused by the question : Are the methods and the results of the individual sciences open to rcinterpr elation and trans- formation, and, if so, to what extent and in what manner ? This question is answered positively and definitely by the majority of philosophical systems, most notably by Phenomenalism, by Idealism, and by Naturalism. As an excellent example of the complete reinterpretation and transformation of the results of science, we may cite that philo- sophical position — of great influence in recent thought — which holds that all the entities of the enormous quantitative and. qualitative midtiplicity and diversity of this universe, are but * See Part II., Section 1, for the systematic and logical derivation of BUch systems. INTRODUCTORY 49 the manifestation of, and are held together in relation and made a universe by, a numerically single, unitary spiritual being. Such a being is frequently identified with the Deity, while the philosophy which holds to its existence, assign- ing to it such "manifesting" and "uniting" functions, is variously called Pantheism, and Transcendental or Objective Idealism. Another example of reinterpretation is the position which holds that all the entities of our immense and yet minutely de- tailed universe are, not the manifestations of a single universal entity, but the partial creations of finite knowing minds. This position is Phenomenalism. Still another position maintains, that this creation is not par- tial, hid complete, so that the whole universe (of time) and of space, and of all other entities, is reinterpreted to be only the sensations and ideas of finite knowing minds. This position is Subjective Idealism. If this view be developed consistently, then clearly everything, both great and small, must finally be "brought within" one finite mind, as only its conscious states. This position is Solipsism. If, now, these positions are illustrative of some of the more important ways in which the results of the individual sciences are reinterpreted and transformed, it is of interest to contrast this universe of the sciences in respect to its immensities and minutenesses, its multiplicities and diversities, with e.g., that numerical unity to which these characteristics are reduced in some systems. It does not in the least, however, lie within our province to endeavor to reproduce that account which the sciences give of the various aspects of this universe, but it suffices our purpose merely to mention some of the most conspicuous of these scien- tific facts. Thus, if we take the results of even one science, namely. Physics, we find that it reveals not only the most striking contrasts between the minuteness and the immensity of things, but also the almost inconceivable numerical manifol'dness. For, on the one hand. Physics holds to the existence of minute enti- ties, called electrons, that are of the diameter of l/100,000th of that of an average molecule, and that move at the rate of 37,000 miles per second ; on the other hand, there are other entities that; 50 HISTORICAL PROBLEMS OF PHILOSOPHY are quite as surprisingly large, and that, nevertheless, are made up of such extremely minute parts. For example, as regards the spatial size of "things," there are stars or suns which are many hundreds of times as large as our sun (this being 864,000 miles in diameter) and from which light reaches us only in 100,000 "light-years," a light-year being the total distance that light travels in one year at the rate of 186,000 miles a second. If these "scientific facts" are suggestive of the greatness and smallness of things, one can get an inkling of the numerical multiplicity of the physical universe by first contrasting, e.g., the size of a sun with that of an electron or even an atom, and then by realizing that these minutenesses are the components of those immensities. But nothing has been said thus far of the qualitative diversity of things, in regard to which science is not less startling. It may be doubted, if any two individual entities are ever exactly similar, but, whether they are or not, there are kinds or classes, and the multiplicity of these is here again almost overpowering. Thus, e.g., Biology recognizes that there are 500,000 different species of plants and animals, and Chemistry, that there are :iillions of qualitatively different compound substances. These few examples must serve the purpose of suggesting, though most inadequately, how very complex and manifold this universe is. But they may suffice also to show hoiv very extensive is the "material" that is to be manifested by a single unitary being, or held together in relationship or perhaps in an organic unity by such a being, or created in whole or in part by finite minds, if the fact of such activities is the conclusion that we accept as the result of our philosophizing, thus to maintain that the entities of science must be transformed. However, whether it is one of these positions or some other that is the conclusion with which we issue, in any case, the scien- tific account of things forms, together with the religious, the political, the aesthetic, and the common-sense realms, that en- vironment to which our philosophy must adapt itself as well as contribute its part, and of which it must be interpretative. But this is, indeed, now as it always has been, even when it was not science, but other influences that were paramount. For, from the time of the Greeks to the present philosophical problems THE ONTOLOGICAL PROBLEM 51 have arisen because they have been presented by that varied and complex universe in which men have found themselves as reflecting beings. CHAPTER V THE ONTOLOGICAL PROBLEM This problem is examined first because of a certain precedence over the other problems of philosophy. This precedence is in part historical, in part psychological, and in part methodological. Historically the ontological problem antedated the other prob- lems of philosophy in the form of the question as to ivhat is the fundamental "stuff" or "stuffs," the "material" or "ma- terials," out of which other "things" are "made," or which play the role of ultimate reality to other "things" as manifesta- tions and appeara7ices. This is shown by the well-known an- swers which were given to the problem, e.g., by Thales (624-548 B.C.), that all was water, by Anaximenes (about 588- 534 B.C.), that all was air, and by Empedocles (495-435 B.C.), that there were many fundamental materials, namely, fire, water, earth, and air. Quite analogous answers to the problem are, however, offered at the present day in both those monistic phi- losophies which maintain either that all things are ultimately psychical or spiritual, or that they are all material, and in those pluralistic systems which hold that not one, but many irreducible "stuffs" are in the universe. These answers indicate, however, that there are other phases of the ontological problem that strike deeper than does the problem as to what is the fundamental stuff, material, or sub- stance of the universe. Logically antecedent to this problem are the questions (1) whether the universe is made up of stuff or substance at all, rather than of events, or relations, or even disembodied qualities, or neutral entities; and (2), if there is anything ultimate, whether it is 07ie or many? The ontological problem may have come first historically be- cause of its psychological preeminence in the intellectual interest 52 HISTORICAL PROBLEMS OF PHILOSOPHY of the Greek race, and this priority it still possesses, since for many the bare question, what ''things" ultimately are, quite outranks in interest the question, ivhat ''things" do, or what happens. But to others the problem is of greatest interest because of the practical bearing on life which certain specific solutions of it are held to have. Thus, if investigation will only lead to this result, many a person attaches a peculiar sanctity to the con- clusion, e.g., that all "things" are ultimately psychical or spiritual, — a position which is identical with certain idealistic and theological doctrines. Indeed in this conclusion some find the only ground or justification for conducting their lives in accordance with certain ethical principles, especially those of optimism, whereas a debasement and a pessimism would be attached to the opposed conclusion, that all "things" are material. The ontological problem thus becomes not only prior in inter- est, but also in procedure for many. The position is taken, that law and order in the universe, and especially purpose, and a victory of good over evil, can be guaranteed only if the universe has a specific ontological character, — namely, that ultimately it is all rnental or spiritual in its being. Others, on the contrary, hold that the solution of the problem as to the law and order and purpose of the universe should not in the least he made dependent on the solution of the ontological problem. For, it is argued, if the universe has these characteristics, then they are ineradicahly there, whether the further character of the universe be one of complete and exclusive spirituality, or of materiality, or of something else. Still others contend, that, while the ontological problem may be first historically, and also psychologically — for some, — it nevertheless cannot be the first to receive solution. The reason for this contention is the posi- tion, held very widely in the philosophy of at least the last hundred and fifty years, that the solution of all other problems is dependent on the prior solution of the problem of knowing. Thus, after this manner, many a philosopher maintains that, indeed, no other philosophical problem can be satisfactorily considered, much less solved, until a solution is found for the question, as to ivhat is involved in the fact, that all things which THE ONTOLOGICAL PROBLEM 53 are known, even an ultimate "stuff," are in relation to a know- ing process or mind. It is evident that those who take this position regard, not the ontological, but the epistemological problem as prior to all others, — certainly as a matter of method, and perhaps, also, in respect to psychological interest. However, at the present time, not all philosophers accept this much protested priority of the problem of knowing, — indeed not even as regards its psychological interest, and there is much evidence to confirm such a disavowal. For the very outcome of the study of the problem of knowing may be the conclusion (1) that the fact that knowing is related to every known "thing," has no bearing as to the character of what is known, so that, (2) "things" can be genuinely known without previ- ously ascertaining how, whence, and ivherefore we know them. Such an absence of the prior investigation of the epistemological problem has characterized the greater part of the development both of common sense and of science. Indeed, ever since the epistemological problem came to the fore in philosophy, espe- cially with Kant (1724-1804), the larger part of scientific de- velopment and discovery has been the work of men who have ignored this problem, and who have contributed directly to the detailed solution of other problems. For a number of reasons, therefore, the ontological problem is placed first in our list. It is a relatively simple problem to state, if not to solve, and it arises very naturally in our reflective thinking. It also came first historically. Stated broadly, how- ever, in the form, Is substance ultimate, or are relations and events and qualities f and, How is the less idtimate related to the more ultimate? the ontological problem is part of a still more inclusive problem, namely, the problem of cosmology. In- deed, within this last problem there also falls the problem of knowing, or of knowledge, since it may be asked, whether it is not alone within a law-abiding universe, a cosmos, that knowing has its ''place," its function, and its specific relations to other entities.^ » See Chap. XLIV, i. 54 HISTORICAL PROBLEMS OF PHILOSOPHY CHAPTER VI THE COSMOLOGICAL PROBLEM Briefly, this problem may be said to concern the question of the order, the laws, and the organization of the universe. It is the problem of Cosmos versus Chaos. More specifically it is the question as to whether law and order, e.g., classes, series, correlated series, and the like, are present among, or absent from the universe, and, in the former case, what the character and source of this law and order is. Clearly, however, the logically prior problem here is whether law and order are present in or ahsent from the universe, i.e., whether the universe is a cosmos at all. For, if there were no law and order, then it is clear that there would be no further problems as to their character and source. According, of course, to the prevailing scientific point of view, this prior problem seems quite artificial, but it is, nevertheless, regarded as a genuine problem by at least one contemporaneous philosophical school. Thus the pragmatists and the modern humanists, the romanticists, and some of the mystics, frankly contend, that all that there is of law and order is what human beings "read into," or impose upon a universe that is of itself chaotic, ca- pricious, lawless, and orderless.^ However, whether those very conditions that, on the one hand, permit of, and, on the other hand, lead to, such an accession and imposition, are not them- selves identical with law and order and cosmos, is a question that is not considered by the philosophers of this school. Opposed to this there is the position, which is much more frequently taken, that law and order are '' resident'' in ''things," and thus present to be discovered, whether by methods difficult or easy, and notwithstanding that error may precede success. Differing but slightly from this there is also the position, that the source of all law and order is a single, infinite spiritual Being, God, who is either the one substance of the universe, or ^ E.g., James, Some Prohlems of Philosophy, Chaps. X., XIII.; and Schiller, Studies in Humanism, 1907. THE COSMOLOGICAL PROBLEM 55 its creator, or its architect, or at least its legislator. Each of these subordinate positions is taken as a result of the endeavor to solve minor cosmological problems, or groups of problems. The general cosmological problem is, however, the 7nost in- clusive of all the philosophical problems. Thus, if there are ultimate entities, one or many, that ynanifest themselves in other things as appearances, there is the problem as to the relations between and among these entities, both manifesting and mani- fested, both realities and appearances. The cosmological prob- lem thus includes the ontologieal. But it also includes the teleological, the theological, the epistemological, the valuational, and the psychological prrblems. For such questions as those (1) as to the absence or presence of purpose in the universe, (2) of the fact and character of the Deity, (3) of the relation of knowing to that which is known, (4) of the fact and character of values and worths, and (5) of the nature and function of consciousness, are each directed to some specific problem con- cerning one or more aspects of a universe that is a cosmos. A good part of philosophy and science is to be regarded, therefore, as aiming to solve the detailed problems of cosmology. But there are also cosmological problems of more general character than these last. Thus there is the problem as to whether, by any possibility, the many laws of the universe (assuming that there are laws in some sense) may not be merely specific instances of one fundamental law, so that, side by side with an apparent pluralism, there is a fundamental logical monism. There is also the similar question as to whether there is one fundamental law that applies to all entities. To this there is, e.g., the affirmative answer, that causation is such a law, and that all, indeed quite all the entities of the universe causally affect one another, so that the universe is like, or, indeed, is an organism." Or, is the universe patterned after the model of a classification of plants and animals,^ with differences yet with similarities, so that finally an all-denoting class-concept is reached that denotes everything, even as "living being" is the generic class for all plants and animals. And what is such 'E.g., in the philosophy of Fechner (1801-87) and of Paulsen (1846- 1908). ' Aristotle, and, with certain limitations, Plato, and Spinoza. 56 HISTORICAL PROBLEMS OF PHILOSOPHY an ultimate siimmum genus, if it exists? Is it "existential entity," with the physical and the mental as species, or is it mere "entity," or "being," or "subsistent," with "existent" and "non-existent" (such as, e.g., a perpetual motion machine) as species ? Or, again, if the universe is not organized either in this way or as an organic whole, do its various basic laws form a complete mutually implicative system, or, are they merely consistent with one another,* after the model of the postulates (axioms) of geometry? Or, finally, is the universe stratified, after a rough analogy with the layers of rock in the earth, so that there are certain entities, called logically subsequent, that are dependent on others that are logically prior, but with the latter inde- pendent of the former? If this is the case, then would not each later "layer," as being something more than all the pre- ceding ones, possess the positive freedom of following the law or laws of its own positive peculiarities? For example, would not life be "free unto itself," yet law-abiding at that level where life first exists ? And would not a free will be the law of moral- ity in that "stratum" where morality alone occurs, namely, where conscious 'beings first form a society?^ Each of these views can be found somewhere in contemporane- ous philosophical literature, — a fact which indicates that, taken broadly in a psychological as well as in a logical sense, they constitute a list of solutions to a set of problems that concern the nature of the cosmos. But there are still other specific and very important cos- mological problems. One of these concerns the question as to the types to which the complex entities of the universe belong. For example, are there not groups of individuals in the universe that not only resemble one another, so as to form classes, but that also have an order and form series, after the manner of the positive integers in order of magnitude? Also, if there are series, are there not relations betiveen series such that a particular individual of one series is correlated with one and only one of another series, after the manner of the correlation of a particular velocity (of a moving body) with one and only * The position of modern science. See Chap. XLI , vi. • See Chaps. XLIII., v., and XLIV., n. THE TELEOLOGICAL PROBLEM 57 one particular instant of time? Another closely allied cos- mological problem concerns the questions as to what entities in the universe are strictly continuous in the precise scientific sense of this term, and what ones are as strictly discontinuous. Are there, also, both infinities and finitenesses? Which of these, indeed, is the universe itself as a whole — in respect to, e.g., its spatial and temporal characteristics ? All of these are problems of cosmology that have for the most part long persisted in both philosophy and science. However, through recent investigations they have, in some instances at least, received a seemingly definitive answer, while the princi- ples and the logic discovered and used in their solution go far toward solving the other prohlems of cosmology.^ CHAPTER VII THE TELEOLOGICAL PROBLEM Stated briefly, the teleological problem may be said to concern the question, whether or not there is purpose in the universe as a whole, and, if so, in what sense. It is clear, however, that this problem logically precedes the problem as to ivhat is the source and origin of such purpose, since, if purpose were not in some sense a fact, there could exist no question about its origin or source. However, for psychological reasons, these two problems are frequently confused and their order reversed. The fact of pur- pose in at least some sense undoubtedly becomes first known in the realm of our own human desires, ideals, and deeds. Al- though the analysis that is made of it in this sphere varies somewhat, nevertheless, in general, purpose is held to involve (1) the desire or acceptance of something not yet a fact as (2) worth realizing in the future, and (3) the adoption of some means to attain this end. But with the idea of purpose thus once become present, its transfer to other realms is made with ease, so that it soon may be held to characterize even the uni- • See Chap. XLIII. 68 HISTORICAL PROBLEMS OF PHILOSOPHY verse itself as a whole. This specific transfer is accelerated, and the order of the two problems as to the source and fact of pur- pose is confused and reversed, if the conclusion has been previ- ously derived, that the universe is a vast order and uniformity of "things," a realm of law and adaptation, and that all this demands an Orderer, a Lawgiver, even a Creator.^ For from this conclusion there readily follows the conviction, that such a Being is also a Purposer, and that the Cosmos is one great system of means to the accomplishment of ends. Thus, without prior and independent investigation as to whether or not there is purpose in the universe as a whole, a positive answer to this problem is derived from one of the specific solutions of the cosmological problem, i.e., from the possibility of there being purpose, the conclusion is drawn, that this purpose is actual in the realm of existing "things." If, now, for some, the teleological problem receives a positive solution in this manner, it is clear that the further character of the teleology that is accepted will depend largely upon the char- acter of the cosmology from which it is derived. For in each case here. Lawgiver, Source of law, Orderer, Purposer, on the one hand, and universe, on the other hand, are held to be in some sense apart."^ Thus, as one possibility, the two may be regarded as distinct in the sense that, the universe having once been made a Cosmos of law and purpose, the Lawgiver and Pur- poser then withdrew, to leave His work alone ever afterward, and, indeed, perhaps quite unable subsequently to interfere. This position is Deism.^ Or it may be held, that the Lawgiver and Purposer can interfere at any time, either to institute new instances of law and purpose, or to withdraw old ones, so that He is ever present and never remote. This view is one form of Theism.* Both Deism and Theism, in that they are positive * The Physico-theological argument. * Cf . H. Hoflding, The Philosophy of Religion, pp. 14-05. ' A product of modern scientific speculation as this developed into 18th century rationalism, and a position taken by a great many of the philosophers of that (18th) century. See Leslie Stephen, History of English Thought in the 18th Century, 2 vols.; J. G. Hibben, The Philosophy of the Enlightenment. * The position taken by most orthodox Christians and one whose apolo- getics is found in the works of Kant, Berkeley, Leibniz, Descartes, Aquinas, and a host of others. Galileo, Newton, and Robert Boyle were theists. THE TELEOLOGICAL PROBLEM 59 solutions both of the cosmological and of the teleological prob- lems, tend to accept a Being who is Himself prior in time to that Cosmos which He is held io order, perhaps even to create, but, at least, to use as a means to an end. Opposed to these there is also the position in which the Or- derer and Purposer of the universe is regarded as The Ultimate Eeality, who is eternal in the sense of being timeless, and who, as thus apart, manifests Himself in the universe of temporal and spatial things. This view is a modified Theism, which tends to become Pantheism.^ It is held to account logically for an immanent as opposed to a transcendent or external teleology, which is the position of Deism and the first kind of Theism, Deism, Theism, and Pantheism are all in agreement, however, in holding not only that there is order and law in the universe, but also that this establishes the fact both of purpose and a Purposer. They are in agreement also in holding that this Pur- poser is external to that to which purpose is given, at least as a means to an end, namely, the universe. The first two positions maintain this very clearly, but the third position. Pantheism, does so, also, since the manifestations of a Deity cannot be identical with Himself as Manifestor, but must be numerically distinct from Him. However, it is quite evident, as has been said, that the teleol- ogy which each of these three positions accepts, is entirely subsequent to and dependent upon that specific solution of the cosmological problem which holds that order and law demand an Orderer. For, having once reached this last conclusion, it is easy to attribute purpose to this Being in analogy to the fact of purpose as we discover it in our own conduct. But the situation becomes radically different, if the argu- ments for such an Orderer and Purposer are invalid, for we are then thrown back upon the bare question. Does purpose characterize the universe quite hy itself and independent of any entity that is. external to the universe? But through this ques- tion the teleological problem leads at once to the further prob- lem as to whether there are in the universe, side by side with ' The position held by a Jargo number of the great philosophers of history, notably Roger Bacon, Spinoza, Fechner, Schopenhauer, Hegel, Bradley, and perhaps Royce. 60 HISTORICAL PROBLEMS OF PHILOSOPHY those entities which are non-values, such as the physical sciences deal with, still other entities that are, in contrast, worths or values.'^ Indeed, it may be asked, whether, if there is purpose, this does not itself presuppose these value-entities? For, does not purpose mean, ends deliberated about, chosen among, and sought for, because they are ultimately worth while for them- selves, and not merely as means to an end? Are not such ulti- mate ends worths? Indeed, if some "things" are valuable as means, does not this imply still other "things" that are valuable as ends? This question states the teleological problem in perhaps its most modern form, but in a way that is, indeed, almost as old as philosophy itself, since it is the very center around which the philosophy of Plato turns, and the answer usually given to it is affirmative. Just as, e.g., there are the realms, or fields, of motion and of spatial extension, yet with the two not identical, so it is maintained, there are the two realms of values or worths and of non-worths, with the two quite distinct and different. And further, just as it is conceivable that the laws of motion are not of necessity "legislated" for moving things by an external agent, but are of "the very nature" of moving "things," so may values not come from without, but may them- selves be entities or facts side by side with other kinds of facts. But also it may well be that, just as one and the same entity can be, e.g., both spatially extended and moving, so also can an entity be a value in one realm or relational field, and a non- value in another. Indeed it may be asked if this is not exem- plified by such an entity as a picture, which, as a thing of beauty, is in one relationship an ultimate aesthetic worth, but which is also a physico-chemical complex of oils and pigments, and as such a non-worth or physical fact. However, whether or not one agrees with the positive answers that are given to these questions, they nevertheless indicate problems that strike to the very root of the teleological problem, while in solution of them one may be led to the position, in place of either Deism, Theism, or Pantheism, that there is in the universe an efficient value- or worth-principle, and that this, ' The position of Kant, Fichte, Herbart, and, among recent writers, MUnsterberg ; see his Eternal Values, 1909. THE TELEOLOGICAL PROBLEM 61 rather than the Orderer, Lawgiver, and Manifestor of tradi- tional theology, is "the power, not ourselves, that makes for righteousness. ' ' ^ Still other specific teleological problems concern the questions as to (1) what the specific purpose of the universe is, if it all has a purpose, and (2) whether or not there are entities that are directly opposed to values, or goods, i.e., whether there is an irreducible and ultimate Bad in the universe, — something not merely non-value, but positive Evil. The first of these questions may indeed indicate the proper method of approach to the whole problem of purpose. For, might not the proposition, that there are both purpose and a Purposer, perhaps be best established by first ascertaining what the specific purpose of the universe is? Historically, the happiness, the Avell-being, and the salvation of mankind have each been regarded as the specific end "of all creation," but at the present time there is a reaction against such an anthropocentric point of view. As regards the second question, concerning the reducibility of evil, the fact of at least three different solutions indicates as many specific subordinate problems. Thus it is asked, Is not the ultimate character of all things good, so that evil is mere appearance? The objective idealist answers "yes," since for him everything else is "absorbed" into One Being that is good. The evolutionist and pragmatist disagree with this solution, and maintain that evil is relative to good, and conversely, and that each is relative to the time and the circumstances, so that neither is absolute. In turn the realist disagrees with this, and ad- vances the view that evil as such is ultimate and indestructible either by argument or by action, although the number of its concrete instances may be decreased by fighting them with good. ' Hoffding's position in the Philosophy of Religion, pp. 215-278. 62 HISTORICAL PROBLEMS OF PHILOSOPHY CHAPTER VIII THE THEOLOGICAL PROBLEM The teleological problem leads naturally to the theological problem. Let there be order, regularity, and uniformity in the universe; let there be an adaptation of one "thing" to another, e.g., of the eye to light, of body-color to surrounding foliage, and the like, and the question at once arises. Whence this order and law, this uniformity, this adaptation? Do they not demand an Orderer, a Lawgiver, an Adapter, even as the watch implies a maker, the building an architect, the bridge an engineer? That they do, is the answer given by the Deist, the Theist, and the Pantheist, all of whom infer from the observed order and law and adaptation, the existence of a Being, God, who is their source. This argument for a Deity is called "the argument from design. " ^ It is obvious, however, that it makes of the Deity only the designer, the architect, or the engineer of the universe, and not the creator of its matter and substance. But further, the universe consists not alone of static, un- changeable, resting "things," if, indeed, there are any such "things" at all. Change, motion, and evolution are also facts, and indeed may be universal. Then the question arises, Whence comes this change, this motion, this possibly universal evolu- tion? Who started all this process going, endowing it, at the same time, perhaps, with order and law, whereby to fulfil a purpose ? For must it not have had a starter, an initiator ? Is not one billiard ball moved by another, and the cue ball in turn moved by the arm of the billiardist? And does not food make the player's arm move, while rain and plowing and soil produce foodstuffs? And were not these happenings caused by other, • An argument that is used by all who accept a positive teleology, whether this be immanent or transcendent, and whether it leads to deism, theism, or pantheism. Among those who Tise this artj^ument are Aristotle, Augustine, Anselm in the Monologium, Thomas Aquinas, Berkeley, Leibniz, Ficht?, Hegel, and Royce. 8ee the latter 's Religious Aspects of Philosophy, 188.') ; The Concept of God, 1897; Studies of Good and Evil, 181)8; Th0 World and the Individual, 2 vols., 1900, 1901, and The Problem of Chris- tianity, 2 vols., 1913. THE THEOLOGICAL PROBLEM 6^ earlier happenings, and these by still earlier ones, and so on indefinitely far back? Where shall the stop be made or does there seem to be no stop at all implied in this (infinite?) series of causes and effects? Two positions are taken in answer to this question, the one holding that there is an end, the other, no end to this series. The former is that solution which is accepted as the outcome of the so-called "cosmological argument" for the existence of God. There must be a -first cause, this argument runs, that is itself uncaused, in order that it may be adequate to produce or cause the "world" as a whole. It must itself be uncaused, since, were it not, there would still be another cause "behind" it, and so on, so that the problem is repeated until at last there is reached a first cause which is not in turn effect. This cause is "first" in the sense that it is either prior temporally to all effects, or prior metaphysically in that it "underlies" and con- ditions through all time all other causes and effects. In both cases, however, such a first cause is identified with God.- However, in addition to these several problems as to whether or not there is an architect and possibly a creator of the uni- verse, or a Being who started all "things" going, or one who did this and v/ho also continually maintains "things" in a certain order and to a certain purpose, there is the further aiid related prohlem, whether or not there is a perfect Being, who plays one or more of these roles, and who is complete in His goodness, power, and insight. There is no doubt that the view that there is such a Being, and that this Being is God, is a most widespread one. There is both the idea of a perfect Being, and the belief in His exist- ence, or His reality. Yet in criticism of this belief it may be asked, if we do not have many ideas to which there corresponds no existent object. My idea of a perfectly frictionless machine does not seem to imply the existence of such an object. No more does our idea of universal justice among men mean the actual attainment of this ideal. May it not be asked, therefore, if the idea of and belief in a perfect Being prove that Being's ' This argument is given by Aristotle, Augustine, Anselm in the Mono- logium, Thomas Aquinas, Geulinx, Spinoza, Hegel, Ficbte, Bradley, and many others. 64 HISTORICAL PROBLEMS OF PHILOSOPHY existence? The answer given to these questions by many is "yes." For it is argued, that a Being perfect in many ways, such as goodness and power, would still be imperfect were He not also real or existent. In other words, that perfection implies existence, is the reply given to him who doubts. ''Things" with which we are commonly acquainted, even the whole universe, are imperfect, it is argued, and these imperfect entities imply the perfect. The imperfect leaf implies a perfect one as a pattern or ideal ; the unjust act, a standard just one. We thus at least have the idea of the perfect, though we cannot see, touch, or hear this entity. And, since perfection is held to imply existence, God, as a Perfect Being who is in some relation to this imperfect world, must be concluded to exist.^ Without raising the question at this point whether this "ontological argument" is valid or not, one must admit that it is very widely advanced and accepted, either clearly or obscurely, as are also the teleological and cosmological arguments. Science as such does not, however, concern itself with these problems, taking merely an attitude of indifference toward them, but many individual scientists, prompted by a wider philosophic interest, do attempt solutions of them through the use, perhaps, of scientific data alone. Most philosophers, how- ever, have considered that science as such is not capable of giving either proof or disproof of God's existence, but that both the problem and the means for its solution lie in quite a different realm of fact. In accordance with this view different lines of proof are advanced. One of these argues from the historical fact of an almost universal belief in a Deity and the effectiveness of this belief, to the Deity's existence. This is the historico- pragmatic proof.* Another line of argument bases its proof on revelation/' However, both of these proofs can be reduced to the ontological proof, — the historico-pragmatic proof, since it substitutes for the idea of a perfect Being as "held" by the hidividual, that same idea as "held" hy many, both historically and racially; and the proof from revelation, because it argues ' Anaelm, Proslogium, Chap. III., trans, by S. N. Deane; Descartes, Discourse on Method, and Meditations. * E.g., Father Tyrell, Lex Orandi, 1903; Lex Credendi, 1906. ' The Apologists, such as Justin the Martyr, Tertullian, Origen, Augus- tine, Aquinas. THE THEOLOGICAL PROBLEM 65 from the idea of God as given in revelation to revelation as given by {an existing) God. In this second proof it is main- tained that, if tradition is trustworthy, revelation also is, and then, that God exists because, according to revelation, He asserts His existence. Appeal is then made to the identity of God with the Perfect Being, and from His perfection is deduced His exist- ence and veracity. This veracity guarantees the truth of reve- lation, and from this last there is in turn derived the trust- worthiness of that tradition in which both the belief in God and revelation have been handed down.° This is essentially the argu- ment of both the Protestant and the Catholic churches, with the difference, that the former rests its proof on the infallibility of the Scriptures and the reliability of tradition, whereas the latter bases its proof on what by its own philosophy is its own exclusive, God-given ability and knowledge to interpret both tradition and Scriptures correctly, and to distinguish truth from falsity. Each position is difficult to grapple with, since each logically can deny to him who is "outside" and v/ho may doubt, the very ability to get at truth, maintaining that this is given alone to him who believes and accepts and is within the church. Also, either position may be true, since truth is independent of proof, while disproof of either is impossible, or, at least, difficult, since attempted disproof of either position is possible only from a standpoint that is ' ' outside ' ' the realm of that which it is desired to disprove, and therefore gets no logical leverage. The theological problem in its various aspects is one, there- fore, that has arisen in the past and that still presents itself for solution. Psychologically it is, perhaps, not a problem to the unthinking adherent of some orthodox religion. But to the reverent thinker and critic who does not hesitate to submit any question to the examination of reason, and who holds that all of mankind's beliefs and theories must be so subjected, it is a most important problem. • A. Sabatier, Religions of Authority. c 6Q HISTORICAL PROBLEMS OF PHILOSOPHY ft CHAPTER IX THE PROBLEM OF VALUES The theological problems which have just been briefly Mis- cussed are most intimately connected with the problem of values. A value may be defined, tentatively, as anything that is desired and accepted as an end to be attained, or as anything that brings about the attainment of an end. For example, individual and general happiness are values, as are also a clear conscience, con- tentment, good health, all-round development, honesty, honor, loyalty to friends, love, unselfishness, education, exercise, good laws, and thrift and industry. Some of these, such as the last five, may be means by which other values are attained. These other values might therefore be ultimate ends or goods, and the means to attain them be right ways or mediate values. This may be the difference between the good and the right. As already indicated, the problem of values is closely related to the theological problem. It is, also, no less closely connected with the teleologieal and the cosmological problems. For it may be asked. Have not the order, the arrangements, and the exquisite adaptations which we seem to discover in nature, been instituted by a Supreme Being primarily for man's welfare, or for his happiness and contentment, or, at least, for his strength of character after much trial and tribulation? Do not all "things" seem finally to lead to that which we regard as good or even as best, so that they must have been meant for this purpose by a Supreme Being who so intended and established them, and in this way Jios revealed a proof of his existence and character? In terms of the problem of value, therefore, God is that Being who cares for the good and who also brings about the attain- ment of or the tendency of "things" toward that which is good, let this be human happiness, or contentment from well-doing, or a life in heaven. Then God must himself he good. Indeed, it may be, that He himself is the Good, and that to attain good is to be one with God. But if He is good, and so cares for the good, and brings it about, then must He also be a God who knows and wills and has power. THE PROBLEM OF VALUES 67 This teleological argument both for God's existence and for His nature is advanced. It is clear, however, that, leaving open the question whether it is a valid argument or not, there would be no occasion for making it, were one not convinced that there is something of value, either as an ultimate end, such as happi- ness and justice on earth, or as a means to these ends, such as thrift and foresight, honesty and brotherly love. But there is no denying that values are discovered. Thus, e.g., we speak of that inherent worth of each personality or soul which commands our respect, and our recognition of the princi- ples of duty and justice. Happiness, too, seems to be, under certain conditions, worth while of itself, and even more cer- tainly do the sublimity and beauty of nature, as well as of some of man's creations, such as the beautiful picture and statue. Or, if these are not inherent worths, then they are at least valuable as means to some end as a final value, and the- essence of the situation remains the same. There are values or worths, some ethical or moral, others assthetic; some are means to ultimate ends, others are these ends themselves. Every-day life in all of its relations of love, friendship, occupation, citizen- ship, religion, art, science, and philosophy is based upon them. Indeed, to deny values is to presuppose them — unless one's denial be quite unmotivated. The existence of values, then, is a fact that has been uni- versally admitted by all people, of all times. Concerning the relationship and classification of values, however, there is a specific value-problem. Is there one highest value to which all others are subordinate? Is there a highest ethical value? Ought we, e.g., to make the attainment of happiness, especially of others, our chief aim of life ? Or ought we to set the unflinching doing of the right, even at the cost of pain and suffering, above all else? Or, again, is the harmonious development of our mental and physical nature that for which we ought chiefly to strive ? Which standard shall we accept? Indeed, by what test ot standard shall we be able to reach a decision in this issue between standards? This, after all, is the important question. For, with the ultimate value once decided, other values can be "measured" by it. Yet it may be that there is no ultimate standard, or, at least, not one that is known. For to know that there is a 68 HISTORICAL PROBLEMS OF PHILOSOPHY standard, and to knoiv what this standard is, are two distinct "things." Or, there may be only a standard that changes from generation to generation, even as it also differs from nation to nation. Here, therefore, is another problem of values. It is the problem, not of what the standard is, but whether there is an absolute and eternal standard that is knowable, though perhaps now unknown, or, whether there is only a changing standard, created by the past for the present, but to be supplanted in the future by that which grows out of this present. Here we have the contrast and perhaps the conflict between Absolutism, on the one hand, and Relativism or Evolutionism or Pragmatism, on the other. Yet, while it is admitted that we recognize values, accept them, and act upon this acceptance, since we are concerned with character, with happiness, with duty and the like, it is still to be asked. Just what is a value? To exemplify and be specific, let us ask, whether there would be happiness and character, if there were no conscious human beings to be happy, to have char- acter, and to seek these as ends? Or, do these values exist also for other living beings than man ? However, even granted that they do so exist, are they not limited to beings that are con- scious, so that there may be desires, interests, and ideals f This question is answered in both the affirmative and the negative. Thus it is held that all values are in some way dependent upon the presence of consciousness as this is found in living beings, and that values are facts 07ily if there are beings that have purposes and interests and ideals, and that use means for the attainment of ends. This position is taken with reference both to ethical values and to aesthetic values, such as beauty, in which latter case it is not unconvincing. For is not that which is accepted as beauty either in the concrete or as a standard of beauty known to vary both with the individual and with the nation or race, as is exemplified by the different Eesthetic standards, e.g., of the European and the Oriental? Is not beauty, therefore, dependent upon a subjective factor? Is the picture beautiful except to the observer? By itself is it not just so much paint and line? The completely subjective view of the nature of value, thus suggested, is accepted by some thinkers. By others, however, it is maintained that at least THE PROBLEM OF VALUES 69 certain values are quite objective, in the sense that they exist quite independently of all desire, interest, and appreciation, — indeed of all consciousness. For example, one may hold the view, that there must have been value in the universe 'before consciousness existed, in order that there might be at a later stage that situation in which there is consciousness and those values which are dependent on consciousness. Accordingly we have the problem, Are all values dependent upon consciousness, or are only some values so dependent; or, are all quite independent of this entity? Several solutions are given to this problem, and each has interesting consequences. Thus, let us first consider the view that all values are wholly dependent upon a consciousness. It follows from this position, that there would be no values prior to the existence of con- sciousness, — a conclusion that is not invalidated by the argu- ment which maintains, on the one hand, that there always are values, because there always is a divine consciousness, and, on the other hand, that there is this divine consciousness, because there are values. // all values are thus dependent upon a human or an animal consciousness, and God is defined as that Being who is identical ivith values, — a current definition — then it fol- lows either that there is no God in the orthodox sense of the term, or that God is man-made, or both. However, as opposed to this extreme, subjectivistic view, it may be, that there are some values which can be demonstrated to be independent of all consciousness, so that the Deity may be identified with that which is value in the universe. For the conviction, that there exists or that there is actual in the uni- verse, such a principle of the conservation or even of the increase of value, may, after all, constitute the deepest and most fundamental religious consciousness, so that there is a rational defense of the belief in a Deity who is not a mere replica of human personality, but who is a Being supra-personal, and perhaps supra-conscious. It remains to consider one more phase of the problem of values, namely, whether Truth itself is not a value} Is it not ' The pragmatists and humanists would say that it is. Cf. also W. VVindleband, Wiile zur Wahrheit, 1909, and H. Kickert, Die Grenzen der Naturwissenschaftlichen Be griff shildung, 2nd. ed., 1913} Miinsterberg, op. cit. 70 HISTORICAL PROBLEMS OF PHILOSOPHY this, because, e.g., in searching for truth in the spirit of "truth for its own sake" and quite regardless, as we may think, of values and their fate, we are nevertheless seeking for something that is of value? From this cannot the inference be, drawn, that, because our valuing truth conditions our search for it, and because truth is valuable, therefore truth is conditioned hy its value, or by our attitude toward it ? The reply to this inquiry is, that, while truth undoubtedly is a value either quite for itself or because of its usefulness, or both, nevertheless the value aspect of the truth does not con- stitute the truth, but that the truth and the value are merely two aspects of one and the same "thing" in different relations. In support of this position it wall be admitted, that, e.g., one and the same individual man may be a brother in relation to one person, and a father in relation to another. Further, while a father is not of necessity a brother, nor a brother a father, these two characteristics are quite compatible in the same indi- vidual. By the same logical principle, there may be, therefore, "something" that in one relationship is truth, and in another, value, so that not only is truth a value, but values, as known, are truths. To explain this further, let us assume that there is a world of fact, with no minds or consciousness present in it. Let us assume, next, that under certain conditions consciousness, awareness, or "knowing" appears, and that accordingly our world becomes known (as it really is) in certain details. When there is this very specific relatio'nship between a knowing process and that which is known, we will say that truth exists or sub- sists. Yet it must also be granted that conscious processes can take place, and yet this specific relationship be lacking, i.e., that there can be error as well as truth. Truth, then, is a specific relational state of affairs that sub- sists between certain conscious processes and that which is known. It can, perhaps, be defined only in a circle, namely, as that relational complex which subsists when things arc known as they really are. But this specific complex is also a value, since either its attainment is desired or purposed, or it is a means to something else that is desired. In other words, a certain relation is, by itself, truth; but this relation may in turn be related to THE PROBLEM OF VALUES 71 something else even as, e.g., hrotJierliood is a relation that is , related to sisterhood. Thus that relation which by itself is V truth, is, in relation to purpose, also a value. CHAPTER X THE EPISTEMOLOGICAL PROBLEM The discussion of the preceding chapter has already intro- duced certain phases of the episteraological problem. Is truth a value? And, if it is, what is to be inferred from this fact regarding the further character of science, philosophy, and common sense ? What is the nature of knowledge and of truth ? Are they distinct from one another, and both in turn distinct from fact; or, does knowing in some way itself ''make" fact? Again, are truth and fact identical? What is the origin of knowledge? Does it all come from sensation, or does some knowledge have some other source? What are the limits of knowledge? Are there realms to which we cannot penetrate by either intellect, intuition, feeling, or sensation? These are all special epistemological problems, around which, as a center, most philosophical investigation of the modern period has turned. One of the most important of these problems concerns the possible distinction between fact, knowledge, and truth. The prevailing view in both science and common sense is, that fact is independent of the knowledge of it, that knowledge is a specific kind of mental process, and that truth is a relation of "correspondence" between knowledge and fact. Accordingly, a true idea is regarded as a sort of mental picture of that of which it is an idea. This view, however, is not only challenged now, but it also has been frequently questioned ever since the time of the Eng- lish philosopher, John Locke (1632-1704), who was its modern sponsor. All philosophers do not accept the distinction between fact, knowledge, and truth, and among those who do not are 72 HISTORICAL PROBLEMS OF PHILOSOPHY the pragmatists, the phenomenalists, and the idealists. Yet each of these "schools" raises different questions concerning the distinctness and the relation of these three "entities," and thus each discovers specific epistemological problems. The pragmatists, or, at any rate, some pragmatists, maintain that the very nature of truth, namely, that which is sometimes called the "correspondence" between an idea and its object, is only the later experiencing of that to which the idea previously "pointed." They contend that an "idea becomes true," and that that which is commonly regarded as the independent object is only the content and the product of an idea to which truth has happened, because the idea has led to success and satisfaction of one kind or another.^ The idea merges, as it were, into an object, and, behold, there is truth ! This point of view is not altogether easy to understand, but a figurative description may help us to make the matter clear. The position may be said to mean, that truth is "made" in a single line of experience, of ideas, of purposes, and the like. The opposed and usual position may, in contrast, be described as the right-angled view. According to the latter there is one series or line of ideas, and another series of facts, and between the two, striking across at right angles, as it were, there is the relation of correspondence. A problem arises, therefore, because it is so difficult to under- stand and especially to justify such a "copy theory," as the "parallel line" and "right-angled view" may also be called. For there is the question as to how, if we as knowers are on or are identical with "the idea line," as we seem to be, we can ever "get off" this line so as to compare it with, and thus dis- cover that it is a copy of, "the object line." In the case of a picture and its object one can do this, but one then has the two entities before him, and readily discovers the "picture" — or cor- respondence relation. But the critical question arises. How could a picture itself discover that it is a picture, since it could never get outside of or beyond itself, thus to look back and compare itself with its object? Would not a third "point" be necessary, on which to stand, in order to make the comparison and the ^ E.g., James, Pragmatism, especially Chaps. II., VI., and VII. Cf. also the works cited in the later discussion of Pragmatism in Chap. XXXIII. THE EPISTEMOLOGICAL PROBLEM 73 discovery? Then it may be asked, How can the ego, or the knowing process, be successful in such an attempt, if the knower is that very series of ideas which are supposed to be the "copies" or ''mental pictures"? Is there any proof, or any way of prov- ing, that an idea is in any sense a copy? Indeed, is it not an unwarranted assumption, both of common sense and of science, that such a relation in any way constitutes true knowledge? This is the problem, and this the criticism made by the prag- matist, who reaches the conclusion, therefore, that the truth of, an idea does not consist in a "right-angled" correspondence between the idea and its object, but that an idea J)ecomes or is made true through that later experience in which there is some sort of confirmation, successful working, and satisfaction.^ The pragraatist, therefore, does not distinguish in the same way as do some other philosophers, fact, truth, and knoivledge. Fact, for him, is that which fits consistently into a system of ideas whicii are made knowledge or truths by later experiences. Fact is the content of that knowledge which thus becomes true. And, finally, everything is ''experience"; for it is inferred that, because everything that we mention, think of, and experience, is mentioned, thought of, and experienced, no object can exist apart from thinking and experience, and all objects are merely content of experience or are, indeed, themselves experience. Truth, knowledge, and fact are thus all reduced to a common "something," experience, and in this respect do not differ from one another.^ The phenomenalists and the idealists agree to a large extent with the pragmatists in this conclusion, although their mode of approach is somewhat different. For both, facts or "things" are "made" or constituted, at least in part, by virtue of their relation to perception, or knowing, or, in general, to experience ; i.e., since it is held that experience can never he eliminated from the "things" which are experienced, it is concluded, that the experienced world is constituted, in part at least, hy the experi- ence, so that we are confined to experience (as regards that * See James, Pragmatism, especially Chap. VI. ' This position is taken by, e.g., Professor Dewey all through his writings of at least the last thirteen or fourteen years; cf. the bibliography of Chap. XXXIII. 74. HISTORICAL PROBLEMS OF PHILOSOPHY which we experience). It is thus that the idealist argues that the universe itself is psychical or mental* and the phenomenalist that the knoivn or experienced world is psychical. But the latter philosopher holds that there is also another, a possibly non-mental world beyond, that never can ie known, since to experience it is to alter it.'^ For both idealist and phenomenalist, however, fact, truth and knowledge are mental in nature. In \ this respect at least there is no difference between these two ' philosophies. All philosophers, however, do not agree with the three posi- tions just presented. For example, the realist does not, and, as he maintains, for good reasons. He agrees with the prag- matist that truth may not be identical with a "picture-like cor- respondence" between idea and object, and that at least some ideas are tested for their truth by their outcome. But, against the universality of this last doctrine the realist finds that, while every idea has an outcome of some sort — an outcome presumably satisfactory to some mind, especially when there is belief in the idea — the mere outcome nevertheless fails to give the requisite distinction between the true and the false. It is not the mere /outcome, he finds, but the differeyice among outcomes that dis- itinguishes the true from the false — a difference that may itself Iwell be conditioned by the respective truth and falsity of that which has an outcome. Truth and the test of truth, therefore, may be two very different "things." The truth of an idea may, indeed, be that very characteristic which conditions the specific kind of outcome which is a successful test for truth, when the idea is not antecedently held to be true. Thus con- ditioned, this outcome in turn is of the kind that may serve as a test for truth.® From such discussions, given us by the pragmatists, another , epistemological problem emerges. Is there an absolute truth to { which our knowledge may approach nearer and nearer, though \never reaching it? Realist, idealist, and phenomenalist for the ■ most part agree that there is, and in this respect are "abso- * For the subjective idealist the experience is that of a finite conscious being, while for the objective idealist it is that of an absolute, divine, conscious Being. Cf. Chaps. XXX., and XXXIV.-XXXVIII. " For Kant and the Kantians, see Chap. XXIX. ' See Chap. XXXIII., rv., and Chap. XLIV. THE EPISTEMOLOGICAL PROBLEM 75 lutists." But the pragmatist demurs.'^ For him, since truth is "made" by a shifting, evolving experience in which success and satisfaction may finally emerge, trut\_cfianges. It is rela- tive to the time, the place, the nation, the sect, and even the individual. Therefore there are 7nany truths, even though they conflict, as is well illustrated by the "truths" of Christianity and of Buddhism. For the pragmatist, both of these religions, so far as they contain doctrines that succeed, or that have satis- factory effects, are (theoretically) true. The argument advanced for this view is two-fold. It is main- tained, on the one hand, that, because experience "makes" both truth and fact, and yet itself grows, changes, and varies, there is also only a shifting truth and fact.^ On the other hand, it is argued, that the very ideal of absolute truth, as well as all tests therefor, and all the methods of proof, do themselves but shift and vary, imbedded as they are in an ever-changing experi- ence.^ With this view the absolutist disagrees. For him there is only one truth, one state of affairs, one set of facts, to he dis- covered in each field. This position, he contends, is established by the reductio ad ahsurdum of the opposite position, since to claiyn that all truth is relative and shifting, is to presuppose that this claim or position is itself an absolute and permanent and not a relative and shifting truth }° But it is also argued, that, since truth and fact may be independent of their tests and of proof, there may be absolute truth and fact, although we have no absolutely certain methods of identifying or "recognizing" these in the process of obtaining knowledge.^^ Truth, however, supposing there is one truth about each fact, or each set of facts, consists of many truths. Truths form a system. There is the problem, therefore, as to hoiv truths form this system, how they are related, or what kind of system truths form. Does, e.g., the relatedness of truths imply that each truth is dependent upon other truths, so that it is impossible to get '' E.g., James in his Pragmatism, Schiller in his Humanism, and Dewey in Essays in Experimental Logic, 1916. ^ James and Dewey, ibid. ® Schiller, ibid. '" Royce, " The Eternal and the Practical," Phil. Revieio, Vol. XIII., p. 103 ff., and "Principles of Logic," op. cit.j cf. Chap. II., supra. " Cf. Chaps. XXXIII., XLII., XLIV. 76 HISTORICAL PROBLEMS OF PHILOSOPHY at the truth about any one "thing" unless we also get at the truth about all other "things"? Or, are truths related and yet independent, so that it is quite possible to discover now one truth and now another, as knowledge progresses? The first view, that truths, because they are related, mutually depend on and modify one another, like the parts of an organism, is called the "organic" or "coherence" theory of truth/' The second view may be called the pluralistic theory. Obviously the basic problem here is again the question, whether relatedness as such carries with it a mutually modifying action of related terms on one another, or whether this is only sometimes the ease, and thus presents a specific type of relation? ^^ At this point, therefore, the further problem arises, if it is not to the growth of our united social attempt to obtain knowl- edge, rather than to the system of truths, that the organic view applies, — while the system of facts, which we endeavor to know, is pluralistic in the sense above defined. Indeed, is not even this very difference itself a state of affairs that is a typical ease of such pluralism ? Truth, however, might either be an organic whole, or consist of truths related to and yet independent of one another, and yet there might be but One Truth, i.e., one system of truths.^'^ But there would still be the problem as to how we can discover or make certain that this One Truth has been attained either in whole or in part, i.e., there is still the question as to what is the test of absolute truth, and of genuine and certain knowledge. Indeed to have such truth and knowledge, must we not have an absolute test? But to have this must we not in turn have a test for this test, and so on indefinitely ? ^^ Or could a test he used to test itself f These questions are raised, and many an- swers are given. Various tests for truth and knowledge are advanced, but in every case more than one interpretation is made of their character. Consistency, freedom from internal contradiction, presupposition by attempted denial, immediate, direct, and undeniable experience, subsequent verification, self- evidence, and the inconceivability of the opposite, are among the tests and criteria that are accepted and used, one or more ** Joachim, The Nature of Truth. " See Chap. XLI., xv. " Sec Chap. XXVI. " See Chap. XLI., ix.-xi. THE EPISTEMOLOGICAL PROBLEM 77 of them, by each of the several philosophies.^® Disagreement exists, however, as to which of these tests is superior. But against all other parties the pragmatist maintains that all of these tests are but useful means to an end, or kinds of satisfac- tion and success, and thus relative and not absolute. From this he infers that truth itself bears, or is the same characteristic, — namely, usefuhiess. From this inference the absolutist demurs. He grants that tests and testings may be fallible (though he usually insists upon the high degree of probability of certain tests as absolute), but he also maintains not only that there is an absolute truth and an absolute state of affairs to be discovered, but also that these may be actually revealed in certain instances even though abso- lute proof of this is lacking. Truth and knowledge are inde- pendent of proof, although certainty may not be, and one may "really know," without being able to demonstrate that he does}"^ Indeed, were this not the fact, then whoever advances the con- trary position would be quite precluded from maintaining that his position is itself true, unless it were absolutely established by absolute tests and proof. '" Still another epistemological problem emerges in the question as to what is involved in the fact that knowledge and knowing appear in many individuals. Is it not therewith necessitated that these individuals are essentially alike? Must not their knowing processes, their "thinking machinery," be quite the same in order that they shall be able to get at the one truth, or the one set of facts in each case? But how can these con- ditions be attained, and where can they be found? Are two individuals ever quite alike? Are not their sense organs dif- ferent? Do they not, therefore, perceive differently? Are they not also of different temperaments? Will they not, therefore, rely upon different tests of truth, and start their arguments from different convictions? Will even the same word convey the same meaning to two individuals? With such obstacles as these, how can there be any such thing as knowledge, which, by / its very nature, should be the same for all? How can two iudi- l viduals ever have one fact revealed to them in precisely the '" See Chap. XV. " See Chaps. XXXIII., XLII., and XLIV. 78 HISTORICAL PROBLEMS OF PHILOSOPHY same way, unless it be by pure chance? Will not one or the other, perhaps both, distort it? Both the individualistic position, thus suggested, and its opposite are taken by philosophers. The problem is that of the "universality" and common validity of knowledge, and of the conditions for this. Both positions are compatible with the view, that facts are facts, — to be got at if possible, — and that there is but one system of truths, the attainability of which is an ideal ; but they differ on the question, as to whether it is possible to get at facts at all, or to attain to the one truth? In the one position it is maintained that, while there are differ- ences among individuals, this does not preclude likenesses and identities in our "knowing apparatus," and that, relying upon these, we are justified in further claiming that the ideal one truth may, at least in certain cases, be attained. This is also possible, since, although there may be no absolute test of absolute truth, truth may be quite independent of proof and of testing. The other and opposed position, if it will not admit of likenesses in knowing processes in the midst of differences, has only one recourse left. It must acknowledge complete individualism in respect to intellect, moral judgment, and testhetic feelings and appreciation. Each individual can rely only upon himself, and that completely in each of these fields, with no apparent means of bridging the chasm from one individual to another. Destructive as this position seemingly is of all motives for social intercourse and cooperation, it has, nevertheless, been theoretically maintained now and then ever since the Sophists first advanced it. But, it may be asked, Is not the means for the refutation of this position rather freely offered by him who argues it? If one cannot get beyond the individual peculiari- ties and differences to that in which individuals are alike, as they are supposed to be in their "pure reason," then, on the one hand, why should one ever attempt to convince others of the truth of the individualistic position? But, on the other hand, if one makes this attempt, does he not therewith presup- pose that there is something which is common to and alike in individuals side by side with differences — something, namely, that is "over-individual," even as reason is supposed to be? It suffices to say, that the latter alternative is accepted by most THE EPISTEMOLOGICAL PROBLEM 79 philosophers, and that the first alternative is regarded as worthy of little attention. Yet the problem must be regarded as a legitimate one, with individualists and "antis" as the eon- tending parties, and with various ramifications, from both posi- tions, extending into the solutions given to other philosophical problems.^** Suppose it be granted, then, that, side by side with feelings, desires, motives, and the like, which may be purely individual, there are also reason, knowing, and knowledge that may be the same in many individuals, there remain still other problems. Hotv does knowledge arise? "What is its source? Using the term "cognition" to designate all perception, memory, imagina- tion, and reasoning processes, there is the problem, Does all cognition have the same source? Does it all come ultimately from, and is it all like in kind to, sensation? Or, is some cogni- tion, notably reasoning, together with its principles, an inde- pendent and peculiar kind and source of knowledge in con- junction with, but different in kind from, sensation?^'* Two positions are taken in solution of this general problem. Ac- cording to one, namely, Sensationalism, all cognition, all knowl- edge, comes from, and is but a transformation of sensation. Ac- cording to the other, Rationalism, at least spwe knowledge does not thus originate, but is reason's own peculiar contribution. Empiricism, in the historical and narrow sense of the term, either agrees with Sensationalism in '^ reducing" reason to sensa- tion, or, if it does not go quite so far as this, at any rate denies reason's independent ability to discover fact and to get at truth, and allows it by itself only the function of vain speculation and castle-building. However, we are all empiricists in the broad meaning of the term, since experience of some kind must be accepted as the one source of discovery. But historically the term "empiricism" has been almost exclusively used to designate the view, that hoth the source of all knowledge and the test of all truth is ultimately sensation. Then the term "rationalism" may be used to designate the position, opposed to this narrow empiricism, that all experience, evei? sensation, must be subjected to reason's test as the court of last resort. " See Chap. XLI., vin. " Bee Chaps. XLI., xiii., XLIII., and XLIV. 80 HISTORICAL PROBLEMS OF PHILOSOPHY Distinct in some ways from this problem as to whether reason or sensation furnishes the ultimate test for truth, is the question, whether reason reveals fact and reality to us, or only invents schemes that are useful methods for the accomplishment of practical results and purposes. Both positions are taken, the former by the intellectualists, the latter by the "antis," and ioth parties present arguments for their position, the anti- intellectualists tliereby placing themselves in the embarrassing position of using intellectual and rational means and principles in order to establish the very position which denies the validity of the means by which it has been established. One of their arguments is that that analysis with which reasoning methods are at least partly identical, leads to results that are self-con- tradictory, and therefore false.^° Thus the claim is made that only immediate and intuitive experience reveals fact, and that the great fact revealed is that of an ever-flowing and ever- changing universe, which intellectual analysis "makes" into a manifold of unchanging elements or parts. Motion is the typical case selected; and it is argued (falsely) that the analysis of motion shows, that at every instant a moving body is at a specific point, and so at rest — rest being tlie contradictory of the "thing" analyzed, namely, the motion. Thus the conclusion is reached, that only non-intellectual, non-rational methods, such as intuition, appreciation, and feeling, reveal reality and fact, and that accordingly we must be intuitionists, emotionalists, and evolutionists. The intellectualist opposes all this with the position that, although non-rational processes may reveal fact, they are not the only processes that do this. For it can be shown that reason and intellect, and the methods of analysis in general, also reveal reality, and that the falsifying character that is ascribed to them disappears, if one but state tlieir analytical results correctly,^^ It remains yet to present one other, very important epis- temological problem, upon the several solutions of which there depend some of the most distinctive features of Idealism, Phenomenalism, and Realism. This problem concerns the ques- "" E.g., by Bergaon in Creative Evolution in any number of statements. " See Chaps. XXII., XXIII., and XXIV. THE EPISTEMOLOGICAL PROBLEM 81 tion as to what is involved in or implied hy the fact, that every reality, every fact, even every illusory object that is known, thought of, conceived, mentioned, or perceived, and the like, is a reality that is known, thought of, conceived, mentioned, or perceived, so that any attempt to know a reality as it is as not so known, is apparently doomed to failure. For, it is asked, Is not the only world which we can ''get at," one that is related to our knowing, or to our experiencing in some manner? There- fore, is not the question, what the world is, as not so related, incapable of solution, since to attempt to answer it is but ogavn to relate the xcorld to some "knowing" or "experiencing"? The difficulties of this situation constitute the so-called ''ego-centric predicament." ^' The possibility of a solution to this problem depends on whether or not the fact, that all reality which is experienced is related to an "experience" or an "experiencer," implies that a difference is thereby made to the reality or the entity experi- enced.-^ For, on the one hand, if the "experiencing" does make a difference to or does affect the experienced reality in some way other than to make it "experienced," then clearly unexperienced realities are different from experienced ones, though we may never be able either to know in what respects they differ, or, indeed, experience them in any way. But, on the other hand, if the "experiencing" makes 7io difference to the reality experi- enced, then, of course, the reality is the same "when" experi- enced as "when" not, and exists or subsists as quite independent of experience, to be experienced only when those specific condi- tions exist through which experience arises. In fact, objects as experienced might themselves give evidence not only of their own independence of experience, but also of the existence or subsistence of still other objects that have never before been experienced, at any rate in certain specific ways. The second position is the one that is at least tacitly held by the common sense man and by most scientists. It is not, how- ever, looked upon with favor by many of those who are sophisti- '' R. B. Perry, " The Ego-centric Predicament," Jonr. of Phil., Psych., and Scientific MetJiods, Vol. VIII., pp. 5-14; also see The New Realism, E. B. Holt and others, Introduction, and Perry, Present Philosophical Tendencies, Chap. VI. "' Cf. Chap. XXVI, on The Theories of Relations. 82 HISTORICAL PROBLEMS OF PHILOSOPHY cated in the ways of philosophy, and who find one reason or another for maintaining Qiot only that "the world" is always an experienced one, but also that "experience" affects "the world" in some way and makes it what it is either in whole or part. One may be of the opinion that the issue thus raised is to be' easily settled by appealing to fact, and, indeed, each party seems to think that it makes just this appeal. But the facts to which the appeal is made are not simple, especially since such a means of settling the issue only again repeats the difficulty of finding a fact that is not experienced in some way.-* However, let it be granted that all that we can perceive, think of, appeal to, and the like, is thereby experienced — in some way ; and let it be granted also — as it must be — that, in the case of all experi- enced reality, the "experiencing" and the reality are related. Then what follows from this experienced factf Can it be (cor- rectly) inferred from the ever repeated presence of "experi- ence" to "experienced fact," or from the mere fact of the relatedness of experienced reality to "experience," that the experiencing affects the reality? Assuredly not! This infer- ence can be made only provided it is universally true, that, because entities are related, they affect one another. But this is the very question at issue. Does relatedness universally carry with it, or imply, causal dependence and action ? Or is this the case only with some instances of related terms? And if it is thus the case, may not the relation in question, namely, that between "experience" and "object experienced," be one of the exceptions, so that we should be justified in concluding, with the realists, that, although "experience" and "experienced entity" are related, the latter is quite unaffected by the former, and is experienced as if the experience were not present ? Whether this conclusion can be established or not, it is, nevertheless, one that is not accepted by most philosophers, notably by the idealists and the phenomenalists. These phi- losophers insist — unconsciously, perhaps, — that relatedness im- plies dependence, or causal modification; and, secondly, that experiencing is related to all realities experienced, i.e., re- dundantly, that all (experienced) realities are experienced reali- ties. From these premises are derived those consequences which '* The ego-centric predicament again. THE EPISTEMOLOGICAL PROBLEM 8S are identical with the main features of their philosophical systems.^^ However, as regards this procedure it is quite clear, that, if it is assumed (1) that all related terms are mutually dependent on and affect one another, and (2) that all realities are experi- enced realities, and so are related to experience, then it follows, of course, that all experienced realities are experience-modified- realities. But it is also quite clear, that from this second premise alone this conclusion cannot be correctly inferred. It is correctly inferable only if this premise is taken with the other, the major premise, namely, that all related terms are mutually dependent on and affective of one another. It is only these two premises together that imply that an experienced object is affected by the experience of it, whereby it becomes the experi- ence-object. The question at issue between the realist and his opponents is, therefore, whether this major premise applies to all related terms, and so to the specific relational situation of "experience" and reality. Accordingly it is important to ask hoiv the idealist and phenomenalist endeavor to establish this premise or princi- ple. The answer is, that there are certain instances in which the related terms do seem to exert a causal and modifying influ- ence on one another. Good examples of this are the mutual dependence of the parts of any organism on one another, the causal influence of physical masses in accordance with the prin- ciple of gravitation, and the mutual induction between positive and negative charges of electricity. Let the knowing, the ex- periencing, the cognizing of an object be of the type of these instances, — and that they are is precisely what the phenomenalist concludes in generalizing from them as typical instances, — and it then follows (1) that "things" '^ outside" of the "knowing" and "experiencing" relation are different from what they are "m" it; (2) that knowing and experience do affect things; and (3) that the nature of "things" "outside" of this relation can never be known, since to attempt to know "things" is to affect and change them. In other words, it follows, on the one hand, that there is a realm of unknowable, and not merely unknown, things-in-themselves, and, on the other hand, that our world " See Chaps. XXIX., XXX., and XXXIII. 84 HISTORICAL PROBLEMS OF PHILOSOPHY or universe — the only world that we know — is made what it is, at least in part, by 'being known. To the support of this conclusion the idealist brings what he regards as the discovery of certain instances of related terms that are constitutive of one another either partially or totally. This seems to be the case, e.g., with dream-objects and, indeed, with illusory objects in general, as it seems to be the case, also, with color, odor, and temperature, — provided the world outside our skins consists only of hard, fast-moving particles or masses. Why, then, should not all experience be of this type that is creative of its own content? Certain idealists unhesitatingly conclude that this is the case, and there results either Subjective Idealism, if the experience is that of human beings, or Objective Idealism if it is the experience of a universal consciousness. The realist opposes both of these conclusions and arguments. For him, "things" depend upon knowing in no other way than for being known; knowledge does not condition reality; and epistemology is only psychologically prior to other philosophical problems; i.e., one is first interested in the problem, only subse- quently to arrive at the conclusion, ( 1 ) that knowing and experi- ence do not make any difference to the "thing" known and experienced, and so (2) are virtually separable from that "thing." The realist reaches this result by finding certain instances of terms that are related to and yet independent of one another, and by then looking for other instances. The knoivi7ig processes of the idealist and the phenomenalist and the theories that they propose as known and experienced ^'states of affairs" prove to be excellent initial instances of this compatible relatedness and independence. For, while the knowledge and the "state of aft'airs" proposed as true — in their respective theories, are cer- tainly related, it is nevertheless presupposed, as the very con- dition for such a "state of affairs" being "the real genuine one," that it is independent not only of the specific knowing and experiencing process in the knowing individuals who main- tain it, but also of any implied repetition of knowing in other individuals. Other instances of terms that are both independent and related are found in the case of the points of space and the THE EPISTEMOLOGICAL PROBLEM 85 instants of time. Points and instants are absolute simples that are not made up of other elements on condition that, if they were so made up, there would still be some other absolute "simple" which we should then call a point or an instant. But as "com- posing" space and time respectively, these "simples" are re- lated in a very definite way, namely, so as to form a series with the same relations present as are found, e.g., in the series of real numbers in order of magnitude. But no point is affected hy heing related to oilier points on condition that, if it were, it would be, not simple, hut complex, since it would then be hoth itself and the affects thus resulting; or, it would be affected by an infinite number of other points, and so would be infinitely complex, and thus again presuppose ultimate, simple "ele- ments" that would be the real points. Then it would be these elements that would be related and yet independent in the sense that they would not be affected by other elements. In a per- fectly analogous way instants can be &hown to be independent of one another, and yet to be so related so as to form that specific series which is time. Still other instances of cosuhsisting relatedness and inde- pendence are as follows: Space as a whole is related to matter, but is independent of it. Empty space is quite conceivable, and is examined scientifically in geometry with no implication of matter, or of physical forces. So also are matter, motion, and change in general related to time, and time to them; but time is independent of all these entities. The clock does not create time, nor affect it causally in any way; it only measures time in ^inits that are relative to one another, but time itself is not relative. If there are these cases of related and independent terms, then can it be consistently argued from the fact of mere related- ness, either that knowing modifies, or that it is in any way necessary to the existence of, (known) entities? And also can it be consistently maintained that, if all finite minds were anni- hilated, there must still be, as necessary to the existence of the universe, an "infinite" mind or spirit, analagous to a human finite mind ? For the realist the answer to these inquiries can only be **No." For, if there is a single case of the knowing of a genuine 86 HISTORICAL PROBLEMS OF PHILOSOPHY and true "state of affairs/' then the knowing and the (com- plex) entity known are, together, one instance, at least, of the principle, that some entities are related and yet independent, — and there may be other instances of this principle. This is the paradox. "Things" are known and are related to the knowing; but they are known as if they were not known. But further, entities can become specifically related, and then cease to be so related. Thus a moving body of a certain volume occupies a certain space for an instant, and then no longer occupies it. "Occupying" is the relation that is both gained and lost. By this and innumerable other instances the realist is supported in his contention, that "things" can get into and out of the relation of being known without being affected thereby, — which alone is the condition on which "things" can be known as they really are, i.e., on which there can be genuine knowledge. But, still further, an entity in gaining and losing a specific relation can retain its relations to other entities. Thus a man can retain, his several blood-relationships, and yet gain new relations of friendship. So also may an entity retain its several relations to other entities, and yet gain that relation to an organ- ism which is identical with being experienced in some specific way. These are instances of the evidence which the realist finds in proof of his contention (1) that entities can be related and yet be independent, (2) that specific relations can be gained and lost, and (3) that, with this the case, other relations can stiir persist. Especially does the realist maintain that these principles apply to the knowing and experiencing situation, and that thereby a solution is obtained for the ego-centric predicament. This solution is essentially the same logically as that which is obtained in the analysis of space. A point of space cannot be annihilated in order to determine what effect this annihila- tion would have upon other points. But by an analysis that leaves all the points in situ it is found that, as the condition for a point being a point and not a complex, a point is related to another point as if it were not so related, i.e., without being affected in its simplicity by being related. Similarly, while THE EPISTEMOLOGICAL PROBLEM 87 knowing and experience cannot be annihilated in the instance of a known and experienced object, it is discovered by an analysis in situ, that, as the condition for there being genuine knowledge in any specific instance, the object is known as if the knowing were not present. This sohition is presupposed even for that situation in which the opposed "state of affairs" is asserted and claimed to be true, as it is in fact by the idealist, the phenoraenalist, and by some pragmatists. For, notwith- standing that these philosophers attempt to base their respective positions on the insolubility of the ego-centric predicament, they themselves tacitly solve it by an analysis in situ, when they present specific states of affairs as true. But further, wdth the realist presenting well-established ex- ceptions to the position, that all "things" are what they are because of their relations to other "things," his opponents cannot maintain the universality of the theory of internal rela- tions.-® One is thus relieved from the necessity of admitting the positions frequently taken in epistemology, (1) that no problem can be isolated, since it is related to, and so modified by, other problems; (2) that we cannot know the truth about anything until we know the truth about everything; and, (3) that truth cannot be truth because it is a value. Contrary to these posi- tions, which condition various specific tendencies in philosophy, the evidence just considered shows it to be possible, (1) that one problem at a time can be studied and solved; (2) that the knowledge of the "things" involved in one problem will not be changed by the knowledge of other "things"; and (3) that truth remains truth, although, as related to appreciation, desire, / and purpose, it is also a value. The epistemological problem in its several aspects still per- sists. In fact it is the problem that is most discussed in con- temporaneous philosophy. But only one party thinks that it is not a problem that is logically prior to all others, and this party — the realists — takes this position because, having considered the problem, it finds that, in order to know, one need not first fin4 the how or whence or wherefore of "knowing." ="« See Chap. XXVI., ii., 2 and 3. 88 HISTORICAL PROBLEMS OF PHILOSOPHY CHAPTER XI THE PSYCHOLOGICAL PROBLEM AND THE NATURE OF CONSCIOUSNESS The preceding section has already introduced us to the psy- chological problem. Perception, thinking, knowing, and, in general, experience, are undoubtedly facts of some kind, but, of what kind, is the question. Already two fairly distinct answers to this question have been found and to some extent examined, especially as to their implications. By one group of philoso- phers, the idealists, the phenomenalists, and the pragmatists, it is maintained, that the cognitive consciousness is such that it modifies, or even constitutes known and experienced objects. This position is based on the assumption, that terms which are related affect one another. Clearly this view makes of con- sciousness, of knowing, of experience, the kind of "thing" that can causally affect or even produce the object, and a term that is a sort of substance is able to do this} By another group, the realists, it is argued, that the basic condition for genuine knowl- edge is, that the "thing" which becomes known shall enter into, and, perhaps, pass out of the cognitive situation without being affected thereby. This is possible only if the knowing is not a substance, but a relation, or a dimension, or a quality, or, possibly and indirectly, an event.^ Although there may be other sets of conditions in which there is knowing, nevertheless there is much evidence that the knowing situation arises when the complex or simple entity that is to become known gets into certain specific relations with another entity, i.e., with an organism having a nervous system of a certain degree of complexity, and in a certain physico-chemical condition. Knowing situations — at least those with which we are best acquainted — disappear when this specific complex disappears. But this means that specific knowings appear and disappear. It follows that knowing cannot be an absolutely simple term, since such a term, ' See Chap8. XXIX., XXX., XXXIV.-XXXVIII. * !See Chaps. XLl., xiv. ; XLllL, iii. and XI. THE PSYCHOLOGICAL PROBLEM 89 illustrated by a point and an instant, cannot appear and dis- appear. Only on the hypothesis, therefore, that knowing is a relational complex — of a specific kind, — and involving, of course, a relation between terms, themselves either simple or complex, can the experienced fact of the appearance and disappearance of specific knowings be explained. This is, in brief form, ''the relational view of conscious- ness." It is one solution of the problem as to ivhat kind of an entity consciousness is, and is held at the present time by a number of philosophers.^ It is a view that is also quite com- patiMe with the more orthodox position of experimental psy- chology, that specific consciousnesses are events. For events are themselves relational complexes, — e.g., a specific accelerated motion is a series of velocities, — and relations can themselves he related — as are, e.g., ''greater than" and "less than," brother- hood and sisterhood. Therefore consciousness as an event could be a complex of specific conscious relations that are themselves related in a specific way. This theory is also compatible with the view of a certain very modern school of psychologists, that the important thing in psychology is to study the objective manifestations, i.e., the behavior of organisms.* For, ivhen there are specific physio- logical conditions in this organic complex, and this in turn is related in a specific way to the entities to be known, i.e., to the stimulus, then the knowing is also present, perhaps as a char- acteristic of the whole complex, organism a7id stimulus. Some- thing occurs, something is done when this larger complex arises, and this can be studied as the behavior of an organism stimulated in a specific manner. The interesting corollary of this position is, that the knowing can not, in all cases at least, be said to be located within our bodies. Strictly speaking, it has no locus or place or position. Its conditions have, but it has not. "E.g., by F. J. E. Woodbridge, E. B. Holt, W. B. Pitkin, and by the writer. * See E. P. Frost, "The Belief in Consciousness," Jonr. of Phil., Psych., and Scientific Methods, Vol. XIII., No. 10, and " Cannot Psychology Dis- pense with Consciousness?" Psych. Review, Vol. XIV., No. 21; D. Miller, "Is Consciousness a Type of Behavior?" Jonr. of Phil., Psych., and Scien- tific Methods, Vol. XL, No. 8; E. A. Singer, Jr., "Consciousness and Behavior," Jonr. of Phil., Psych., and Scientific Methods, Vol. XII., No. 9; Watson, " Psychology as the Behaviorists view it," Psych. Revieio, Vo) XHI., No. 20. Watson in his Behavior gives a complete bibliography. 90 HISTORICAL PROBLEMS OF PHILOSOPHY This view that consciousness is a relation is perhaps a difficult one to grasp. Relations seem to be evasive, evanescent, indeed, almost negligible "things." Yet are they not facts? And should we hesitate to admit that consciousness in each specific instance of its occurrence is a relation, or else a "new" dimen- sion, if this conclusion is necessary in order to explain other facts ? However, many philosophers and psychologists hesitate to accept this "relational" or "dimensional" theory, and indeed historically it has not been a widely favored one. Consciousness has seemed to be, perhaps, too tangible, "solid," and substance- like, and to involve too much of a continuity and unity of personality to be a mere relation or a dimension. Indeed, the traditional view is, that empirically, both by introspection of one's own mind and by observation of other minds, an entity is discovered that is an ego, a self, a soul, a "something" that is of absolute constancy, and anything hut a relation, a dimen- sion, an event, or a disembodied quality. In fact, it is argued, that absolute unity and constancy are necessary in order to account for the continuity of personality and the unity of knowledge, and that this finally demands a numerically simple and indestructible entity somewhere in human consciousness.^ Relations, it is contended, appear and disappear altogether too readily to meet this demand, while complex entities, such as specific dimensions, disintegrate, or, as existing, presuppose an absolute unity to bind them together, and qualities imply some- thing of which they are qualities, and in which they inhere. Thus runs the argument of the opponents of "the relational view," and their names include the great names in the history of philosophy. A very similar position has been advanced in modern days, since the law of the conservation of energy and the theory of evolution have dominated scientific thought, to establish what amounts to a principle of the evolution and yet of the conserva- tion of consciousness. It is argued (1) that consciousness is so different from physical energy, that it cannot "come" from or arise out of this, yet (2) that it is a fact and must come from something; and, therefore (3) that there must be a preceding " E.g., by Plato and Leibniz, and, perhaps, by Kant. THE PSYCHOLOGICAL PROBLEM 91 consciousness out of which it arises or is transformed. Thus the position is derived, that there is either an all-permeating universal, yet impersonal consciousness that exists in varying degrees in animal, plant, molecule, atom,® and even electron, or a great personal consciousness that "wells up" and is present in ail "things," and is, perhaps, identical with God J All this shows that the question of the nature of consciousness is one of the main philosophical problems. Indeed, it is a very pressing problem today in this period of revolt against many of the traditional philosophical methods and positions. His- torically, in reaching solutions of the problem, the "substance view" of consciousness has been dominant. But this has been the case primarily because of the influence of the Aristotelian tradition, with its preeminent concepts of siibstance and cause. The other psychological problems are more specific, and fall within the realm of empirical psychology as this is carried on by experiment and observation and by statistics. But this is not to say that the more general and philosophical problem as to the nature of consciousness is not to be solved by the use of similar methods, or that the solution of some of these more specific questions does not aid in the solution of this wider problem. On the contrary, two at least of the specific psycho- logical problems are espevrially important philosophically. Whatever consciousness may ultimately he, we nevertheless know some of the "things" that it does, and we have an em- pirical classification of its different forms. Thus we speak of knowing, feeling, and willing, or of cognition, emotion, and voli- tion; of deliberation, instinct, and impulse; of attention, dis- crimination, and analysis; and of perception, memory, imagina- tion, and reason. If, now, evidence is found for holding that consciousness evolves along with the evolution of life, then the question arises, what kind of consciousness was first. Was it sense perception, or the mere feeling of pain and pleasure, or an "elementary" will, and are all kinds of consciousness only gradual modifica- tions or outgrowths of a first kind ? But these questions suggest 'E.g., by Paulsen, Introduction to Philosophy, trans, by Thilly. This is also the position that is at least implicitly taken by most text-books on psychology. ^ The position of many objective idealists; see Chaps. XXXIV.-XXXVIII. 92 HISTORICAL PROBLEMS OF PHILOSOPHY others. Thus, instead of arguing, that in order to account for consciousness in higher forms, notably in man, its presence must be granted in the lowest forms, and even in atoms and electrons, could we not start with what we directly find in the lower organisms, namely tropisms, reflexes, organic discrhninations, and the like, and then ask, if what we call consciousness in higher forms is not merely a complex of these purely physio- logical modes of behavior ? ^ But there is a second psycho-philosophical problem. Certain philosophical systems that are great not only in their influence as philosophies, but also in their alliance with the dominating religions of the world, find reasons for concluding that tlie whole universe is ultimately conscious or spiritual in nature. What, then, is the character of this universal spirit or consciousness? Is it a self, an ego, a spiritual unity? Is it will, knowing, or feeling? Or, if it is all three of these together, ivhich is domi- nant, and what is the relation by which the three form one relational complex? In answering these questions the great idealistic or spiritualistic philosophers have differed and still differ.^ One further psychological problem must be mentioned be- cause, through the solutions that have been given to it, it has been of great influence on certain philosophical systems. This problem concerns the nature of illusions, of dreams, and of hallucinations, and is stated in the question, Are, or are not, our dreams and especially the things of ivhich we dream wholly "within our heads," wholly in our "dream-consciousness"? And yet, it may be asked, are not dream-objects quite real to us ivhile we dream them. Then the further question arises, whether it might not be, that every- thing in the universe, stars and sun and planets, this earth and all that lives thereon, is but a persistent dream in which we all share. Here one might still further ask, whether you would not be only my dream-object, so that I would be all, and all would be in mef This position, that everything except you and me and other human beings, as spirits or souls, is a sort ' This is done by, e.g., Jacques Loeb in Physiology of the Brain, and in The Mechanistic Conception of Life. • See Chaps. XXXIV.-XXXVIII. THE PSYCHOLOGICAL PROBLEM 93 of dream in which we all share, with dream "effect" following dream ''cause" with regularity and according to law, is Sub- jective Idealism. But what right, once thus started, to make exceptions? To be consistent must one not also grant that all other human beings are only one's own persistent dream? This consistent position is Solipsism, But the instances of normal illusions also set a similar prob- lem. For example, the rails of the railroad are parallel, but as we look down the track they appear to converge. Also, the stick that is straight appears bent, if it is immersed in the water. But can the rails actually be both parallel and not parallel, the stick be both straight and bent? Are not parallel and not parallel, straight and not-straight respectively contradictories, so that in each instance each characteristic must exist at a different place or locus? Much traditional philosophy and psychology have solved these problems by making the "parallelness" and the straightness in each case the real "objects," and by "put- ting" the contradictory entities, i.e., the illusory appearances, ifito some particular consciousness, thus identifying their esse with their percipi.^'^ For their existence consciousness is held to be necessary. Therefore, it is further asked. Is not conscious- ness necessary for the existence of all "things," even of all so-called real "things"? Could not they also be mere appear- ances and exist in some personal consciousness, or, if not this, then at least in some divine consciousness? This position is again Subjective Idealism, or, carried to its logical conclusion, Solipsism, The reply to these arguments can be stated briefly, and, indeed, on the principle, that one cannot lift himself by his own boot-straps. If some "things" arc concluded to exist only "in" consciousness, because other "things" do not, then it cannot be consistently inferred, that these other "things" also exist in consciousness. The scientific solution of the problem of these normal illusions, — if illusions they are — is one that cuts the very foundation from beneath that argument for idealism which is based on them. This scientific solution is, that the illusory appearances do not exist "in" consciousness at all, but are real parts of that same world of which the real *" £. g., by A. O. Lovejoy; see the refprences given in Chap. XLIII. 94 HISTORICAL PROBLEMS OF PHILOSOPHY objects are also parts. Rails and stick hy themselves are re- spectively parallel and straight. But the complex, rails and light, has the characteristic of convergence, and the complex^ stick and water and light, the characteristic of bentness. Each of these contradictory attributes has, indeed, a different locus from that of the original object, but this locus may quite as well be another part of the physical world as a part of a consciousness. SECTION III METHODS AND PROBLEMS OF METHOD I. THINKING CHAPTER XII REASONING BY WORDS, AND THE PSYCHOLOGY OF THINKING I. INTRODUCTORY In this section there will be considered the various methods that are used in attempting to solve philosophical problems. But, since these methods present problems of their own, we shall have problems of method, in addition to problems of points of view, of ontology, cosmology, epistemology, and the like. The methods to be examined will, however, not be limited to those that are correct, but will also include those which, though un- sound, have, nevertheless, been frequently employed to solve certain problems which have arisen in the development of certain historical systems of philosophy. II. THE THINKING SITUATION ^ It is an important, although rather obvious fact, that all philosophical systems, whatever their differences, must use 'Compare with the account that follows: E. B. LeRoy, La Langue, 1905; H. Odier, Essai d' Analyse Psych, du Mechanisme du Langdge dans la Comprehension, 1905: H. Steinthal, Einleitung in die Psychologic und Sprachivissenschaft, 1881; W. Wundt, Sprachgeschichte und kiprachpsy- chologie, 1901 ; B. Erdmann, Psychologische Untersuchurtgen iiber das Lesen, 1898; G. VVolil', Psychologic des Erkennens, 1S97; A. Binet, Psy- chology of Reasoning, 1912; F. Brentano, Psychologic vom empirischen Standpunkte ; K. 8. Woodworth, " Non-Sensorj' Components of Sense Percep- tion," Jour, of Phil., Psych, and Scientific Methods, Vol. IV.: also, " Image- less Thought," Jour, of Phil., Psych., and Scientific Methods, Vol. III., 1906; and " The Consciousness of Relation " in Essays Philosophical and Psycho- logical, in Honor of Wm. James, 1908; James, Principles of Psychology, Vol. 1., p. 243 ff.; J. K. Angell, "Thought and Imagery," Phil. Review, 95 g6 METHODS AND PROBLEMS OF METHOD words in their processes of reasoning, since they are argued about and defended, and are thus presented for our acceptance as true. This is the case even in such an extreme position as mysticism, where, it is claimed, intuition and ecstasy reveal certain facts which reason cannot apprehend. When rationally defended, even such a position is reasoned about by the use of words, and thus the possibility that reason can discover at least some facts is presupposed. The problem as to what is involved in reasoning by the use of words, or of some kind of symbols, is, therefore, a general problem of method that concerns all philosophical systems in one way or another, and all philosophiz- ing to some degree. Common also to all philosophizing is the method of examining the "world" about us by some mode of approach, i.e., either by the senses, or by some other mode. But different individuals accept different methods of approach, and the regarding of anything as fact is made dependent on that which is antecedently regarded as the correct approach. For example, the mystic regards intuition as the one correct method, and so holds that all-adsorbing miity which this approach reveals, to be the im- portant fact, while the intellectualist finds that analysis and reasoning are correct approaches, and that plurality and differ- ences are quite as much facts as is unity. Thus, in all philosophizing and in all philosophical systems there are ttvo methods, the one, that of reasoning by words and other symbols, the other, that of observing in some way, both of which are accepted and used, and freely allowed to supple- ment each other. Of these the former will be first considered, since it is that method to which we are of necessity committed in our endeavor to investigate philosophical problems, methods, and systems. III. THE PSYCHOLOGY OF THINKING; SYMBOLS Words are by themselves only physical objects, i.e., they are either printed or written marks, or, as spoken words, waves of air. These objects are words in the usual sense by virtue of Vol. VI., 1897; E. B. Titcliener, Eaperimental Psychology of the Thought Processes, 1!)09; VV. B. rillsbury, The Psychology of Reasoning, 1910; J. JJewey, IJoio We Think; B. Erdmann, " Umrissc zur Psycholofjie des Denkena," in Phil. Abh. Chr. Bigioart zu seinem lOten Oehurtstage, 1900, pp. 3-40. REASONING BY WORDS 97 being associated with certain specific mental processes, namely, with those which reveal the objects or "things" that are experi- enced when these mental processes are taking place. The physical words are, then, symbols for these objects or "things." It results, that when one perceives or thinks of certain specific marks or sounds that are word-symbols, one also tends to be conscious of the objects for which the symbols stand, i.e., to be conscious of their meaning. This "meaning" consciousness, therefore, and the consciousness of the words as such, become associated, and thereafter, each tends to "arouse" the conscious- ness of the other. But further, the consciousness of a meaning, once aroused, arouses the consciousness of other meanings, and so on, at the same time that the consciousness of the words for these "things" is aroused, and there then occurs a series of word-images, the earlier images suggesting later ones. Accord- ingly, when we read or hear words, these suggest or arouse the appropriate meanings, and when we think quietly, or speak, the meanings seem to come slightly ahead of the words, and to suggest them. Three aspects, therefore, are to be distinguished in the situa- tion presented by the use and meaning of words. There is (1) the psychological aspect, Avhieh concerns the consciousness both of the word-symbols and of the objects and meanings with which they are associated; (2) the grammatical aspect, and, (3) the logical aspect, which merges into the grammatical, and conversely. These last two aspects are, of course, also most intimately connected with the first aspect, since logical and grammatical facts are known and have word-symbols associated with them. The psychological processes with w^hich we are concerned are classified as follows : Consciousness, or psychic or mental process, is the genus, and its three main subdivisions are: cognition, emotion, and volition, or, using synonyms, knowing, feeling, and willing. The meaning of each of these is sufficiently well known to the reader not to demand a discussion. Knowing may, however, he defined as awareness. Cognition is in turn classifiable into its specific kinds, namely, sense perception, memory, imagination, and conception, and there are, in turn, as many kinds of each of these processes as 98 METHODS AND PROBLEMS OF METHOD there are specifically different senses, namely, sight, hearing, "equilibrium," touch, taste, smell, and the "heat," "cold," "muscular," and "organic" senses. This means that, with dif- ferent kinds of sense perception, also memory-, imagination-, and conception-processes can take place in terms of each sense, although vision, hearing, touch, and muscularity are the dominant senses. There are also processes of self-perception, or of introspec- tion, that do not take place through the medium of the special sense organs. In this process of self-perception we become aware that we are perceiving, remembering, imagining, con- ceiving, willing, having emotions, and the like. Thus self- perception also furnishes material or content for subsequent processes of memory, imagination, and reasoning. This classification of cognitive processes means that all sorts of entities, such as things, qualities, events, and relations, can be perceived, remembered, imagined, conceived, judged, and reasoned about. Some of these entities are physical, others are mental, while still others belong to neither of these two classes. Among these non-physical and non-mental entities are terms, qualities, relations, and perhaps also events, luhich our reason shows us would still he facts, even if all physical and mental entities were annihilated. A good example of such entities, which may be called (non-existent) subsist ents, are the positive integers, 1, 2, 3, n — 1, n, n -f- 1, — not these physical marks, of course, — hut that which these signs symbolize, and that which is presupposed, biit not made by counting. Written, printed, and spoken words are used as symbols or signs by which to indicate both specific individuals and specific classes of individuals, and classes of these classes, and so on. To illustrate this, and at the same time to give examples of some of these classes of entities, the reader's attention may be called to the fact that he can now experience, by introspection, a series of (existent) mental processes as he visually perceives these very words (physical existents). Thus his experience is at least twofold. However, words or symbols that are used in reasoning can be known in any one of the several cognitive processes, and not alone in sense perception; i.e., there are remembered, imagined, and conceived, as well as perceived REASONING BY WORDS 99 words. Words read are visually perceived, and words heard are perceived in hearing. But tvJien we reason in order to write or speak, we tend to formulate our thoughts in words that are conceived, though, as ive ivrite or speak, and see and hear, there are also perceived words. But any kind of a word can be associated with any particular object or class of objects that is brought to our knowledge in any way whatsoever. Thus we have words not only for what we perceive in sensation and in terms of sensation, but also for what is revealed in our reasoning processes and in our emotions and acts of will. IV. GRAMMAR The differences among the entities that we perceive, remember, imagine, and get at by reason, or become aware of emotionally, as in cesthetic and moral feeling, and the like, receive a certain recognition in the grammatical distinctions and differences of language. Thus, nouns for the most part symbolize ''things" and qualities; verbs, prepositions, and conjunctions symbolize events and relations; and adjectives and adverbs, qualities or attributes. The grammatical structure of sentences also ex- presses and reveals to a certain extent the relations between and among the entities to which our judgments, as psychological, knowing processes, are directed. In general, grammatical dif- ferences correspond to objective characteristics of the entities that are symbolized b}^ the words, and that are known in the judgment which is verbally formulated. CHAPTER XIII THE LOGICAL ASPECTS OF THINKING INTERPRETATIONS OF THE NATURE OF LOGIC We use our senses to perceive, we remember, we have emo- tions, and we describe what is thus revealed to us, but sometimes we do more than this. We reason about "things." It is a most important question, then, to ask, What is it, when we reason, by 100 METHODS AND PROBLEMS OF METHOD virtue of tvhich we are enabled to do this? or, Just what do w& do when ive reason? As at least a tentative answer to this second question it may be said, that to reason is to infer, or to learn from something that is known, something that was previously unknown. To reason may also mean to systematize, and to ''put" many "things" together consistently, as is done, e.g., in any science, though to do this seemingly demands reason in the former sense. But the first question is more important for our purposes than the second, which concerns only the psychological char- acter of reasoning. What is it in or among the entities that we reason about that enables us to infer? The answers given to this question have been both varied and involved. Among them three principal tendencies are distinguishable, namely, the realistic, the psychological, and the pragmatic. These are the three main views as to the nature of logical principles and entities. All three agree that we reason by using in some way the peculiar, interesting, and very important relation of implica- tion, but they differ in their interpretation of the nature and locus of this relation. I. THE REALISTIC VIEW OP LOGIC According to the realistic view, implication is a relation that is objective in the sense that, although related to, it is inde- pendent of, the reasoning process that is, in part at least, an awareness of it. Just as there are relations of similarity, of difference, and of whole and part, so also, it is held, there are relations of implication, or of the non-causal, yet necessary con- nection between "things." By discovering and making use of these relations in specific instances, we discover other relations, and from certain entities, other entities} Just what all the typical situations are that present the rela- tionship of implication, is difficult to determine, but the follow- ing is a simple illustration of one such situation: Among the entities that are discoverable in this universe of many entities are relations, as has already been emphasized. Instances of relations are "father of," "equal to," and "precedes." If, ' See Chap. XLI. THE LOGICAL ASPECTS OF THINKING 101 now, the terms that are related are symbolized by a, h, c, etc., then we can have the relational complexes, respectively, a the father of h, a equals h, and a precedes h. However, it would seem that none of these relations subsists without, in each case, another and distinct relation also subsisting, this other relation being the inverse, or what is sometimes called the converse of the original. But at the same time that this inverse relation is distinct from the original relation, it is also necessitated by it, though not in a causal, but in a logical manner. This specific logical necessity is an instance of implication. Thus, in the case of one of our examples, "father of implies or necessitates the inverse relation, "child of," and these two relations are not identical. So also a = b implies that h =^ a, and "a precedes b" implies that "ft follows a." In general we may say that every relation implies its inverse or converse.' This being so, we have a most interesting situation. The proposition just stated means that, with the original relation aBh given, there is of necessity the inverse relation, hRa. But this means that aRb and bRa are themselves related both by implication and by "inverseness." Then, if the proposition above stated is correct, each of these relations also implies its own inverse. But this is precisely what we find. The relation of implication that subsists in that aRb implies bRa, itself implies the inverse, namely, that "bRa implies aRb, i.e., "aRb implies hRa" itself implies "bRa implies aRb.'* This situation need not be analyzed further for our purposes, for the analysis thus far made discloses the fact, both that the relation of implication subsists in the midst of, or side by side with, or on the basis of, other relations, perhaps of very specific ones, and also that it is itself a basis for still further relations. Another situation in which we find the relation of implication cosubsisting with other relations is one that is identical with the orthodox categorical syllogism of the Aristotelian formal logic." The traditional logic of Aristotle is essentially the logic of classes. A class subsists by virtue of the relation of similarity, together with, in most cases, that of difference among entities, and quite independently of their order. This is quite evident =■ Cf. Chap. XXVII. ' Cf. Chap. XIV. 102 METHODS AND PROBLEMS OF METHOD when we consider simple examples such as the two classes, men and vertebrates. Any one individual of the class is in the relation to the class of being ''a member of" it. But classes are themselves related by complete, partial, and negative inclu- sion (i.e., exclusion). Thus, to illustrate, all mew are included in the larger class vertebrates, but the class vertebrates is only partially included in the class men, and, finally, the whole class vertebrates is excluded from the whole class triangles. Such relations of similarity, difference, member of, and inclusion, positive and negative, between entities are, now, propositions, or objective ''state of affairs," and the knowledge of such rela- tional complexes is in each ease a judgment. One and the same class, further, can be in one relation to one class, and in another relation to another class. Thus the class vertebrates includes the class men, but is included in the class living beings. With this specific state of affairs subsisting, there also subsists of necessity the relation of inclusion of the class, meyi, by the class, animals. This relation is numerically distinct from the other two relations of inclusion, namely, of men in vertebrates, and of vertebrates in animals, yet it is related to them. It is, first, similar to, and, second, implied by them. Thus we have another case of the relation of implication "resting on" other relations between terms (in this case those of in- clusion), and of still another relation or relational complex resting on it. In the example just given, if we let S symbolize the class (all) men, M the class (all) vertebrates, P the class (all) living beings, < the relation ''included in," and ) the relation of implication, then we have S <. M and M < P, ) 8 < P. This relational situation holds good for any classes, 8, M, P, that are related to one another as are the classes, men, vertebrates, and animals. In a very similar way the relation of complete exclusion of a class 8 from a class P is implied by the two relations (1) of the complete inclusion of the class 8 by M, and (2) of the com- plete exclusion of 31 from P. Thus, to illustrate, if all proposi- tions are included in the class of analyzable entities, and all analyzable entities are completely excluded from the class of simple entities, it is implied, that all propositions are excluded from the class of simple entities. THE LOGICAL ASPECTS OF THINKING 103 Other instances of the relation of inclusion, complete, partial, or negative, between two classes ''at a time," are discoverable, and the several relational complexes that thereby subsist, taken in pairs as premises together with the propositions which they imply, make tip the several moods of the four figures of the Aristotelian categorical syllogism. The detailed examination of these moods and figures may be found in any text-book on logic, and need not be presented here. There are a number of other, perhaps many other situations in which the relation of implication is present. But the instances given will, it is hoped, make clear what the realistic position is in regard to the problem of what it is (in the situation rea- soned about) that enables us to reason, or that we discover and become aware of when we reason. The solution of this problem is, that, just as there are "things," qualities, events, and such relations as membership in, similarity, and inclusion, so also is there the relation of implication, which, if the former entities are objective and discoverable, is also of this same character.* There are many further questions, some of them of extreme interest, concerning the problem of implication. Thus, if cer- tain relations are implied by others, which we find to be the ease, then it may be asked, whether implication is itself implied, or whether it merely occurs as one among many relations, i.e., as one that accompanies, but is not necessitated by other relations. The writer is strongly convinced that the second alternative is the ease. Although all the circumstances that surround and perhaps condition implication may be difficult to discover, nevertheless the realist holds that to reason correctly, even in the study of the reasoning situation itself, is to discover (objective) relations of implication that are independent of the reasoning process, though related to it. For example, there are i7idividual * The problem of the nature of implication, the circumstances of its occurrence, etc., have not as yet been given much attention in philosophical investigation, although Russell has dealt with it somewhat in his Principles of Mathematics. The objective view here presented agrees, e.g., with that of G. E Moore in his article, " The Nature of Judgment," Mind, N. S., Vol. VIII., p. 177 ff., and is accepted, I believe, by all realists. Cf., also, on the realistic interpretation of logic and a criticism of the psychological and pragmatic tendencies, Husserl, Logische Untersuchungen, especially Vol. 1., 1900, and Vol. II., 1901. 104. METHODS AND PROBLEMS OF METHOD "things," that, through the relations of similarity and differ- ence, form distinct classes. Then there are also the objective states of affairs of both similarity and difference. But in turn there are classes that are related to one another by inclusion, i.e., if A, B, and C are classes, and < symbolizes the relation of inclusion, A < B, and B <. C. Then, discovering and following the "threads" of implication, we discover that A <.C. This is typical of that situation which is present when we reason by what is called the categorical syllogism. The categorical syllogism, however, is not the only technical method of reasoning. There are also other methods, which will be presented later. Yet in regard to all of them the realistic position is the same. Not only are indiviO.ual "things" inde- pendent of knowing, but relations also are, not excepting those relations of implication which must be discovered when we reason and reason correctly, and by the discovery of which we are enabled to ascertain from certain facts other facts that are necessitated by the facts from which we started. Indeed it is precisely this objective point of view that is at least tacitly accepted by every philosopher when he reasons in order to philosophize. Every philosopher aims to arrive at or to discover "large" general facts or states of affairs that are quite independent of his own or anybody else's knowing proc- esses ; and in presenting his philosophy for acceptance, he tacitly assumes that he has succeeded. In this respect every philosophy is realistic. Eeason may not be the only "method" by which facts are revealed. Sense perception, memory, emotion, and intuition must also be admitted to be such avenues of approach. But reason alone is that method by which these other methods can be examined, and a conclusion as to their reliability and char- acter be obtained. Also it is reason alone that can thus examine itself. Reason is, then, the court of last resort. Indeed it is accepted as such even by those philosophers who write books in advocacy of anti-rational positions. Thus, e.g., the mysticism of a philosopher like Bergson can he ratio)ially supported only by intellectual methods. The foregoing analysis presents the realistic view of that situation which is involved in any attempt to reason and to THE LOGICAL ASPECTS OF THINKING 105 philosophize hy the use of words. Words are the conventional instrument for this thinking, and for testing its correctness by communication with others. But that for which certain words and phrases are the signs is not the concrete individuals, nor the consciousness of these, but the various and diverse states of affairs that hold of these individuals. Certain of these states of affairs are logical, or involve logical entities, including im- plication, and when these are discovered, the way is clear to discover other "things" or entities. II. THE PSYCHOLOGIZING TENDENCY The realistic position, that logical entities are objective and independent of reasoning processes is, however, not accepted by every one. It is certainly not the traditional view. The traditional logic is, as we have seen, the logic of classes, of things, and of qualities. In it the paramount "principles" are those of identity and of contradiction, and these are made "laws of thought," or psychological and subjective principles. To make this statement clear, let us consider, e.g., the proposi- tion, a stone is hard, i.e., all stones are hard. But there are also other hard things than stones. Our proposition would seem to mean, then, that a certain class, stones, are, as a whole, included in, or identical with a certain part of, a larger class, hard things. In both cases, now, the principle of identity appears. There is an identity of "extension" between stones and a certain specific part of the class, hard things, and, also, hardness is (identical with) a quality of stones. Now in accordance with the teachings of the traditional logic it is impossible to reason without presupposing and using the principle of identity in both of these senses. Thus, whether we start with the proposition, "hard things are not mental," or with "hard things are physical," and from these and the proposition, "stones are hard things," conclude that stones are not mental, but physical, we are presupposing and using iden- tity in both of the senses just mentioned. Yet that the principle of identity is not only presupposed in such instances but also that it is a law of our thinking, i.e., that it is a psychological and subjective law, is the traditional logical 106 METHODS AND PROBLEMS OF METHOD doctrine that is reached by the following argument, used either implicitly or explictly. Thinking is held to be specifically different from other entities, or to be sui genesis in at least some aspects, and thus to have a "nature" peculiar to itself. The proposition is then main- tained as self-evident, that thinking cannot act in contradiction to this "nature," but must act in agreement with it. A similar argument could, of course, be made for almost any entity, e.g., for electricity. The next question accordingly is, what those laws are which, when thinking acts in accordance with them, "fulfil" and reveal its nature? This question is answered by finding what laws thinking must follow, whether it will or no, since, if it can be shown that there are certain laws that thinking must follow, this necessity can be accounted for by the hypothesis, that such laws are resident in the thinking process itself, and "make up" that nature in agreement with which thinking must act. But, what laws thinking must follow is ascertained by finding what laivs or principles are such either that their opposite cannot be conceived or thought, or that they are presupposed by their own (attempted) denial.^ By applying these tests, the conclusion is reached, that such laws must be used, when we think, indeed even when we endeavor to think without them, hecause they are laivs of thinking. This is the argument that is used, either tacitly or explicitly, in the traditional logic in order to show that not only the law of identity, but also the laws of contradiction and of excluded middle are "laws of thought," i.e., laws of a psychological process. We may now examine the application of this argument to each of these laws, at the same time that we give each law a formulation. The Law of Identity. Even in the endeavor to think without /it, the principle is used, (1) that each entity is identical with itself, i.e., that it is that particular entity and not any other, and (2) that it retains its peculiar character and its indi- viduality. The Law of Contradiction. Even in the attempt to think " See Chap. XV., iv., 5, 6, 7. THE LOGICAL ASPECTS OF THINKING 107 without it, the principle is used (1) that each entity cannot be both that entity and not that entity, and (2) that it cannot both belong and not belong to a specific class, either as an individual member or as itself a class. The first formulation of the prin- ciple is but a restatement of the law of identity as the principle of the individuality of each entity, even where, as in the class of the points of space, all individuals seem to be qualitatively alike. The principle, in this sense, does not mean, however, that one and the same entity cannot be in two relational com- plexes at once. For that an entity can have such a dual rela- tionship is exemplified by a point, which, as the apex of an angle, is a member of the two lines that form the angle. The principle of contradiction may be illustrated by that proposition which concerns it, namely, that it itself cannot he both a {psychological) law of thought a7id not such a law. The Law of Excluded Middle. Even in the endeavor to think without it, the principle is used (1) that each entity, either as an individual or as a class, must belong either to a class, A, or to that contradictory class, non-A, which logically includes everything that the other class does not include. Thus, any logical principle must be either a (psychological) law of thought or not such a law. This position that certain logical principles are laws of thought, or of mind, or of psychical processes, is well called **the psychologizing tendency."*^ Its consistent outcome is, on the one hand, that all logical principles are subjective or mental, and, on the other hand, that that which shall be regarded as logical is determined by finding what principles (1) are pre- supposed by the very endeavor to think without them, or (2) are of such a character that their opposites cannot be conceived, or (3) are, perhaps, also self-evident. Historically, as this tendency has developed, a numerically single "transcendental ego," and also such "concepts" as quantify, quality, relation, causation, substance and attribute, possibility, actuality, neces- sity, unity, plurality, totality, positive, negative, and even time and space, have been "found" to be such logical principles. This is notably the case in the Kantian philosophy and tradi- tion, in which some of these "concepts" are called "categories." ' See Husserl, op. cit., for a criticism of this tendency. 108 METHODS AND PROBLEMS OF METHOD The argument has been, that one must think in accordance with some one, or a number of these ; that the very attempt not to do so but reveals the compulsion to do it; and, therefore, that this compulsion is to be explained alone by the hypothesis, that these "concepts" are principles of thinking.'' The sharp difference between this psychologizing tendency and the opposed realistic position may be brought out by con- sidering certain consequences of the former position. The critical examination of the traditional development in philosophy shows, as we have already found, that there has been a strong tendency to use the principle, that all entities, because they are related in any way, are also causally related. This principle is, therefore, applied to the fact of the relation between knowing and that which is known. If, now, this knowing has a nature that consists of laws of thought, categories, and the like, then those ways in which knowing will affect the entities that are known will be just these laws and categories. It follows, that, given an indeterminate "something," an x, to he known, this X will, as known, bear the "stamp" of these laws and cate- gories, and any attempt to know an entity without this * ' stamp ' ' will be self-defeating. In the psychologizing tendency, therefore, logical principles and entities are "made" subjective or psychical entities that are attributes of and that inhere in the knowing mind, and that also are wholly absent from the realm of unknown x's, but that nevertheless appear to be in the realm of known "things" be- cause they are "read into" that realm by the causal influence of the knowing on that which is (to be) known. This philosophy ' Aristotle himself would seem to have accepted the realistic interpreta- tion of the proposition and the syllogism and, also, of logic. In the assertion of a proposition he recognized two aspects, a subjective and an objective. In the subjective there is revealed the speaker's belief or dis- belief; in the objective the "state of affairs" to which such belief or disbelief corresponds. See De Interpretatione, p. 23, a 32; p. 24, b 1; p. 17, a 22. The later subjectivistic and psychological view seems to have grown up in the tradition because of some lack of clearness in Aristotle's own mind, and because of the influence of the " thing " and " substance concepts." This view seems to have been held in modern philosophy by Descartes, Spinoza, Leibniz, Kant, Fichte, Hegel, and by most writers of current text-books on logic. The germs of opposition to it are found in Locke's Sensationalism and Empiricism, in Berkeley's Nominalism, and in Hume's Positivism; and these "germs" came to their full development in Pragmatism and Healism. Cf. the later chapters on these positioua. THE LOGICAL ASPECTS OF THINKING 109 is called Phenomenalism. Concerning its logical genesis it is only fair to say that the assumption, that there is a causal influence of knowing on the thing known, while it is made, per- haps, quite unawares, is due to the influence of the tradition that comes from Aristotle. The general realistic criticism of this whole position is, that, if it is a condition of genuine knowing that "tilings as they are" should be got at, then (1) the act of knowing cannot alter the "thing" known, and (2) all categories and logical principles must subsist, or be facts, in and among the entities known, whether or not these categories and principles are present in the knowing process itself.* Indeed, even granting that there are laws or principles of the psychological process of thinking, which laws this process follows, nevertheless these same princi- ples might also hold of other entities, such as physical objects and events, numbers and space and time; or, it might be, that certain logical principles hold only of these other "things," and that, accordingly, reason viust follow these principles be- cause, in order to give genuine knowledge, reason must conform to "things." In fact, that reason must so conform, and not project itself into and alter those entities that are known by its means, is the very position that is tacitly assumed by the ad- herent of the psychologizing tendency, when he reasons about the character of reason in general, in order thereby to discover the facts concerning this.^ III. THE PRAGMATIC TENDENCY The criticism just made of the psychologizing tendency can also, with equal justification, be directed against that tendency which has recently received the name of pragmatism. The pragmatist sets out to study the function and develop- ment of knowledge, and, within this field, the nature of logic. He solves the problem by discovering certain "states of affairs" both by reasoning and by other methods, and, finally, by sys- tematizing and unifying his results. But in doing all this he tacitly grants that certain states of affairs imply others, and " See Chap. II. • Prominent names among recent writers who take the psychologizing position in logic are: Sigwart, Bosanquet, Ueberweg, Wundt, Creighton, Hibben. 110 METHODS AND PROBLEMS OF METHOD that, in the whole complex state of affairs which his own prag- matic theory presents, implication, identity, unity, consistency, and the like, are quite objective in the sense that they are not dependent on their being known, and also are not invented in the sense that that part of the human race which is European in its culture has unconsciously contrived certain means of thinking, or has formed the habit of thinking in certain ways. This is the position that the pragmatist takes toward his own theory, but not that for which he contends explicitly within that theory itself. For, according to the detailed theory of prag- matism, all logic is either a mere invention, an intellectual instrument and machine, or a custom, a belief, that has developed in the tradition,^^ but in either case something that is useful as an adaptation to man's environment.^^ Its seeming necessary character is accounted for by the argument, that we cannot get out of the tradition in which we are reared, because the very attempt to do this is itself imbedded in the tradition. This implies that, had the tradition or the original invention been different, our logic would also be different. But it is also argued, that, since the only world which we know is one that is affected by being known and, therefore, by the "nature" of the knowing, our present (known) world is made in part by that very logic which forms part of the tradition. Originally, and even now, perhaps, there is another world, amorphous and plastic and quite different from our known world. And, had another logic been invented and grown up as a racial habit, then would all mankind be thinking in a world quite different from that in which they now think and live.^" This is the pragmatic view of the nature of logic as a method or as a set of principles by which we reason and investigate situations, even those that furnish pragmatism itself with its problems. Clearly this view has many resemblances to the psychologizing tendency. The latter regards logical principles as laws of certain psychological processes; the former inter- " E.g., James, Pragmatism, Chap. V., and Schiller, Riddles of the Sphinx, Chap, v., §§ !J-12. " Dewey, Studies in Logical Theory, 1!)03, and James and Schiller, ihid. '" Schiller's Humanism, discussed by James in all four of his later volumes, Pragmatism, Meaning of Truth, Pluralistic Universe, and Some Problems of Philosophy. THE LOGICAL ASPECTS OF THINKING 111 prets these principles merely as something which, like word- symbols, beliefs, and superstitions, are arbitrary and contingent, and are handed down in the general stream of social transmis- sion from generation to generation. This inheritance is con- ditioned chiefly by the psychological process of imitation, while certain principles have survived and have been transmitted only because of their usefulness. This usefulness is, indeed, their truth even as it is the truth also of every principle, hypothesis, law, and theory that survives and persists. In further criticism of this pragmatic view, it suffices to com- ment that, if logic is held to evolve and to be a mere adaptation together with other "things" like eyes and hands and nervous systems, and perhaps atoms and worlds and stars, nevertheless everything cannot evolve. The priiiciples of evolution cannot themselves be of this process. It is quite pertinent to ask, then, whether these principles may not themselves be in part logical. But if they are, then the universality of the pragmatic theory is invalidated, and we must conclude that at least not all logic, and, indeed, perhaps no logical principle is merely an evolving racial instrument and habit. XL THE TRADITIONAL TECHNICAL METHODS OF REASONING ^ CHAPTER XIV THE CATEGORICAL SYLLOGISM It is not proposed to give in this and succeeding chapters a detailed account of all the technical methods of reasoning, but to present only certain typical methods. All the methods pre- sented will, however, be understood to be open to each of the three interpretations just discussed, although the writer holds the realistic interpretation to be alone the correct one. ^ A complete presentation of the traditional methods will be found in almost any text-book on Logic as well as in such larger treatises as Sigwart's and Bosanquet's. 112 METHODS AND PROBLEMS OF METHOD One very common method of reasoning is by what is known as the categorical syllogism. This method should be presented and analyzed, since it is one by which much philosophizing is done, as is illustrated by any of the usual arguments for, or defenses of, philosophical positions. In making this presenta- tion the distinctions discovered in the previous analysis of the thinking situation should be borne in mind. A typical situation in which a categorical syllogism subsists is illustrated by that complex state of affairs in which (1) the class plants is included (related by complete inclusion) in the larger class living beings, and (2) roses are included in the class plants, so that (3) they are also of necessity included in the class living beings. In this situation there are present (1) relations of similarity, by virtue of which groups of indi- viduals form respectively the classes, roses, plants, and living beings, denoted in each case by the concept of the class, namely, rose, plant, and living being, respectively. (2) Each member of each class is related to that class as ^'a member of" it, and the class as a ivhole, i.e., the state of similarity of its members, is a fact that is different and distinct from the fact of each individual member. Each of the relational complexes involved in this situation is a proposition, but that complex to which we elect to give our attention at this point is that which is generated (3) by the relation of the inclusion of one class in another, e.g., of the class, roses, in the class, plants. One type of proposition is, therefore, that state of affairs which is identical with the relationship of inclusion of one class in another. But even as classes, and so, also, concepts or states of affairs that hold of individuals, are related, and, as related, are iden- tical with one type of proposition, so, in turn, (4) are these propositions themselves related ; or, as the situation may also be stated, one class may be related to another class as including it, and to still another class as being included by it. (5) Such a relational complex we will define as a specific type of the cate- gorical syllogism. Thus we have, in the case of the example given, using the sign < to mean "are included in," roses < plants < living beings. But 7-oses < plants, and THE CATEGORICAL SYLLOGISM 113 plants < living beings, are two distinct states of affairs. They are each a proposition. Yet together they necessitate or imply a third distinct proposition, iiamel}', that roses < living beings. A still further analysis can be made of this specific, yet typical situation. The printed words, "rose." "plant," and "living being" are symbols or signs that stand for concepts, the concept in each case being the objective state of affairs that holds of all those individual things that share in certain specific characteristics. Thus, e.g., there is something that "holds good" of a certain group of objects by virtae of which all are roses. This something, this state of affairs, is, however, not itself a rose, but it is a concept that consists of a number of character- istics which are familiar to all, and which are used when we recognize a flower as a rose. These characteristics form the con- notation or intension of the concept, rose; rose connotes them. On the other hand, the individuals of which the concept holds form its denotation or extension. In general, the fewer the characteristics that make up the connotation, the greater is the denotation of a concept, and conversely. Thus "rose" has a greater connotation, but a smaller denotation than has "flower"; "flower" a narrower connotation and a wider denotation than "rose." A concept denotes the individuals of the class of which it holds, whether we are conscious of those individuals or not. It must do this as that state of affairs which holds of these indi- viduals, whether we are aware of them or not. Therefore, in order to reason about individuals, once we have discovered the concept for them, ive need deal only ivith the concept with itsi connation, and with its relations to other concepts. In some cases we must first discover the individuals specifically, before we can get at the concepts for them. This we do in induction. But in other cases we find the concept first, thus to discover that there are certain classes of individuals, although, in some instances, we can never perceive (in any sense) any particular one of them. This is the case, e.g., in dealing with the points of space. Such a discovery of a new concept may be made by discovering what other, related concepts imply — a procedure that is most important for science and philosophy, since, by it, we discover certain classes of individuals no one of which, we 114 METHODS AND PROBLEMS OF METHOD can ever see, touch, or get at by any of the senses. For example, it is in this way that we are forced to deal with everything that existed or took place before we who now live were alive. In accordance with our previous analysis a distinction is to be made between (1) the words or signs, (2) the percepts of these signs, (3) the states of affairs or objective concepts holding good of classes of individuals, (4) these individuals themselves, and the consciousness both (5) of these individuals and (6) of the objective concepts. We are not always aware of these dis- tinctions while we are reasoning, but to fail to distinguish is not to do away with distinctnesses. As we reason we can give our attention either to the concepts or to the individuals, but to the reasoning it makes no difference, in most cases, which we do. Thus, whether we say *'a rose is a flower," or "roses are flowers" is, for reasoning, a matter of indifference. The example just analyzed, namely, the complex state of affairs, that roses < plants, plants < living beings, implies or necessitates, roses < living beings, is typical of a class of specific situations or relational complexes, called categorical syllogisms, in which the relation of implication is present. Prom many such cases that have been examined, the generalization is made, that wherever there are similar situations, there, also, will im- plication and the complex terms between which it holds be ''present. Some of the essential characteristics of these situations are formulated in the text-books as the rules of the categorical syl- logism, but they are to be regarded as rules for thinking only because thinking must conform to the structure of reality in order to issue in knowledge. One of these rules or principles concerns that which is evident in our example, namely, that while roses possess certain specific properties that are not possessed by all flowers, nevertheless they are included in this larger class. Accordingly, if some- thing is a fact concerning roses, it is not implied, and should not be inferred, that that something is also a fact for all flowers. In general, if something holds of part of a class, that "some- thing" cannot validly be inferred to hold for the ivhole of that class. Also, that which holds of a smaller class does not of necessity hold of the larger class of which the smaller is a part. THE CATEGORICAL SYLLOGISM 115 It might hold, but. also, it might not. When we infer, that which we infer should be implied or necessitated. Conversely, that which is necessitated must be inferred, if we are to infer, and infer correctly. That which is necessitated by a proposition or by propositions of the type we are considering depends upon the objective circumstance, whether some or all of the individuals of a class are involved in the specific relationship of inclusion, complete, particl, or negative, between two classes. Thus, in the proposition, Boses are flowering plants, while all rose^ are involved in the relationship asserted, it is only some flowering plants, namely, those that are roses, that are also involved. Therefore the converse proposition or relational complex that is implied by the original one is only that Some (not all) lowering plants are roses. However, in the proposition, No men are fishes, or its equivalent. All men are not fishes, both all men and all fishes are involved in the relationship of complete negative inclusion, i.e., of complete exclusion. The converse proposition that is implied is, accord- ingly, No fishes are men. But, as different from this example, in the proposition. Some triangles are symmetrical figures, neither all triangles nor all symmetrical figures are involved in the relationship, so that the converse proposition (that is) implied is, Some symmetrical figures are (some) triangles. However, in the case of the proposition just given, it is not implied that All triangles are symmetrical figures, though by the proposition, that All roses are flowering plants, it is implied, that Some roses also belong to this larger class. Likewise the proposi- tion, No men are fishes, implies that Some men are not fishes. But, as different from this, the proposition that Some Euro- peans are not Frenchmen does not imply that No Europeans are Frenchmen. These examples serve to illustrate an important principle, which is, that the relationship of the whole of a class, either hy inclusion, or by exclusion, to another class, necessitates the same relationship for some of the individuals of that class; hut that, conversely, the relationship of part of a class, either hy inclusion or by exclusion, to another class, does not necessitate the same relationship for all the individuals of that class. / 116 METHODS AND PROBLEMS OF METHOD This is but another formulation of the celebrated Aristotelian axiom known as the dictum de omni ct nullo, which may also be stated in the form that Whatever is predicated of a term dis- trihuted, whether affirmatively or negatively, may be predicated in like manner of everything contained under it. In explanation of this formuiation it may be said that a term is distrihutcd if all the individuals which that term denotes are involved in any specific relationship either of inclusion or of exclusion. Not to observe this dictum, i.e., to distribute, in the conclusion, as the proposition that is inferred, if not implied, a term that is not distributed in the premises, is to commit the technical fallacies either of illicit major or of illicit minor. However, if the dictum de omni et nullo is a principle that must be followed in those situations where our reasoning con- cerns relations of inclusion and exclusion, it is, nevertheless, not a principle that itself generates that relational complex which is the syllogism. Rather this complex subsists by virtue of that twofold relation which a '^middle term" bears to two other terms, provided, also, all the individuals denoted by this middle term are involved in one or the other of these two relationships. This specific condition is usually stated in the form, that the middle term must be distributed once at least. But it may also be given the formulation that a syllogism subsists (1) if there is a class 31 which is related by inclusion or by exclusion, partial or complete, to each of two other classes, S and P, so that there is the complex, S R M R P, and so that all the individuals of the class 31 are involved either in its relation to S or in its rela- tion to P. HSR 31 R P is the situation or state of affairs in which M is distributed once, then this complex implies the com- plex, or proposition, S R P. However, in endeavoring to dis- cover this implication in any specific case, we must observe the dictum de omni et nidlo; i.e., 8, the subject, and P, the predicate, must not be distributed in the conclusion unless they are dis- tributed in the complex, S R 31 R P, i.e., respectively in the major premise, 31 R P, and in the minor premise, S R 31. The syllogism consists in the implication of a proposition, 8 R P, as conclusion, by two propositions as premises. But, since every proposition implies its inverse, or converse, there THE CATEGORICAL SYLLOGISM 117 may be, as a major premise, either 31 R P, or P R M, and, as a miliar premise, either S R M, or M R S. The several combina- tions of these four propositional forms give what are technically called the four figures of the syllogism. Thus M R P, S R M, S R P,is the first figure ; P R M, 8 R M, 8 R P, the second figure ; 31 R P, M R 8, 8 R P, the third ; and P R 31, 31 R 8, 8 R P, the fourth. But further, since the relation, R, may be that of inclusion or of exclusion, partial or complete, between the two terms of each premise, there are the several so-called moods, which consist of a7iy two of the four kinds of propositions subsisting as pre- mises, and of any one of these four kinds subsisting as conclusion. These four kinds or types of propositions are: The universal affirmative, All x's are y's, A; the universal negative. No x's are y's, E; the particular affirmative. Some x's are y's, I; the par- ticular negative, Some x's are not y^s, 0. Universal propositions distribute their subjects, negative propositions their predicates, as do also exclusive propositions of the type, only x's are y's. Although the text-books on logic present a list of the several valid as distinct from the invalid moods of the four figures, such a presentation and the committing of it to memory are both quite superfluous, if only the following principles are observed in using the categorical syllogism : (1) The middle term must be dis- tributed at least once. (2) No term may be used distributively in the conclusion, if it is not distributed in the premise in which it occurs; it should not be so used for the simple reason, that it is not so implied; i.e., ''some" does not imply "all," nor does "some not" imply "none." (3) Two negative premises give no conclusion, for the exclusion of the whole or of part of two classes from the whole of the third class does not i)nply the exclusion of those two classes from each other; they may be so excluded, but, also, they may not. (4) The middle term must be the same in the two premises; or, stated negatively, one must guard against an apparent constancy in the meaning of the middle term, while, nevertheless, a change is introduced through the use of ambiguous words and phrases. This rule of procedure also applies both to the minor term, as it appears in the conclusion as subject, and also in that premise in which it 118 METHODS AND PROBLEMS OF METHOD occurs, namely, the minor premise, and to the major term, as it occurs as the predicate of the conclusion and in that premise which is made the major premise by its presence. Briefly, it is the same terms, 8 and P, that occur in the complex, 8 B M R P, and in the conclusion, 8 B P, that is implied by this. As illustrative of violations of these four rules, the following examples may be given : Illustrating false syllogisms in which the middle term is not distributed: — I Some symmetrical figures are triangles. A All rectangles are symmetrical figures. A Therefore all rectangles are triangles. Illustrating false syllogisms that employ two negative pre- mises : — E No true proposition is dependent on being proved. E No postulate of geometry is dependent on being proved. E Therefore no postulate of geometry is a true proposition. Illustrating false syllogisms in which the major term is dis- tributed in the conclusion, but not in the premise in which it occurs : — A All structures of living beings are " things " that evolve. E No mineral is a structure of living beings. E Therefore no mineral is a " thing " that evolves. Illustrating false syllogisms in which both the middle term and the major shift in meaning: — A All that perceives is mind. A The existence of objects consists in being perceived. A Therefore the existence of objects depends on mind. THE TRUTH OF PREMISES 119 CHAPTER XV THE TRUTH OF PREMISES I. THE REGRESS OF PREMISES In the process of reasoning by means of the categorical syl- logism, as well as by syllogisms of other types, one can distin- guish the formal correctness of the process from the "' material" truth of the premises and the conclusion. The reasoning process is formally correct, if, in the case of the categorical syllogism, it conforms to some one of the several situations determined by the principles just laid down. But formal correctness is not of itself a guarantee of material truth. However, leaving unde- termined at this point what the nature of "material truth" is, but distinguishing it only from "formal correctness," it is clear that there are the following types or variations of reasoning processes: (1) the syllogism formally correct, and also both premises and conclusion materially true; (2) the syllogism formally correct, but premises and conclusion materially false; (3) both the syllogism (?) formally incorrect, and the premises and conclusion materially false; (4) the syllogism ( ?) formally incorrect, but premises and conclusion materially true as proposi- tions, although not so related as to form a sj^llogism. The last three "variations" are both interesting and im- portant, yet it is with the first type that we are here most con- cerned. For the desideratum is, ivhen we reason by means of the categorical syllogism, that hoth our reasoning process should be formally correct, and our conclusion be materially true. The formal correctness of the reasoning process seems, how- ever, to be relatively easy to obtain, or to certify. To do this one need only observe the rules for correct formal reasoning, such as those rules that have just been presented for the cate- gorical syllogism. But a more difficult problem is that of making certain of the material truth of the propositions thati appear as premises, or as conclusion. Although, now, there are a number of different interpreta- tions, by the several philosophical positions, of the nature of 120 METHODS AND PROBLEMS OF METHOD truth, these can be neglected at this point, since no position fails to recognize truth {and error) in some sense. Accord- ingly, without defining truth, it may be said that, in the formally valid categorical syllogism, the conclusion is materially true, if the premises are materially true. But the premises are, like the conclusion, propositions. Accordingly, tlie prohlem of getting a materially true conclusioyi becomes that of getting two ma- terially true premises, and of again finding, if possible, tiva materially true premises that in turn imply each of these pre- mises. However, these "premises of premises" in turn "rest on" and presuppose others "still further back," and so on, indefimtely. What, then, is the outcome of this repeated pre- supposition of premises? Is there an infinite series of premises which it is quite impossible to complete, so that the best one can do is to plunge in mcdias res and boldly assert certain premises? This might be done either on the ground that, although not actually inferred deductively from others, these premises might, nevertheless, be materially true, or on the ground, that there is a "stopping place" where certain propositions imply, hut are not implied. But it may also be asked, if there are not other methods of establishing premises than by means of the cate- gorical syllogism, or, finally, if all three of these suggestions might not conform to fact? May not implication be limited in its range, so that certain propositions are (1) consistent with other propositions, but not implied by them, and, therefore, are (2) deductive "starting-places," and must, accordingly, be dis- covered non-deductively? To the answering of these inquiries we now turn. II. COMMON SENSE AND THE SOCIAL TRADITION The physiological transmission of structural and functional characters is not the only kind of heredity. There is also a psychological inheritance through imitation and by precepts, and the like, from all who have contributed to that whole social tradition in philosophy, religion, literature, art, science, and common sense into which each one of us is born. It is in this way that we obtain a mass of general knowledge to be used as premises from which to reason, as is illustrated by our common law, our system of morals, and our common sense. Such sur- THE TRUTH OF PREMISES 121 vivals are based on a method which in the main conforms to the canons of correct observation, analysis, and generalization. This method is, broadly speaking, induction, practised in- formally, uncritically, unconsciously, almost instinctively. III. INDUCTION ^ So long as men relied chiefly upon a tradition that vras rooted in uncritical observation and generalization, comparatively little ftiat was new was discoverable. Yet it was in this tradition that men lived until the realization came that the secrets of nature were beneath the surface, and that, if they were to be revealed, nature must be analyzed by a method more penetrating and more discriminating. The time came, first at spasmodic intervals, but later more continuously, when, by carefully con- ducted experiments, the aspects of nature were isolated and their relations to one another ascertained. At the same time it was fair and natural to suppose that there were otJicr, indeed, many other instances of these "things" that were thus exam- ined. But all of these instances could not be observed, e.g., either because they were too numerous or too remote, or because they were in the past or in the future. Yet the conviction was present, that nature was orderly, that it acted in accordance with law, that it had uniformity, and that the orderliness, the law, the uniformities were revealed by the few cases examined with care and by experiment. It was in this manner that, e.g., Galileo (1564-1642) discov- ered that the velocity of bodies falling to the earth increases with the time, — at that rate, namely, which is given by multi- plying the time-interval taken to fall a definite distance by this same time-interval, i.e., by the time squared. Galileo made his observations on bodies which he either let fall from different heights on the leaning tower of Pisa, or rolled down different distances on an inclined plane. From his observations, measure- ments, and analysis of these motions, in which he distinguished the distances, the times, the rates, and the change of rate, Galileo generalized. Thus he discovered the laws of all falling bodies. But he did not observe all. Too many bodies were ' The best complete discussion of induction is by B. Erdmann, Logik, 2nd ed., pp. 730 ti'.; cf. Venn, Principles of Inductive Logic, 1907, p. 344 ff., and J. S. Mill, System of Logic, 7th ed., Bks. III. and IV. 122 METHODS AND PROBLEMS OF METHOD falling elsewhere than in Pisa, too many, indeed, in Pisa itself, for him to do this; too many also had fallen before, and too many would fall after his day. It is in ways such as the method of Galileo illustrates, that the scientist proceeds in order to get laws, principles, and gen- eralizations that can subsequently be used as premises for making deductions, — such deductions, indeed, as enable men to control the forces of nature and to make predictions, computations, and plans that are realized in the concrete facts. One is not compelled, in all cases, therefore, to continue the search for premises indefinitely far hack. There is ultimately an appeal to concrete fact, and a basis for precise generalization. This procedure may be formulated as follows : — I. A certain number of typical, particular cases, c^, c,, Cg — Cq, such as the instances of the motion of falling bodies, are exam- ined, and are found to have a specific property, P, such as the property, that the velocity of a falling body is at any instant directly as the square of the time — typical cases being such as are taken at random. II. It is assumed, though not proved (since, e.g., all cases of the motion of falling bodies cannot be examined) that all C's are like the relatively few typical cases examined. This assumption is more justified if the cases are examined by scien- tific methods of analysis than if they are not. From I. and II. it is concluded, that III. All C's have the property, P. This principle and procedure are present in all induction, as this is used both in common sense and in science. Clearly, how- ever, there is an element of risk, of uncertainty in it. Are all diseases caused by micro-organisms? Science has shown that at least some are. Are atoms absolutely simple? Science used to maintain that they were, but does so no longer. In induction, then, a "leap" is made from "some" to "all," and this leap is hazardous. For, while "some" is included by "all," "all" is not implied by "some," as we have previously seen. IV. HOW FACTS ARE GIVEN Induction proceeds, first, by examining, in various ways, con- crete, particular facts that are, if possible, typical cases, and. THE TRUTH OF PREMISES 123 second, by generalizing from these. Science is built up in part in this way, as are also common sense and tradition, religion and philosophy, since each of these is characterized by at least the claim that facts are given which warrant a generalization from them. In a broad sense, then, all knowledge is inductive, ^ut ivJiat is a factf Concerning this important question there is disagreement, not only as regards what shall be accepted 05 fact, but also as regards the criteria, the tests, the methods by which a distinction is made between that which is accepted as fact and that which is not. We may, therefore, examine these two questions together, relying upon the actual procedure which we find adopted in different fields, both as to what are accepted as facts, and what as criteria. 1. Sense Experience In daily life and in scientific investigation we get at what in these fields are certainly regarded as one class of facts, namely, those that "come" to us through our senses. Vision, hearing, touch, smell, and taste and other modes of sensation are held to reveal facts to us, and, if there are occasional illu- sions, this fact is itself disclosed by the senses a7id by reasoning about those data which the senses give us. However, it is not necessary to go into many of the details of this familiar field. Things, qualities, events, and relations in the world round about us become known to us through our senses. For example, this red book and that brown one, the howling of the wind outside and the odor of this burning tobacco, the motion of the smoke as it curls upward and its height from the floor, — all these are, for me, facts as my senses now reveal them to me, as I sit in my laboratory. In our usual sense experience we do not go beyond this, although science and philosophy take us beyond, finally leading us even to doubt, e.g., that our real eye sees its own real image in a real mirror. For the process of sense perception has itself been made the subject of much study in both psychology and philosophy, one of the important typical problems here being whether, in perceiving, we get at the object directly, or have a mental state that is perceived and that copies the object, so that we perceive the object only indirectly. There are many other questions concerning sense perception, but common sense 124 METHODS AND PROBLEMS OF METHOD does not raise them. Rather, whatever may be the manner and the mechanism of perceiving through the senses, in common sense it is held that such perception gives us facts. A great part of scientific investigation, perhaps practically all of it in the field of the natural sciences, is based on the same assumption. The perception of the scientist is, however, dif- ferent in some respects from that of the layman, since his is a perception that is controlled and assisted by instruments of observation and of measurement. Telescopes and microscopes, and, indeed, a variety of machines and instruments enable the scientist to observe what the layman cannot, and technical methods of experimentation that are suggested by hypotheses and theories, reveal to the scientist realities which, without such methods, would remain hidden. Yet, however much the sci- entist's perception may be thus controlled and assisted, still, in the last resort, it is to his sense perception that facts are revealed, and upon its deliverances that the discovery of specific laws, principles, and generalizations is based. 2. Intuition, Feeling, and Emotion} Sense perception, however, is not limited to the disclosure of "things" that are not ourselves. For we perceive our own bodies through both vision and touch, and also through our muscular sensations and a whole group of organic sensations. But we also perceive, though not through the senses, that ive have sense percepts, memory, and reasoning processes, and the like, i.e., we perceive that we are conscious, in several specific ways. This is self-consciousness. We discover in this way, that we are also, at times, in certain specific moods, such as those of joy, sorrow, and expectancy. There is often, also, a feeling of the wholeness and unity of "things," even of the oneness of ourselves with nature, as opposed to the analytical and dis- criminating perception of common sense and science. Must it not be admitted, that such emotions and feelings also reveal facts? If we accept the evidence of those generalizations that con- ''Cf. E. Underbill, Mysticism, 4th od., 1912; F. Von Hiigel, TJxe Mystical Elements of Religion; A. B. Sharp, Mysticism, Its True Nature and Value, 1910; cf. also James, Varieties of Religious Experience, XVI. -XVII.; Bergson, all through Creative Evolution, Matter, and Memory, and Time and Free Will. THE TRUTH OF PREMISES 125 stitute a good part of traditional religious systems and beliefs, of moral ideals, of standards of art, and the like, then we can only answer this question affirmatively. Religion, morality, and art are based on the deliverances of certain specific emotions and modes of appreciation, and the facts thus given are often called values. Sometimes they are given only once in a lifetime, though more often they are repeated, and they come, also, to many individuals. But even in those eases in which it is not so much either the emotion, or the analytical perception of parts, as it is the in- tuition of wholes, that is to be emphasized, does not this intuition also give facts? For example, is not the whole space that the reader now perceives quite as much a fact as are its parts, i.e., hoth the smaller spaces, and the points, of which both whole and part are composed ? Is not a year as much a fact as a day, the ivhole motion of a stone as much a fact as the occupation of specific points at successive instants? Indeed, do not stone and motion and path and time together form one whole and unitary fact? And is not the similar fact sometimes experienced, of the unity of the self and all else, with no distinctness between the two? To each of these inquiries the answer "yes" is sometimes given, with certain definite scientific, philosophical, and religious positions resulting. But, while in science the whole is given a status which is equal, as fact and as value, to that of the parts, in philosophy a more extreme position is frequently taken. The whole is given a higher status, and the part is regarded as de- serving and winning a place 07ily in the whole. "With the whole thus "made" reality, the part is, also, frequently "made" only appearance, or, when analysis is regarded as serving only our practical needs, the part is allowed to be only an artefact. Thus it is that in religion and theology the whole is often identified with God, while all else is allowed to be but His manifestation. Self-consciousness, emotions, feelings, and intuitions, then, as well as sense perception, are accepted as ways and means by which facts are disclosed, and from which generalizations are made, thus to furnish premises for deductive procedure, and to cut off the indefinite regress of premises that seemingly would otherwise obtain. 126 METHODS AND PROBLEMS OF METHOD Memory is that specific conscious process hy or in which what has been experienced is now represented to us. We can remem- ber, with greater or less detail, that which has been experienced, and also, perhaps, the time and jylace of the experience. Much of that which is remembered is imaged in terms of some one of the senses, but some "things," as e.g., past emotions, are dif- ficult to image, although they can be remembered. However, the question that here concerns us is whether memory gives us facts from which to generalize. Obviously, by definition, facts that are remembered have been experienced before ; the memory is not the original experience of these facts. And yet we rely on it, and must do so, in order to secure the requisite basis for our generalizations. Without memory there would be no imngination, since this process depends upon the materials that memory furnishes. Ac: Qordingly, without memory, on the one hand, to represent the past, and, on the other hand, to furnish a basis for the presenta- tion of the future, our awareness of "things" would be limited to the immediate present (whatever, in the last analysis, this "present" may prove to be), so that, unless we could get at a sufficient nmyiber of concrete facts in the immediate present to furnish a basis for generalization, we could derive no general propositions to use as premises. Such propositions are ob- tained by comparing and analyzing a number of concrete cases, so as to discover, if possible, similarities, and then to generalize. But, it would seem, that if there were no memory, no com- parison would be possible, and, therefore, no similarities be discovered, and no generalizations be justified. Indeed, if we were organisms with an awareness of only the immediate present, we would not even have the tendency to generalize, and then we could neither think nor reason. But the fact is, that we do retain, do remember, and, on this basis, do compare and generalize. 4. Imagination Does imagination also give us facts, and furnish material for generalization? Imagination is that conscious process in which we are aware of at least some entities, or combinations of en- THE TRUTH OF PREMISES 127 titles, that have not been presented in the past. However, the materials for imagination to work with must have been given or be now given in some way, although the complex is new. Oftentimes, indeed, in fancy and creative imagination, the mode of the relating of formerly given parts is such that distinctly new qualities of the whole result. Such a creation is character- istic of those facts that are given to the imaginations of the painter, the architect, the sculptor, and the musician, and also, oftentimes, to those of the scientist and the philosopher. Turner imaging his sunsets, and Beethoven his symphonies, are cases in illustration, but Newton also must have reached out in imag- ination to discover gravitation, and Plato, to get to his Theory of Ideas. Imagination is to a large extent free ; it must accept its ma- terials, but with these once given, what restrictions can be placed upon it? For example, who would be so bold as to prescribe future accomplishments of miagination in art? Yet, free as it is, imagination gives us data, which are facts of some kind, and from which, especially in the development of re- ligion and art, generalizations are drawn that oftentimes become the dogmas for posterit3^ In some fields, therefore, imagination may act as freely as it will and can. Has imagination this freedom also in science, or must it in this field be kept within certain bounds by the exigencies of prediction, of explanation, of consistent systematization, and the like? Hypotheses, theories, laws, all play their part in science, but there are also threads of compulsion, either of im- plication or of consistency, that are not on the surface. Im- agination in science plays its part, therefore, by folloiving these threads as much as possible, until it is finally led to entities that, previously unknown, thereby become known. It is in this way that, e.g., gravitation, electro-magnetic waves, osmotic energ\% and, indeed, a very large number of the other entities of modern science have been discovered. These were, fir'st, mere hypo- thetical entities, with possibly feiv connections with observed facts. But, subsequently, deductions and predictions from them led to their confirmation. Imagination, having done its work, was subsequently supplanted by reason. In contrast with imagination in art, therefore, where it is, 128 METHODS AND PROBLEMS OF METHOD perhaps, free without limit, in science imagination must be controlled by the discovery of relations of implication, or, at least, by such relations as are prescribed by the exigencies of explanation, prediction, and system. Which example shall philosophy follow? Shall it be the example of art, in which imagination, by the freest play, leads to data that we appreciate and value, or the example of science, in which lue guard ourselves as much as possible from accepting anything as fact merely hecause we value it, and in which, seemingly, ''truth at all costs" is the chief concern. This question is perhaps one of the most fundamental philosophical problems. Both motives are present in contemporaneous phi- losophy, though usually in disguised form. The one motive would have philosophy an art, an appreciation, a personal reaction ; the other would have it a science.^ This concludes the consideration of one class of means by which premises for deductive use are obtained. Appeal is made to the concrete facts of sense perception, of emotion, of intuition, of memory, and of imagination. All facts, thus presented, can be represented in memory, and from typical cases, generaliza- tions be derived. These generalizations are of the type that such and such is the positive or negative "state of affairs" for such and such a class. This method of discovering general propositions and of putting an end to the indefinite series of premises is induction. Our next question is whether there are still other methods by which premises for deductive purposes can be found. As a matter of fact, in the history of science and philosophy, a number of such methods have been accepted as fulfilling this function. Thus certain geiieral propositions in such sciences as logic, mathematics, geometry, physics, and ethics have been held to he true either hecause they were self-evident, or hecause their opposites were inconceivable, or because they were presupposed by their aiicmpted denial. Indeed, in many cases, it is on these grounds tliat certain propositions have been regarded not only as factually, but also as necessarily true, and have, there- fore, been called axioms. Frequently, also, some of those prin- ciples which have been mo>it important as a basis for certain " Cf. W. T. Marvin, First Book of Metaphysics, Chap. I. THE TRUTH OF PREMISES 129 specific philosophical systems have heen established hy these tests. 5. Self -Evidence^ The principle of self-evidence may be stated briefly in the form of the proposition, that that which is self-evident is true, or is a fact. As applied, this means that some proposition or principle appears to be true ''on the face of it," or, that it does not need proof, or, indeed, that it is, perhaps, incapable both of proof and of disproof. Examples of propositions that have been regarded as self-evident, and, therefore, as ultimate and neces- sarily true, are: (1) the whole is greater than any of its parts; (2) every effect has a cause; (3) the cause equals the effect; (4) everything in its individuality is identical with itself and distinct from every other thing; (5) of two contradictory propositions, one must be true; (6) everything must act in accordance with its own nature; (7) we can know only our own ideas; (8) through a point, C, not on a straight line, D, there is only one line parallel to D. However, the position taken at the present day toward the test of self-evidence is, that it is not a criterion of absolute or necessary truth, but, at best, only an empirical test, which, though it may be used on occasion, is very liable to error. Indeed, the critical examination of, and perhaps the inductive generalization from, a large number of important historical instances of principles that have been regarded as absolutely true because of their self-evidence, but that are now known not to be true, or, at least, not necessarily true, demands this inter- pretation. On the other hand, the necessity of using self- evidence as an empirical criterion, which, though it is liable to error, nevertheless reveals a fair and perhaps high degree of probability, can also be shown. For example, that there is a rigorous logical connection of implication between the premises and the conclusion of a syllogism, is ultimately accepted only because of its self-evidence. For if we doubt any specific * The principle of self-evidence was used, e.g., by Euclid in arriving at his axioms, and by Aristotle in getting at the intrinsic properties of things. It was really recognized as a criterion by Descartes, in both his Meditations and his Discourse, and by Leibniz in his Meditationes de Vognitione, Veritate et Ideis. 130 METHODS AND PROBLEMS OF METHOD instance of syllogistic reasoning, and therefore test it for its validity by further reasoning, then we must accept the logical connection of the several steps in the final reasoning process, on the ground alone that they are self-evidently valid or correct. However, it is evident, perhaps self-evident, that a criterion of truth can be such a test provided only that it itself is true. As applied to the criterion of self -evidence this means that the question must be raised whether it is self-evident, that that which is self-evident is necessarily true. To the writer of this book it is 7iot. This alone suffices to show that self-evidence cannot be an unequivocal and absolutely certain test of truth, for here there is at least one exception. The principle of self- evidence is itself not self-evident to every one. It does not stand its own test. Then it cannot be a necessarily true and abso- lutely certain criterion. "We must conclude that self-evidence is only a psychological test of truth. What is self-evident to one is not to another. Therefore, so far as this test is accepted and used, as perhaps it must be in certain cases, there is always the proviso, that it is liable to error, and is not absolute. 6. The Inconceivability of the Opposite ^ Almost the entire characterization and criticism that has just been made of the criterion of self-evidence holds also of this second test or criterion. Historically, this test has been applied to many principles to which the test by self-evidence has also been applied, i.e., that which is self-evident has been further tested by attempting to conceive its opposite, and, with this attempt failing, has been regarded as necessarily true. This test may be stated, in the form of the proposition, that that ivhose opposite cannot he conceived must itself he conceived and he true, so that we cannot think without it, — if to think is to conceive. For example, if we cannot conceive that the part should be equal to, or be greater than the whole, it would be concluded hoth that it is necessarily true, and that we must think, that the part is less than the whole. Historically, this ' The principle of the inconceivability of the opposite was recognized, e.g., by Herbert Spencer, Principles of Psychology, §§420-437; cf. J. S. Mill, Logic, 8th ed., II., VII., 1-4. THE TRUTH OF PREMISES 131 proposition as regards the relation of whole and part was estab- lished as a principle in just this way — though it is now known to hold only for finite wholes. For infinite wholes the relation- ships of "less than," ''equal to," and "greater than" do not apply at all, or, more accurately, are not -present at all. As further examples, one may ask, if it can be conceived, (1) that a "thing" should be hoth itself and something else; and, accord- ingly, provided mind is different from matter, (2) that mind should act in contradiction to its own nature. Also, can one con- ceive, (3) that a thing should cease to be itself and become something else, i.e., that it should change; or (4) that two "things" should be related and not influence each other? If one cannot conceive these propositions, then must one not think the opposite of each 07ie of them, and conclude that this opposite is absolutely true? Such examples might be added to almost indefinitely, with the result that a list could be obtained which would include many a proposition or principle that has been of great influence on both philosophy and science. But the test of the inconceivability of the opposite proves, after all, to be, like self-evidence, only a psychological test. It cannot be absolute, since it has been applied to establish the truth of many a principle, in both science and philosophy, that subsequently has been shown to be false. Many an inconceivable "thing" has turned out to be quite conceivable; as, e.g., the propositions, that the earth is round; that a moving body con- tinues to move with no outside force acting on it; that, in a plane, there may be, through a point, more than one parallel to a line not containing that point. Therefore, some things at least that formerly were inconceivable are now no longer so. Also, that which is inconceivable to one mind is not to another. All this is evidence that this test does not reveal what must be conceived. Indeed, to the writer it is not inconceivable, that the proposition, that that whose opposite is inconceivable is true, should itself be false. The test does not establish itself, but, like self-evidence, reveals, not what all must think and conceive, but only what some must and do think — for psycho- logical reasons. It is a test that is, at best, only empirical and quite fallible, having been derived, in fact, by induction from 132 METHODS AND PROBLEMS OF METHOD certain positive eases for which it has seemed to work success- fully. But that which is inconceivable today, may nevertheless he true, and tomorrow be conceived, primarily because it is dis- covered to he a fact. 7. Presupposition hy Denial " This principle differs from the tests of self-evidence and the inconceivahility of the opposite in that it is a logical test, whereas they are psychological criteria. For to he presupposed is to he implied. Only if we take something to be presupposed which really is not, does the psychological factor enter, for then there is error. The principle of presupposition by denial is, however, closely connected with the test by ''the inconceivability of the oppo- site" and also with the "reductio ad ahsurdum." This latter test proceeds by first assuming the contradictory of that principle which is to be established, and by then finding that this con- tradictory is, in some way, absurd, so that the opposite, the original principle, must be accepted as necessarily true. But this raises the question as to what the absurd is. Is it that which is inconceivable, or, that which is ')>ot yet known, hut seems most improbable, or, that which is self-contradictory? The first two kinds of absurdity are, however, only psycho- logical, for, the absurd, thus defined, has oftentimes proved to be fact. To this extent the method of reductio ad ahsurdum turns out to be only a very fallible test. Wireless telegraphy, and automatic adding machines, and six-day trans-Atlantic steamships were at one time absurd and inconceivable, but they subsequently proved to be facts. However, when the absurd is identified with the self-contra- dictory, the reductio ad ahsurdum becomes the test of (or proof by) "presupposition by (attempted) denial." Within the field of seemingly self-contradictory "things" one can distinguish self-contradictory terms, such as round-square. But, as distinct from such terms, there are also self-contradictory propositions; " The best statement of the principle of presupposition by denial is by P. Coffey, Logic, 1!)12; ef. Jevons, Principles of Hcienee, 1874. This is also the principle of Kant's "deduction" of the categories; see Miiller's translation, p. 21 and p. 4. THE TRUTH OF PREMISES 133 such as the proposition, there are no propositions. This is self- contradictory, since it is itself a proposition. Terms as such do not imply, and so it may be, that, strictly speaking, there are no self-contradictory terms. Accordingly, a term that seems to be self -contradictory, such as round-square, may be a mere join- ing of symbols. But, if this is the case, then it can be proposi- tions alone that are true on the ground that they are presup- posed hy their own attempted denial, and by their contradic- tory. Such a denial is also an ahsurdity, in that it contradicts itself by presupposing the very "thing" that it denies. Fop example, the position of the skeptic, that there is no truth, is self-contradictory and absurd in that it is itself advanced as a truth, and so presupposes that there is some truth — to the extent, at least, of one truth. Therefore, the proposition there is truth, is one that is established by its own denial. Other examples of propositions which are established or proved in this manner are: (1) There is thinking; to deny this, is to think and, therefore, to presuppose that there is thinking; (2) there are propositions ; that there are not, is itself a proposi- tion; (3) the principle of excluded middle; to deny this, i.e., to assert that there is a third possibility between two contra- tradictories, presupposes that there is no third possibility be- tween the two contradictories of the universality of this princi- ple and some exceptions to it. But if there are certain propositions which are estal)lished by the principle of "presupposition by denial," it is important to determine by what test this principle is itself true. The necessity of putting the principle to some test is evident, since, if it itself is not true, it cannot be a (true) test for truth and fact, even when it is correctly applied. However, as at least a partial response to this just demand it can be shown, that, unlike the tests of self -evidence and the inconceivability of the opposite, this principle does apply to itself, i.e., that it is true by its own test. This demonstration can be made as follows, though in a manner that is, perhaps, of necessity somewhat involved. The question is, whether the principle that "that which is presupposed by its own denial" is itself presupposed by its own denial. If it is, then it is true by its own test. To give one proof, let us call this principle, A, and then deny that this prin- 134 METHODS AND PROBLEMS OF METHOD ciple is true, i.e., assert that it is false. The problem then is, Does this denial presuppose the principle in question, namely, that that which is presupposed by its own denial is true? The answer to this question is "yes," and the reasons for this answer are as follows: If the specific denial under consideration is true, it is true only on the ground of a specific principle, namely, one that concerns the relationship between a universal affirmative proposition, A, and a particular negative, 0. litis principle is, that if a particular negative, 0, is true, the corresponding uni- versal affirmative. A, must be false, and, conversely, that, if A is true, must be false. But this principle, holding between propositions A and 0, is the very principle that, in the instance under investigation, is identical with proposition A. That is, it is the principle, that the reason why a contradictory, either A or 0, must be true, if the other contradictory, or A respec- tively, is false, is, that a proposition is presupposed (implied) as true hy its denial (the contradictory). Therefore the denial of this proposition or principle itself, or the assertion of its con- tradictory, presupposes this very principle. In other words, this principle is itself presupposed by its own denial, and, therefore, applies to itself, or is true by its own test. The original principle thus confirms itself, and in this respect is different from the two criteria previously discussed. For this very reason it is to be regarded as a logical, and not a psychological criterion. Its norm is w^hat is "presupposed" or "implied," as against what is "evident" and what is exclusively "conceivable." The only psychological element that concerns it, has to do with the question whether or not it applies in a specific instance. But, if it does apply, it applies logically, — and not psychologically, as do the other two criteria. Yet it may be difficult to determine whether or not it does apply in a particular instance. For example, does it apply to that situa- tion which is asserted in pragmatism, namely, that there is no ahsolute truth, hut that all truth is relative, since it (all truth) is identical only with that which is adaptative, and works and bring satisfaction? The anti-pragmatist claims that this ivhole pragmatic theory of truth is advanced, not as a theory that is true by its own explicit definition of truth as fluctuating, but as one that is true absolutely, and, therefore, that absolute truth THE TRUTH OF PREMISES 135 is presupposed by its attempted denial in pragmatism^ The pragmatist can repudiate this accusation only by the counter claim of consistency, namely, that his pragmatic theory is itself true only pragmatically. Which party is correct in his claim? It is difficult to decide, since there is no criterion or standard of correctness by which to settle such a question between standards.* The difficulty in such an instance is, however, not in the principle (of presupposition by denial) itself, but in its applica- tion. But there are many cases in which the application of the principle is not so difficult, and the resultant demonstration of truth is entirely clear. For example, geometry is replete with such instances, as are also logic and the whole modern "theory of numbers." Some of these instances will be examined in subsequent chapters. In summary it may be said, that the principle of presupposi- tion hy denial is established by induction from those cases where it applies, and that it also confirms itself. No exception to it has been discovered in the realm of those instances to which it has been applied, nor has it been proved false as have the principles of "self-evidence" and the " inconceivahility of the opposite." Accordingly, both the principle itself and that phase of it which is the reductio ad ahsurdimi are to be accepted as extremely reliable logical criteria. '' E. g., by Royce, the Eternal and the Practical, Phil. Review, Vol. XIII., No. 2, 1904. ^ Consistency, it may be remarked, is open to two interpretations, the pragmatic and the anti-pragmatic. Common to both is the definition of consistency as freedom from contradiction. The pragmatist interprets this as expressing a certain need that we feel, which, when satisfied, is identical with one kind of truth. The anti-pragmatist interprets it absolutely, as a characteristic holding of an objective " state of affairs," especially of that one which characterizes that whole which is the universe. The universe of facts must be marked Vjy consistency. To the anti-pragmatist this is self-evident; its opposite is inconceivable. It is, indeed, presupposed hy its own denial. 136 METHODS AND PROBLEMS OF METHOD CHAPTER XVI THE NATURE OF CONTRADICTION The term contradiction has already been used in a number of discussions. Thus the "law of eontradietion," "contra- dictory terms," "contradictory propositions," and "self-contra- diction" have been referred to, or discussed. The more precise meaning of the term must now be determined. On the one hand, contradiction would seem to mean or to involve negation in some way, and in some sense. Yet, on the other hand, experience always has a content. ^'Something" is experienced. Indeed, it would seem to be impossible to experi- ence, and yet experience nothing. Must there not be, then, something positive when we experience negation and contradic- tion, and, if there is, ichat is this positive " something" f^ An answer to this question may be sought as follows : — Examples of contradictory terms are, red and not-red, one and not-one, moving and not-moving : of contradictory propositions, All even numbers are divisible by two, and. Some even numbers are not thus divisible; No energy can be destroyed or anni- hilated, and Some energy can be destroyed: of self -contra- dictory terms, round-square: of self-co)itradictory propositions, "Epimenides, being a Cretan, said, 'All Cretans are liars.'" Some of these examples and the states of affairs typified by them may now be examined and analyzed. Let us consider first the contradictory terms, red and not-red. It may be assumed that all know (to some degree) what is meant by red, and what red is, and also, that it is generally realized that the term denotes a certain specific group of colors, namely, the different kinds of red. There are many reds. But there are also not-reds, — perhaps, an infinite number of them, includ- ing not only all the other colors, hut also everything else that, like motion, space, time, mass, hardness, and electricity, is not a color at all. ^ Cf. Whitehead, Introduction to Mathematics, on the meaning of zero, Chaps. V. to VII.; also Russell, Principles of Mathematics, and Scientific Method in Philosophy (see his index) ; cf. also Bergson, Creative Evolu- tion, Chap. IV. THE NATURE OF CONTRADICTION 137 Now it is found to be a fact, that e.g., one and the same surface is not at the same time and in the same area both red and blue. It is either red, or some other color. Colors are, as a matter of fact, of such a character that they exclude one another from existing at exactly the same time and place. But a color and something not a color can coexist under these condi- tions. For example, a specific red and a specific degree of hard- ness can simultaneously be qualities of one and the same surface. In relation to a particular red, then, all other "things" are (formally) not this red, yet they are first experienced as quite as positive '"things" as is red itself. Not by themselves, there- fore, but only in relation to red are they negative entities. How- ever, among the not-red "things" there are tivo kinds; the one kind consists of other colors, and these are excluded from co- existing with red at the same time and place; the other kind consists of such "things" as hardness, extension, and motion, that are not so excluded. These other "things" and red can coexist in the same place and at the same time. It is the first kind of "thing," namely, the other colors, that is, therefore, the real contradictory of red, for only between other colors and red '■s there the specific exclusion. But even this exclusion sub- sists only under the specific conditions of the same time and place. For, under the other specific conditions either of dif- ferent times and the same place, or of the same time, and dif- ferent places, there can be both red and some other color. Contradiction in the case of terms is thus shown to be a rela- tion that is dependent upon, or that is identical with, exclusion. When and where there is genuine exclusion, there also is con- tradiction. But the exclusion is itself a positive relation between positives. Contradiction and negation are, therefore, only derivatives of this specific relation. For this exclusion to sub- sist there must be certain specific conditions. The two positive "things" that exclude each other must (1) belong to the same kind, i.e., to the same genus, as, e.g., do blue, red, green, and yellow, as colors. The positive "things" must be, to express the matter figuratively, like the arms of a lever, parts of the same complex entity. But, just as a lever must rest on a fulcrum, so also, in order to have a genuine contradiction or 138 METHODS AND PROBLEMS OF METHOD exclusion, there must be a "logical fulcrum." This fulcrum is given, in the instance of the entities just examined, by the specific conditions of the same place and the same time. The conditions on which a genuine contradiction subsists be- tween propositions are essentially the same as those for con- tradictory terms. In every case of contradictory propositions, one proposition is negative, at least in its "logical form." But a proposition is, as we have seen, a relational complex, and, although there are different types of propositions, all such com- plexes are identical with positive states of affairs. A negative proposition is, therefore, merely the fact of the exclusion of one positive state of affairs by another, but this relationship is itself positive. It may be that in discovering negative propositions, we first endeavor to discover the compatibility of one state of affairs with another, and, failing, formulate the result in a negative judgment. But this judgment, then, only expresses the positive fact of the exclusion. All this may be illustrated by an examination of one of our previous examples, namely, that which concerns the divisibility of even numbers by two. Let us grant that there is the objective state of affairs or proposition, "that all even numbers are divisi- ble by two," and also, that there is another state of affairs of "divisibility by two" only with a remainder. If this is the case, then there is also the state of affairs of the exclusion from all even numbers of "divisibility by two with a remainder." But this specific "state of affairs" is also a proposition, which one asserts in the form of the judgment, that it is false that some even numhers are not divisible by two. This last could itself be a proposition, provided only there were a consistent and implicative number system in which even numbers are divisible by two with a remainder. But, if this were the case, this would be a proposition in a distinct and different universe of dis- course from that in which even numbers are divisible by two, just as, e.g., the several postulates concerning parallels are in those distinct universes of discourse which are known respec- tively as the Euclidean, Lobatschewskian, and Riemannian geometries. The examination of further similar instances confirms our assertion, that the situation as regards contradictory proposi- THE NATURE OF CONTRADICTION 139 tions is the same in principle as it is in the case of contradictory terms. Such terms are positive facts or entities that exclude one another, but that, accordingly , in the case of physical ex- istents, are either in the same place at different times, or are at different places at the same time. In the case of propositions these conditions of place and time do not hold, but, instead, there are conditions which may perhaps best be called logical, and hy virtue of which contradictory propositions subsist in different universes of discourse. These different universes may, in analogy to different places, be called different logical loci. The problem of a proposition that is self-contradictory is per- haps more difficult than that of two propositions that are con- tradictory of each other, yet the solution of this problem is similar to that of the two preceding. Propositions, at least those which are identical with the relation of inclusion, complete or partial, positive or negative, between classes, have two op- posites, a contradictory and a contrary. Thus A and 0, and E and I are pairs of contradictory opposites; and A and E, I and 0, of contrary opposites, with the latter two called sub- contraries, as distinct from A and E as contraries. For example, as opposed to the proposition. Nothing is a proposition, there is the contradictory opposite. Some "things" are propositions, and also the contrary opposite. All "things" are propositions. The first of these is a self -contradictory proposition, and exemplifies the type. Self -contradictory propositions imply or presuppose their con- tradictory opposite. Thus, Nothing is a proposition, implies that So7ne "things" are propositions, since it itself is a proposition. Self-contradictory propositions are false for the reason that they do thus presuppose their contradictory. They are, therefore, one class of propositions that imply, showing that even so called false propositions have some status, and must subsist in some universe of discourse, namely, in one that is excluded from the universe of true propositions. But, further, in the case of the example under examination, whereas nothing is a proposition, implies that some "things" (at least one) are propositions, this last relational complex or proposition does not exclude, but is compatible with, the specific suhcontrary state of affairs, that some "things" are not propositions. These two ''states of af- 140 METHODS AND PROBLEMS OF METHOD fairs" can cosubsist even as red and extension, mass and motion, biological and moral situations can cosubsist. As an example of this we have, within the same universe of discourse both proposi- tions and the '' elements" or terms of these — some of which "ele- ment" are not propositions. From this examination of several instances of contradiction we reach the conclusion, that this relation is a specific one, and that it rests in every case upon the positive relation of exclusion between entities that are themselves positive and not negative in character. Contradiction is, then, not a law that is resident in the thinking process, as the psychologizing tendency in logic interprets it to be, nor is it an instrument invented unconsciously by the collective ingenuity of men of European stock; but it is an empirically discovered fact that is characteristic of many "things" in an empirically discovered world, and thinking must conform to it only because thinking must conform to "things," to facts. And that fact which, above ail, thinking must conform to, in order that it shall be correct thinking in regard to the principle of contradiction, is the fact of exclusion. One of the instances which might be used in our analysis is the very exclusion or prohibition of thinking certain corrollaries of the principle of contradiction to be false. For example, to attempt to think that two contradictories should both be true, or, that something should be both (1) excluded and (2) not excluded from a universe of discourse, presupposes, in form, the very principle of contradiction or of exclusion, and its cor- rollaries, and, in result, is precluded by this principle. In other words, the principle of contradiction is itself presupposed in the very form of the attempt to deny it. It therefore presupposes itself, or, it excludes its own contradictory. THE DISJUNCTIVE SYLLOGISM 141 CHAPTER XVII THE DISJUNCTIVE SYLLOGISM This method of proof need not long detain us. It is appro- priately introduced at this point because of its connection with exclusion and contradiction. A disjunction is an analysis, fol- lowing the objective facts, into distinct and mutually exclusive entities. These entities may be either terms, such as "verte- brate" and "invertebrate," or propositions, such as "all related terms are dependent on one another," and, "some related terms are independent of one another." The fundamental principle of the disjunction, to be observed in all cases, is, that it shoidd he complete. Since it is identical with exclusion, it is complete in fact. It therefore should also be complete in those judgments which aim to assert the facts. The disjunction is expressed as complete, if all the entities that are excluded by that entity which forms one member of the disjunction, are expressed or referred to in the judgment that formulates the disjunction. This completeness of reference can be obtained either by enumerating in positive form all the several entities that are excluded from one another, or by using contradictories, and, with the disjunction thus expressible in either positive or nega- tive form, these two forms can be converted into each other. As an example of these assertions we select the fact that a particular animal, say, a whale, is either a vertebrate or not a vertebrate, i.e., an invertebrate, and also the fact, that a whale is either an invertebrate or a mammal, bird, reptile, amphibian, or fish, for these five "orders" are the suh-classes of verte- brates. But, from the fact that a whale is not an invertebrate, it follows, that it is both a vertebrate and also either a mammal, bird, reptile, amphibian, or fish. And, by further exclusion, if the whale is not any one of these last four, it is a mammal. This example illlustrates the logical structure of the dis- juntive syllogism. The major premise asserts the exclusion — exhaustively, if possible. This is done either by using contra- dicforicr. whiih are always exhaustive, since there is no middle 142 METHODS AND PROBLEMS OF METHOD ground, or by enumerating all the positive possibilities that come under either one of the contradictories. The minor pre- mise consists in the assertion, either that one of the possibilities is an actuality, or, that it is not. If it is one possibility become actual, then, since by the law of identity a "thing" is itself and not something else, and, since by the law of contradiction it cannot be both itself and something else, there is the implication, that it is not any of the other possibilities; conversely, if there is evidence that a "thing" is not any one of a certain set of possibilities except one, it follows, that it is that one. This asser- tion or denial, in the minor premise, of one or the other of the terras of the disjunction in the major premise, follows the usual principle in logic and mathematics, that to negate a negative is to affirm. Thus, if the minor premise is of the form A is not not-B, where the major premise is of the form, A is either B or not-B, the conclusion is implied, that A is B. In constructing a disjunctive syllogism by the use of con- tradictories in the major premise, care must be taken, however, that the terms of the disjunction are such that, if an entity "belongs" to one of the two contradictories, it cannot belong to the other, i.e., is excluded from that other. The danger to be avoided is illustrated by the judgment that a line must he either finite or infinite. This judgment is false for the reason that a line can be hoth finite and infinite — finite in respect to smaller lines, as units of length, and infinite in respect to points. For certainly a line is "made up" of both smaller lines and points, and can, therefore, belong "at the same time" to the two dis- tinct universes of discourse that logically determine finiteness and infinity respectively. The genuine exclusion or contradic- tion in such a case subsists in the fact that as regards points a line cannot be both finite and infinite, and that, if it is the one, it is 7iot the other; also, that as regards smaller lines, it cannot be both finite and infinite, and that, if it is the one, it is not the other. The "material" truth of the conclusion of a disjunctive syl- logism depends, then, upon two conditions: first upon the fact of the complete and genuine disjunction or exclusion with which the major premise is identical, and, second, upon the fact, ex- pressed in the minor premise, that a certain "thing" either is T^E DISJUNCTIVE SYLLOGISM 143 or is not (identical with, or included in) one of the terms of this disjunction. Thus the two premises are "materially" true (1) if the disjunction subsists between genuine contradictories, and (2) if the "thing" under consideration belongs to the genus which conditions those contradictories. For example, a ''thing" must be either red or not-red, i.e., some other color, provided it belongs to the class of colored ''things." Also, in this instance, the major premise is true, if all positive colors are enumerated. In general, the major premise is correct, if all the positive sub-classes of the genus to which the "thing" belongs, are enumerated. However, to ascertain whether or not in any particular case the major premise is materially true in this sense is a problem for empirical investigation, and here our knowledge is always fallible. Evidently it is incumbent upon us in this connection to discover as many actual positive differences among "things" as we can, and to guard ourselves against inferring, from our failure to distinguish, the absence of objective distinctnesses. The minor premise of the disjunctive syllogism is to be estab- lished by any method which will show that the entity under investigation is included in, or excluded from, one or more of the entities involved in the disjunction of the major premise. While the disjunctive syllogism has a certain limited use by itself as a method of elimination, its chief value, however, con- sists in its union with the hypothetical syllogism to form the dilemma. As an illustration, let us assume, in accordance with our previous discussion,^ that there are only three possibilities as to the nature of logical principles and entities, namely, that they are all either (1) psychological, or (2) instrumental, or (3) objective. The establishment of any one of these, excludes the other two, or the disproof of any two establishes the third. This is disjunctive reasoning, pure and simple. But how disprove any of these possibilities? To do this one might show them to be (1) absurd in some sense, i.e., to be incon- ceivable or self-contradictory, or (2) false as a matter of fact, or (3) false because they involve consequences that are not facts. With any of these demonstrations successful for one possibility, the remaining possibilities would be inferable as true. But, ' Chap. XIII. 9M METHODS AND PROBLEMS OF METHOD in a process of this kind, we have a dilemma, or a trilemma, according as two or three possibilities are enumerated, and their consequences developed. This method should, accordingly, be presented in some further detail, with a preliminary presenta- tion of the hypothetical syllogism, which is a constituent of every dilemma. CHAPTER XVIII THE HYPOTHETICAL SYLLOGISM The hypothetical and disjunctive syllogisms and the dilemma, while they are methods of establishing conclusions, do not put an end to the indefinite regress of premises any more than does the categorical syllogism, for their conclusions are materially true only provided their premises are materially true. These premises can in many instances be established by deductions from other premises, but ultimately an appeal to some other method of establishment must be made. This has just been seen to be the case with the disjunctive syllogism. To establish the major and minor premises of this syllogism there must in most instances be an appeal to fact; i.e., by some analytical method one must discover differences among ''things" in order, first, to set up the disjunction, and, second, to include or not include the entity under examination in, or to identify or not identify it with, some one or more of the distinct entities that are asserted by the major premise. As a matter of fact, however, all establishment of our judg- ments is hypothetical or conditioned. This mmt he the case:, in the absence both of any one absolute test of truth and of the means for the certain application of such tests as we do have. All deductive proof, all induction, all self-evidence, all "con- ceivahility," and all proof through "presupposition by denial" lack absoluteness both in themselves and in their application. Therefore, even these methods and tests are, in this respect, hypothetical in character. THE HYPOTHETICAL SYLLOGISM 145 However, although we have no test or method by which to insure the absolute correctness either of our tests or our methods, or of their application, and also no means by which to make ourselves absolutely certain of the material truth of our pre- mises, nevertheless, in both cases, a high degree of probability is attainable in a great many instances. Indeed there is an immense body of knowledge that is true in this sense, and there are methods of establishment and of proof that have the same standing. Thus, a high degree of probable truth characterizes our knowledge of a great many (1) "things," qualities, and events, and also (2) of the connections and relations in and among these entities. One kind of knowledge is, however, almost exclusively, if, indeed, it is not, in some cases, wholly a knowledge of connec- tions. Such knowledge is found, e.g., in pure mathematics and in logic. This means that e.g., in mathematics we freely assume or select various differing sets of propositions, and then proceed to discover their implications. The assumed propositions, pro- vided they give an implicative system, must be facts in some sense, though they need not be existent facts. An illustration of such knowledge is presented by the follow- ing example from the field of geometry: Let it be assumed (1) that the spatial universe is bounded by a spherical film and (2) that all "things," including human beings, change in size in inverse ratio to their distance from the center of such a sphere. Then it follows from or is implied by these two assumptions, that if the boundary of the sphere were ap- proached, it would continue to seem to be as tremendously, even as infinitely distant as it would from near the center. For, although there would be "a smaller and smaller distance to go," nevertheless, as the boundary was approached, a human being and all his means of measurement would approach zero in size. Accordingly, the distance ever still remaining to be covered, would continue to seem quite as great, in relation to any ^mit of measurement, as it now seems to be from our own terrestrial center, and with our bodies of five cubits stature.^ Who can prove that all this is not the case? For, are not * This Non-Euclidean world is described by Poincar6, Science and Bypotheals, trans, by Q. B. Halsted. p. 49 ff. 146 METHODS AND PROBLEMS OF METHOD size and distance wholly relative? But, if all "things" were changing size in the same ratio, could we ever become aware of this from observation? Then is not the above hypothesis one that cannot be disproved, although, also, it cannot be shown to state the existent fact? Yet one can make the hypothesis, and deduce from it, i.e., discover its implications. If we do this, we are introduced, however, to a world and a space which are not described by that Euclidean geometry which we learned in our school-days, but by that other geometry, namely, the Lobatschewskian, in which parallel lines meet at the boundary of a sphere, and the sum of the angles of a plane triangle is less than two right angles. It is to be carefully noted, however, that in this example it is not asserted, that either the original hypothesis or its conse- quences portray the actual state of affairs in the space in which we live. Indeed, there are reasons, due to the grossness of measurement, why neither the hypothesis nor its consequences can be either shown or not shown to accord with this space. Yet if the original hypothesis could be established for our space, say, by measurement or experimentation, then would the conse- quences which have been stated be the fact about our space, provided those consequences as stated are really implied by the hypothesis. Although, now, in this example, the hypothesis can be neither affirmed nor denied to be the existent fact, and although there are any number of similar hypotheses, there are, also, an ex- tremely large 7iumher of propositions, which, as hypotheses for certain consequences, ca^i he affirmed to be existent facts with, a high degree of probability. In fact, propositions of this kind make up the greater part of all the natural sciences. But, with the hypotheses asserted to be existent facts, the consequences likewise are so asserted. It is in this way that science becomes systematic. Connections of various kinds between states of af- fairs are discovered and asserted in hypothetical propositions. Thus, to illustrate, we find that if the moon moves around the earth in a certain path, there will be a solar eclipse. But we discover that the moon does so move, and we affirm the ante- cedent — the hypothesis. But therewith, also, we affirm the con- sequent, namely, the occurrence of the eclipse. THE HYPOTHETICAL SYLLOGISM 147 This example illustrates the structure of the hypothetical syl- logism. In general, this method of reasoning and of establishing conclusions consists of a major premise which is the assertion of a connection between two proposition^, an antecedent and a consequent, in the typical abstract form, if a is h, c is d. By the orthodox rules, the minor premise must be either the affirma- tion of the antecedent, or the denial of the consequent. Af- firmation of the antecedent carries with it the affirmation of the consequent : denial of the consequent, the denial of the ante- cedent. But, denial of the antecedent is usually maintained not to necessitate the denial of the consequent, nor affirmation of the consequent, the affirmation of the antecedent, — for there may be other conditions for the consequent than the particular antecedent stated. These rules are held to apply to all cases. Undoubtedly, however, there are some connections between certain antecedents and consequents so precise and unequivocal that the limitations stated by these rules do not hold, so that denial of the antecedent does necessitate denial of the consequent, and affirmation of the consequent, affirmation of the antecedent. In illustration, this may be said to be the case with the con- nection asserted by the premise, if one atom of hydrogen and two atoms of oxygen combine, water is formed. However, these unequivocal connections do not seem to be universal. For ex- ample, if electricity passes through a copper wire, heat is gen- erated. But from the fact of heat somewhere, we cannot infer the presence of electricity in a conductor. The rules for the hypothetical syllogism can only be so formulated, therefore, as to cover all cases with certainty. This is done by the rule which demands that we must "either affirm the antecedent, or deny the consequent." Our discussion will have made it clear that there is a funda- mental difference between merely asserting a connection of im- plication between two propositions, and asserting the existential character of the antecedent, or denying that of the consequent, i.e., to assert that if a is h, c is d, and if c is d, e is f, and so on, is quite different from asserting that a is h. This difference is most important. Wherever we can discover connections and yet are not able to assert antecedents or deny consequents, we can nevertheless discover whole systems of con- 148 METHODS AND PROBLEMS OF METHOD sistent and implicatively connected propositions which, for this very reason, and in this very sense, are facts. This method offers a means of discovering entities that are not limited to the field of existents. In other vs^ords, it is possible rationally to discover entities and states of affairs that are con- trary to existent fact, or that do not exist, i.e., we can discover what would be the state of affairs, if certain "things" did not exist, indeed, if nothing existed, — defining an existent as that which is correlated either with a specific part of space and a specific part of time (physical existents), or with a specific time alone (mental existents). Such entities — that do not exist, but that are, nevertheless, discovered to be facts by developing consistent systems of propositions, are called suhsistents.^ Indeed, all propositions that concern existents may ultimately presuppose propositions that concern suhsistents. For example, propositions concerning matter and conscious processes presup- pose certain related states of affairs concerning space and time and numher. But space and time and number, though facts, are discovered to be, not existents, but subsistents. This dis- covery agrees with the scientific point of view that these entities are peculiar "things" that concern infinity, endlessness, con- tinuity, and the like, and that are studied, not by physical ex- perimentation, but, independently thereof, by the rationalizing methods of thought and reason.' CHAPTER XIX THE DILEMMA The dilemma is usually defined in the text-books as a syl- logism in which the major premise consists of a disjunction between two hypothetical propositions, the minor premise, of ya disjunction between two categorical propositions, and the con- " See Chaps. XLI., XLIV. " iScientilie proof of this distinction is found in the fact, e.g., that nowhere in the implicative ayatcra of any kind of geometry are such entities as mass, momentum, and the like — entities usually identified with matter and existence — found to be implied. Space is thus demonstrated to be independent of that ivhich exists, and, in this sense, to be a sub- sistent. THE DILEMMA 149 elusion, of a disjunction between either the antecedents or the consequents of the major premise. To illustrate, we may assert as a major premise, that, "If education is popular, compulsion is unnecessary; if unpopular, compulsion will not be tolerated"; and as a minor, that "education is either popular or unpop- ular"; the conclusion is implied, that compulsion either is unnecessary, or will not be tolerated. This example is a constructive dilemma, because a disjunction between the antecedents of the two hypothetical propositions of the major premise is asserted as a minor premise. On the other hand, where a disjunction between the de^iials of the two con- sequents is asserted, the dilemma is called destructive. In either case, of course, either the antecedents or the consequents may themselves be negative in meaning, as is the case with one antecedent and the two consequents in the example just given, and the rule then holds, that the denial (in the minor premise) of a negative is an affirmation. The technical rules for the dilemma are those of its constitu- ents. The consequent must genuinely depend in some way on the antecedent, and the disjunction must be complete. This it is, if it subsists between contradictories, or if, in the case of contraries, all the possibilities are recognized and stated. The minor premise must be a disjunction either between antecedents asserted or consequents denied. For our purposes, however, the dilemma may be advan- tageously defined more broadly as that method of establishing a position, or of showing the necessity of accepting a proposi- tion, by demonstrating that the opposed position or positions lead to consequences that cannot be accepted for the reason either that they are not facts, or that they are absurd, or incon- ceivable, and the like. This may be illustrated by an example, which, though not materially correct in every way, shows the form of this method of reasoning. Let us first assert the disjunctive proposition, that we must either tax ourselves or tax other nations, in order to support our own government, and then show the necessity of accepting the first alternative by developing the consequences of the second, to find that they are not acceptable. This is done as follows: First, the hypothetical judgment is asserted, that, if we tax 150 METHODS AND PROBLEMS OF METHOD other nations, we must do this cither by force or by beggary. If, now, we can show that this consequent must be denied, then its antecedent must also be denied, and, accordingly, the alterna- tive, that of taxing ourselves, be accepted. But this consequent (forcing or begging other nations to pay our taxes) must he denied because of its consequences — i.e., the dilemma in which it places us. For, if we force others to pay our taxes, then we are a pirate nation, while if we ne^ others to pay our taxes, we are a pauper nation. But the taxing of others, asserted by our opponent, means either the forcing of others or the begging of others to pay our taxes, in order to support our government. Therefore it means either that we are a pirate nation, or a pauper nation, — a choice that we cannot, in all conscience, accept. Therefore, with this disjunctive conclusion thus denied, or not accepted, its antecedent, namely, that we force or beg other nations to pay our taxes, is also denied, as is in turn its ante- cedent, and, therewith, the alternative, that we must tax our- selves, is asserted. This example, however, involves a material fallacy in the fact, both that it ignores the real point at issue concerning the nature of import duties, namely, the question, whether direct or in- direct taxation is most advantageous, and, also, that it finally identifies the method of indirect taxation by import duties with taxing other nations. However, this material fallacy does not affect the logical form of the argument. I This method of establishing propositions by the dilemma is used very frequently in philosophy, both in getting at basic positions and in arriving at details. In certain cases it is used in connection with the reductio ad absurdum ^ and the principle of "presupposition by denial." To give an illustration, — and one, also, that is of importance for some of our future discus- sions — let us examine the question as to whether the "^latural numbers" are dependent on counting, in order to show that they are not. Here we shall show that the proposition, that the natural numbers are not dependent on counting, can be demon- strated by the fact that the opposed position reduces to on absurdity; it presupposes its contradictory. ^ Aristotle recognized the reductio ad absurdum, Anal. Prior, 1, v. THE DILEMMA 151 There is the major premise, that, if numbers depend on counting, then "1," as that natural number which has no predecessor, became a fact with the first act of counting; while, if numbers are not so dependent, then "1" was not made a fact by the first act of counting. But there is the minor premise, either that numbers are thus dependent on counting or that they are not. The conclusion follows, either that "1" became a fact with the first act of counting, or that it did not so become. Let us next examine the consequences of the first of the two alternatives stated by this disjunctive conclusion. To do this, let us assume that "1" ivas made a fact hy the first act of count- ing. Now counting is an act, and an act requires time, and begins and ends. Then a time is implied, before this first act of counting took place, when there was no counting. In other words, the time period when there was 7io counting precedes the time period when the first act of counting took place. Therefore this time period — of the first act of counting — cannot be in correlation with the natural number "1" defined as the only natural number that has no predecessor, but must be in correla- tion with, at least, the nattiral number "2," which has a prede- cessor, namely "1." Therefore ''1" does not depend on counting. Our dilemma, therefore, leads to a conclusion consisting of a disjunction between contrary opposite propositions, one of which, namely, that "1" depends on counting, reduces to an absurdity in that it presupposes its opposite, namely, that "1" does not depend on counting. But this opposite is the denial of the consequent in one of the hypothetical alterna- tives of the major premise of the dilemma. Therewith, how- ever, the antecedent of this consequent is denied, and the opposite proposition, that numbers are not dependent on count- ing, asserted. By quite similar arguments — differing only in ''matter," but not in form — one can demonstrate that the natural numbers do not depend on consciousness or knowing in any form, nor on physical things, nor on space, nor even on time.- All these entities are numerical in several ways, but the natural numbers = See Chaps. XLIII., vii.-x., and Chap. XLIV. 152 METHODS AND PROBLEMS OF METHOD themselves are facts that are quite independent of these other entities. This is an important conclusion, — given here in illustration — since upon the principle which it involves there depends one of the greatest philosophical systems of history, the Platonic, with its acceptance of the reality of universals, of abstractions, and of ideals as independent of the concrete, particular ''things" of the physical and mental world. It is, indeed, by the principle just illustrated that such ideals as justice can be proved to be real although they are never realized in a world of human beings that exist in space and time.^ CHAPTER XX ANALOGY Eeasoning by analogy is a method that is frequently used in philosophy. For example, in a great many systems the entire universe is regarded as being like a living organism, and there- fore as having a unity in the midst of its manifoldness, even as the parts of a plant or an animal, especially a highly organized one, influence one another and function together to make one living being. The same analogy is also frequently used to demonstrate, further, that the universe is immanently purpose- ful or teleological. Carried to its consistent outcome, this rea- soning leads to the conclusion, that the universe is, indeed, an organism that manifests, perhaps, all the characteristics of life.^ Indeed, if one finds that it is between the universe and higher organisms, such as ourselves, that the analogy holds, then the conclusion is reached, that this all-inclusive living being, the universe, is conscious in all that this may mean, in fact that it may be self-conscious, have memory, purposes, and aims, and even a moral consciousness, and, indeed, be a person and a self.^ » See Chap. XLV. ' E.g., by Paulsen in his Introduction to Philosophy, and by Bergson in Creative Evolution. ' The position of most modern objective idealists; cf. Chaps. XXXIV.- xxxvm. ANALOGY 153 Another example of an analogy that is frequently used in constructing philosophical positions is the argument from the similarity of the universe to a man-made mechanism or machine. Such a mechanism reveals a delicate and nice adjustment and working-together of parts in order to bring about a certain result and thus accomplish a certain purpose. But this adjust- ment is brought about by a mechanician and contriver. By analogy, it is argued that in nature there are discoverable con- trivances and mechanisms which are even more exquisite and more beautifully adaptative and purposeful as, e.g., the eye, the heart, and, indeed, even the v\^hole universe itself. Accord- ingly it is inferred that for the universe there is also a maker and a purposer. This conclusion is reached in this way by those who accept an external teleology as a position that means a mechanistic view of the physical and even the psychical uni- verse, and the theistic view that there is a Deity, who, as in some sense outside the universe, is its mechanist, its designer, or its architect, if not its absolute creator.^ The logical structure of the argument by analogy becomes clear through these examples. Given two "things," as, e.g., the eye and a watch, that are similar in certain respects, namely, in the mutual adjustment of structures and the functioning- together of parts, then are they not similar in further respects, e.g., that the eye, like the watch, has a maker and a purposer? By analogy one concludes that this is the fact. Stated formally this method of establishing premises is as follows: Certain entities. A, B, and C, are similar in respect to the characteristics, x and y; but A and B are characterized also by z; therefore C is also characterized by z. Clearly the presupposition of this argument is the principle, that whatever is similar in certain respects is also similar in others. But it requires only the statement of this presupposi- tion to make the fact equally clear, that partial similarity does not of necessity carry with it further, much less, complete similarity. In certain instances such further similarity is found ; in other instances it is not. The most that we are justi- fied in concluding, is, therefore, that if there is some similarity, there may be more. That it is even highly prohaMe that there ' Cf. Chaps. VI. and VII. 154. METHODS AND PROBLEMS OF METHOD is more, can be justifiably asserted provided only that analogy ceases to be analogy, and becomes induction. Given two typical and random instances, A and B, with each characterized by an X, but with X, e.g., causally or functionally connected with y in these cases; then, if other entities, C, D, E, etc., are char- acterized by X, they are also, with a high degree of probability, characterized by y. The crucial problem, therefore, in employing the argument by analogy is that of ascertaining whether or not further similarity really holds or not. But if it does, there is some other reason than analogy for it so doing. It is by virtue of the fact that the sev- eral cases are instances of a law, a principle, a type, or a class, that similarity in respect to certain characteristics carries with it similarity in respect to others. Thus there is a resemblance in many respects between the rocks as we find them often in extremely distinct strata, and the layers of material that are deposited by the waters of the earth's surface today. Does the resemblance go further? The geologist advances the inductive theory that it does, but finds in these two sets of phenomena the results of the action of a common cause. Even as the sedi- ments are to be observed today in a process of stratification, so were the stratified rocks slowly deposited in past ages, gradually to harden through the addition of other materials. Can we discover by a similar procedure such features of the universe as will give inductive proof that it belongs to the type, organism, or to the type, machine? If we cannot, then to infer on the basis of analogy that the universe is an organism, or a machine, is extremely hazardous. In general we may conclude, that, if reasoning by analogy is valid, then, paradoxically, this validity rests on some further, non-analogical basis. At best analogy can serve only as a basis for the suggestion that there is a certain range of possibilities within which to investigate. Thus the universe may be an organism, or it may be a machine; hut it may he neither. On the basis of analogy one should neither accept nor reject these possibilities, but should hold his judgment in suspense regarding them until evidence and proof from ether sources are at hand to justify a highly probable conclusion one way or the other. FURTHER IMPLICATIVE SITUATIONS 155 III. ANALYSIS AND THE NEW LOGIC CHAPTER XXI FURTHER IMPLICATIVE SITUATIONS AND NEW METHODS OF ESTABLISHING PREMISES The discussion of the dilemma and of analogy completes the presentation of those tests and methods that are used in ordinary discourse and argumentation in order to establish premises and furnish proof. But such tests and methods, even if they are not discredited, as is, e.g., the test by self-evidence, are inade- quate to deal with all the problems and situations that the universe presents to the inquiring mind. The tests and methods that we have been considering are those that, for the most part, directly constitute the logic of the tradition. This traditional logic is, as we have seen, the doctrine that emanated from Aristotle, and is essentially a logic of classes. As a logic of classes it is, as we have also seen,^ based on the physical thing as that model in analogy to which all entities are conceived of and thought about. Accordingly the principles that form the chief characteristics of this traditional doctrine are: (1) the relations of similarity and of difference, of "member of," of additiveness, of inclusion, complete, partial, and negative, of causation, of inherence, of identity, and of con- tradiction; (2) the subsistence, by virtue of the first four rela- tions, of classes (which are either included in or excluded from other classes completely or partially) ; (3) the principle of iden- tity as applying to each individual and to each class ; (4) causa- tion as holding between individuals, and (5) inherence as holding between the qualities and their sul) stratum, and finally (6) the propositions that are constituted by any of these relations, — in their function of relating terms. This traditional Aristotelian logic has controlled the ma- jority of the great historical systems of philosophy, and domi- nates much philosophy even at the present time. Indeed it ^ Chaps. I.-III. 156 METHODS AND PROBLEMS OF METHOD exercises its influence even on some philosophers who endeavor to criticize both it and the systems that are built upon it.- However, in mathematics and in other fields of research in which appeal is made to fact, and not to authority and tradi- tion, modern investigation has shown that the logic of classes is not the only logic, and that the situations described by it are not the only ones in which the relation of ijnplication is present. By way of sharply contrasting the two logics one may say that, if the logic of the Greek and Medijeval period was, with few exceptions, one of classes, the logic of modern exact science is one of series. In such isolated instances as the geometry of Euclid, the mechanics of Archimedes, and the astronomical theories of Aristarchus, Hipparchus, and Ptolemy, situations were recognized in which series and their logic are present. But this logic received no formulation either from Aristotle or from his successors in that tradition to which he was the chief con- tributor. Indeed, not until the Archimedean spirit of an appeal to nature was revived by such pioneers as Leonardo and Galileo, and continued by the host of their noble successors, was there opportunity for a break with the tradition and the use of the logic of series. Galileo ^ sounded the trumpet call for the coming advance when, with the insight of genius, he showed by experiment that uniformly changing velocity, i.e., acceleration, ife in a functional relaiion to the time series. In such a rela- tionship there is present much of that logic which received at least partial formulation in the Calculus of Newton and of Leibniz, and which has received its more complete statement in the recent work of such men as Cantor, Dedekind, Peano, Eussell, and Royce.* The present knowledge of this modern logic makes it quite clear that the Aristotelian doctrine wholly omits the formula- tion of certain logical principles that subsist in certain situa- tions. These principles are found where there are series. A series is an ordered class of individuals, in which each individual * See the modification and the underlying-reality theories of relations, Chap. XXVI., and the whole of Section 1 of Part II. • Galileo (Jaliloi, Dialogues, ed. by A. de Salvio, trans, by H. Crew, 1914; cf. Mach, Science of Mechanics, on Galileo. *See references for Chaps. I. -111., XXVII., XLI.-XLIV. FURTHER IMPLICATIVE SITUATIONS 157 has a specific "position" in relation to the position of all the other individuals of the series. The Aristotelian logic is wholly- incapable of dealing with such entities (series), since it recog- nizes no principle of order other than that of the positive or negative inclusion of one class in another. It accordingly is identical with the (tacit) assumption that individuals or parts are, in most cases, related only additively to constitute a whole, and is, therefore, incapable of logically accounting for a whole that has properties different from those of the parts, as, e.g., has a chemical compound in contrast with its elements, and a living being in contrast with the chemical and physical forces of which it is composed. For, parts added, i.e., related addi- tively, give only a swm, i.e., a whole which has properties like those of the parts. In contrast with the traditional doctrine, the new logic recog- nizes, therefore, the principle, that a whole may consist of tivo or more kinds of parts, and that the individuals of some of these kinds tnust be related non-additively in order to constitute the whole. Such a non-additive relation is asymmetrical, and is present in every series. But, further, the Aristotelian logic is also wholly ignorant of the functional relationship, which plays such a dominant role in modern exact science. Yet that it must be thus ignorant is to be seen from the fact that it excludes series, and a function is a correlation between scries. Accordingly the traditional logic omits the use of the principle, that two entities can be related and yet be independent.^ This principle is typified in the character of that relation which subsists between the two variables (series) of a function. The Aristotelian logic accepts and insists on the opposed principle, that all relatedness carries with it the mutual causal modification of the related entities. Finally, the traditional logic omits the principle, that a rela- tion itself unites, in some specific way, the entities related, so that a substance or substratum is not needed to hold these entities together and to mediate the relation. Indeed, modern logic centers very largely on the concept of relations, and the Aristotelian logic, in contrast, on the concepts of substance and ' Sep Chap XXVI.. n., 1. 158 METHODS AND PROBLEMS OF METHOD causation. This it must do, since its model is interacting physical things, with a physical thing defined as a group of qualities that inhere in a core-like substance.*^ CHAPTER XXII ANALYSIS The methods of the new logic are both analytical and syn- thetical. To analyze is to discover parts — in or of a whole, — and also the character of the relations between the parts, but, with this accomplished, there is also synthesis. For the pre- liminary to the synthesizing of parts experimentally is, after discovering the parts, to find how to put thera together. But, if experiment is impossible in certain cases, then, with the discovery of parts and the specific character of their relatedness, there already is synthesis. This second method is analysis and synthesis in situ. We start with a whole, and in it discover parts ; but the parts are left undisturhed; still we discover that, related in a certain way, they give the whole "back again." It is this method of analysis and synthesis in situ that is used in mathematics, geometry, and to a large extent also in mathe- matical physics, chemistry, and many other sciences. But it is an important characteristic of this method, that it is not only an analysis and a synthesis in situ, but also a means whereby one discovers facts hy implication and hy type rather than by the specification of each particular indivitlual.^ Such a procedure may be illustrated by the example of that analysis of space which is made by geometers at the present time. In giving this example, some of the teims may be left undefined, since they will be readily understood in essentially their correct sense. The space in which we perceive physical entities is found to e See Chap. III. ^ Cf. my " Defense of Analysis " in The 'New Realism, and the article by H. T. Costello, "A Neo-realistic Theory of Analysis," in the Jour, of Phil., Psych., and Scientific Methods, Vol. X., p. 494 ff. ANALYSIS 159 consist of three dimensions, with each at right angles to the other two. Each of these dimensions is itself a straight line with no breadth or thickness, and thus quite unlike the pencil or crayon line by which it can be represented. But while this analysis of space is being made, these three dimensions are left in situ, since we cannot experimentally separate them. Further, any one finite line is of definite length in relation to some unit of measurement, and, therefore, can be analyzed into smaller lines, even as a foot is analyzable into twelve inches. Each such smaller line, however, is in turn analyzable into still smaller lines. Let this analysis, now, be continued and repeated up to that point beyond which our instruments of measurement do not take us, and it will be then discovered that the analysis can be "ideally" continued. This realization is accompanied by the further discovery that tliere is a limit which the smaller and smaller lines approach but do not reach, and that this limit is a point. Such a point, as the limit, has no length, no breadth, and no thickness. We cannot see or touch it, indeed, in some cases we cannot even specifically name it. Yet, hy discovering implications, we find that there are such points, in fact, a whole class of them. This is knowledge hy type, and not by specifi- cation. But the analysis further reveals both the character of the relation between these points and their numher. The relation is of the same type as is that relation which subsists between the positive integers, 1, 2, 3, 4, 5, 6, n — 1, n, n -\- 1, i.e., it is asymmetrical and tramitive. This means that, if the symbol < stands for the relationship of "precedes," then, e.g., 4 < 5, but not 5 < 4; i.e., the relation is asymmetrical ; also, that, if, 4 < 5 and 5 < G, then 4 < 6; i.e., the relation is transitive, or "goes across" from 4 to 6. This means that, like the positive integers, the points of a line form a series, or that the line is a series of points. Further, the number of points is infinite in the sense that any finite part of a finite line contains as many points aa the whole line does, — a discovery that is made by finding that, in respect to points, the whole line is in one-one correspondence with a proper part of itself, a "proper part" being defined as a part that is like tho whole, i.e., that is itself a line. Again, in this respect iho lino ir-. like the series of positive integers, 160 METHODS AND PROBLEMS OF METHOD since, in this series, there are as many even integers as there are odd and even. In other words, the whole series is in one-one correspondence with a proper part of itself, namely, with the even integers, as it is, also, with the odd integers. The example just given is illustrative of a type of whole that has furnished philosophy and science with many difficult prob- lems from the time of earliest Greek thought to the present. However, some of these difficulties have come from the fact that the analysis which has been attempted has not followed correct logical principles, or that the logic which is actually involved in the entities analyzed has not been discovered. In some cases, also, while the analysis has been correct up to a certain point, it has been incomplete. Often, also, correct analysis has been misinterpreted. Accordingly, in the case of such entities as space, time, and motion, various self-contradic- tions, and peculiar logical situations called "antinomies" have appeared to be involved, and have, indeed, been considered to be back-handed proofs of the correctness of certain philosophical positions, as, e.g., of Phenomenalism. CHAPTER XXIII ANALYSIS BY INCORRECT PRINCIPLES An example of a philosophy that derives support from the difficulties that arise from a fanlty analysis of space and time is Phenomenalism,^ This is the position of the philosopher, Ira- manuel Kant (1724-1804), who is considered b}^ some to be the greatest of all modern philosophers. In one part of his work, The Critique of Pure Reason, Kant develops four so-called "antinomies." By an "antinomy" Kant means a pair of con- trary-opposite propositions each of which can be both proved and disproved. Each can be proved by the rcductio ad ab- surdum of the other, i.e., each is shown to be presupposed by its own denial. Thus it is, also, that each can be disproved. The Second Antinomy is here selected in order to illustrate ' See Chap. XXIX. ANALYSIS BY INCORRECT PRINCIPLES 161 this peculiar situation and the way in which it is artificially created by faulty analysis. Kant 's formulation of this antinomy is as follows: — Thesis " Every composite substance in the world is made up of simple parts, and nothing whatever exists but the simple, or that which is composed out of the simple." Proof *' Assume that composite substances are not made up of simple parts. Then, if we think all composition to be away, no composite part will be left. And, by hypothesis, there is no simple part. Hence, nothing at all will remain, and therefore no substance. Either, then, it is impossible to think all composition to be away, or even after composition is thought to be away, there must be something left, which exists without composition, that is, the simple. In the former case, the com- posite cannot be made up of substances, for composition is merely an accidental relation of substances, which may be taken away without at all affecting their existence as permanent realities. But, by hypothesis, substances do exist, and hence we must adopt the other supposition, that the composite substances in the world consist of simple parts. It directl}' follows, that all the things in the world are simple; that composition is merely an external state of those things; and that, although we can never take elementary substances out of their state of composition and isolate them, reason must think of them as the primary subjects, which exist as simple beings antecedently to all composition." Antithesis " No composite thing in the world is made up of simple parts, nor does anything simple exist anywhere in the world." Proof " Assume that a composite thing or substance is made up of simple parts. Then, as no external relation, and therefore no composition out of substances, is possible except in space, the composite thing must be made up of exactly the same number of parts as the space which it occupies. Now, space is not made up from simple parts, but consists of spaces. Evei'y pai"t of the composite thing must therefore occupy a space. But the absolutely primary parts of every composite thing are simple. Hence each of those simple parts occupies a space. Now, as every real thing, which occupies a space, contains within itself a number of parts that are outside of one another, and is therefore composite; and as this real composite thing is not made up of accidents, since these could not, apart from substance, be outside of one another; we must conclude, that simple substance is composite. . . ."^ ' Watson, The Philosophy of Kant, ed. 1895, pp. 160-161. 162 METHODS AND PROBLEMS OF METHOD Kant's formulation of this Antinomy is, very evidently, rather obscure, but if it is subjected to a rather violent paraphrasing, it is found to mean: — Thesis: Every (composite) substance is made up of simple parts as the condition for there being suhstances at all. For (proof) if there were no simple parts, and yet substances were derived by composition of parts, then we should have something "coming" out of nothing — which is impossible. Therefore there must he ultimate simples (such as are recognized in science today as atoms, or as electrons) in order that there may be substance at all. Antithesis: No substance is made up of simple parts, since (proof) if a substance "occupies" space (and it does), it is as "repeatedly divisible," again and again, into ever smaller parts, as is the space which it occupies, i.e., no "smaller part," such as an atom or electron, is absolutely simple, because, as extended in space, it is divisible, and therefore complex. A clearer formulation of the same antinomy is one that does not run the danger of examining both substance and space "at the same time," but that considers space alone. Such an antinomy of space may be stated in the form : — Thesis: Space does not consist of points, revealed by analysis, but must consist of simple parts or spaces (lines, planes, or volumes). Proof: Assume the contrary-opposite proposition, namely, that space does consist of points. But a point is unextended. There- fore, if extension be derived from points, — in other words, if space of one, two, or three dimensions is composed of points, then something "comes" from nothing, i.e., the extended "comes" from the ttnextended. But this is (for Kant) im- possible (perhaps because it is inconceivable). Therefore that entity to which the analysis of space leads must, by whatever name it may be called, be extended, i.e., it must itself be space or extension. Antithesis: Space does consist of ultimate, unextended simple parts, i.e., of points. Proof: Assume the contrary-opposite proposition, namely, that space does not consist of points, but of spaces, i.e., of lines, ANALYSIS BY INCORRECT PRINCIPLES 163 planes, and volumes. Then, as extensions, these parts are divisi- ble, as are their parts in turn, and so on, until finally unex- tended and absolutely simple parts are reached. Then it is of such parts, i.e., of points that space consists.^ Kant arrives at this antinomy because he unknowingly ac- cepts an incomplete and faulty analysis. This is due to the fact that his attention is directed exclusively to points, and that he ignores the character of the specific relations between the points. But points actually are related in a very specific way, and through the specific relations that hold among them (unex- tended) points do constitute an extended "something" which is space of one, two, and three dimensions. To demonstrate this, one has but to grant the principle, that points are related non-additively, or more specifically, that they are related by an asymmetrical and transitive relation^ It follows from this principle, that that whole which results from points so related, namely, space of one, two, or three dimensions, has characteristics that are different from those of the parts, even so different as to "mean" that extension is derived from that which is not extended, — just as, by the same principle, that which is chemical (atoms) is derived from that which is not chemical (electrons), and that which is life (cells) is de- rived from that which is not life (physico-chemical forces). For it is only a whole which is an additive result of its parts, that must resemble these parts as to its characteristics. Kant, however, quite neglected all such non-additive relations. But he was guilty of this neglect because he was unknowingly shut up within the limitations of the Aristotelian logic, as this had come down in the tradition. The modern Kantian, however, concludes that this second, as well as the other antinomies, confirms the main contention of the phenomenalistic philosophy, namely, that what we perceive and know is only appearance, and not ultimate reality. For, — he argues, that, while we undoubtedly perceive both space and spatial "things," nevertheless, since iy the antinomy space or extension is self-contradictory, no better proof than this could ' Cf. Russell's discussion of Kant's Antinomies in The Principles of Mathematics, pp. 188, 190-193, 259, 458-461. * See Chap. XLIII., vu., for details. I6i METHODS AND PROBLEMS OF METHOD be had, that the perceived ''world" of sense is mere appearance or phenomenon. Modern analytical science, however, solves and disposes of the second antinomy of Kant by showing that both thesis and anti- thesis are true. It succeeds in doing this by discovering that, e.g., the line is made up of two kinds of parts, namely, points and smaller lines. The former are not related additively to make up the line, while the latter are so related in certain respects. Further, the line has certain specific and distinct characteristics by virtue of each of the two kinds of parts. Thus, as made up of points, it is infinite, and may also be continuous, while, as made up of smaller lines, it is finite. It is in this way that both points and smaller lines cosuhslst as the parts of a finite line, and with the result that finitude and infinity are not inconsistent, but quite compatible, as distinct characteristics of one and the same entity. Thus it is that modern analysis rationalizes the line, the plane, and the three-dimensional mani- fold, and avoids those difficulties which were met with by the earlier analysts. Much of modern exact science depends upon principles which the analysis that has just been presented well illustrates. This analysis leads to the discovery of doth the parts and the rela- tions between the parts.^ By it such wholes as time, space, motion, acceleration, and change in general are rationalized without any contradiction or antinomy appearing. Its results are, therefore, to be accepted at their face value, and are not to be regarded either as human inventions, or as mere appear- ances, and the like, until there are good reasons for so doing. And up to the present all the reasons that have been advanced for so regarding these results have been fallacious. They have been fallacious reasons, either (1) because, with the failure of the attempt to analyze and to rationalize in accordance with some one principle, another principle has not been tried ; or (2) because the analysis has been incomplete, and, therefore, has not discovered all the parts and all the relations, one of both; or (3) because the actual results of correct analysis have been misstated. Our second example will, therefore, illustrate those difficulties ' Cf . the writer's " Defense of Analysis " in The New Realism. ANALYSIS BY INCORRECT PRINCIPLES l65 and failures that are conditioned by incomplete analysis, but that disappear if the analysis be made complete. The example is that of the incomplete analysis of the continuity of a line. Because of its incompleteness, the analysis readily leads to an antinomy of continuity, but an antinomy that as readily dis- appears if the analysis be made complete. To demonstrate this, let us consider an instance of an analysis of the continuity of a line that endeavors to account for this continuity by means of the concepts of gaps and of hetweenness. It is then found that it can be both proved and disproved both that the continuity consists in the absence of gaps, and also in their presence. This situation constitutes the antinomy : Thesis: Continuity is the absence of gaps. Proof: Assume that the line is made up of points, so that, from any one point to another, there is a distance, or gap. Then, between these points there are other points, and so on. Therefore, if there are enough points to ''fill in" all such gaps, the line is continuous. But there are enough points, since, not only between any two points is there a third point, but also, in any line or distance, there is an infinite number of points. Therefore the line is continuous in that there are no gaps. Antithesis: Continuity is the presence of gaps in the line. Proof: Assume that the line is made up of points, and, there- fore, since there is a point between every two points, that there are no gaps — all gaps being filled up. Now if, e.g., the line is of unit length, so that the end points are in correlation with and 1, then the other points are in correlation with the rational fractions. For it is the character of these fractions that between any two of them there is a third. But the rational fractions are also of such a character (as is well known) that the difference between any two of them is finite. Accordingly, if the rational fractions are correlated with the points, as they must be, if any two of them are correlated with two specific points by any scale of measurement, then the finite differences between the rational fractions stand for, or are correlated with, 7iot points, but lines, distances, or gaps, between points. Therefore continuity con- sists in, not the absence of gaps, but their presence. This whole antinomy arises from the fact that the analysis is made in exclusive reliance upon intuition and self -evidence 166 METHODS AND PROBLEMS OF METHOD rather than upon intellectual experiment and supplementary analysis and testings. To intuition the repeated "betweenness" of points does seem, perhaps, to explain or to define continuity, but it turns out, in fact, not so to explain or define this, but to lead to contradictions and antinomies. However, by a sup- plementary and complete analysis, in which something more than mere "betweenness" is discovered, the genuine character of continuity is revealed and all seeming contradictions in it are removed." We may next consider an example of getting into a difficulty, an antinomy, a paradox, through rationalizing and analyzing by means of an incorrect rather than a correct principle. Zeno (about 490-430 B.C.) endeavored analytically to ration- alize, or rationally to analyze motion. He tried to do this in a number of ways, but found that every analysis of motion revealed a contradiction somewhere and somehow. Accordingly he concluded that motion and change in general are only illusions, and that rest and permanence are alone real.'^ One of his analyses consisted in reducing motion to an ab- surdity. In doing this Zeno assumed an instance of motion, say from a point A to a point B. Concerning this he then argued, that, before one travels this whole distance, one must travel the first half of it, and, before this half, the first half of it, and so on. Therefore, he concluded, one barely gets started, or, indeed, one does not get started at all. For similar reasons, he argued, one could never qtiite reach a destination, since, if one has gone half the distance, then, before one can go the remaining half, one must cover half of it, etc., so that there is always still remaining a fractional part yet to be traveled. Therefore in neither case is there motion. Where, now, is the error in this reasoning? It must be admitted that analysis does show that a finite distance consists of, e.g., halves, quarters, eighths, etc., and also that one must cover the first of these fractional parts before one covers the subsequent parts. The error in the argument consists, however, in ignoring the rather technical principle, that, if x and y be " See Chap. XLIII., vii.-x. 'See Burnett, Early Greek Philosophy, 1892, p. 331 ff.; cf. Russell, Scientific Method in Philosophy, p. 165 ff., and Principles of Mathematics in a number of places (see his index). ANALYSIS BY INCORRECT PRINCIPLES l67 any two commensurable finite quantities of which x x), cannot be traveled in the time nt, but only the y distance, y —, can be ; in other words it means, that, if a 11/ certain distance x, say, -j- of y, is traveled in the time t, then 4 m the time, ^ X 4, — y cannot be traveled. Obviously, however, this conclusion is false, if there is such an entity as uniform rate. For, if there is, then, if any start at all is admitted, so that a finite distance x is traversed in the time t, at the rate — , it must be granted that in the time, nt, the distance nx {=^ y) can be traversed. One cannot avoid this conclusion by maintaining either that there is no start, or that the rate itself is changing. For, on the one hand, finite distances are implied by that which is the limit of the series of decreasing finite distances, namely, the point, at which there would be no motion, while, on the other hand, if there are finite distances, then, for some distance x, X no matter how small, there is uniform velocity — . However, that there are both finite distances and uniform velocities, is presupposed by those very assumptions which are used by Zeno to demonstrate that motion is impossible. But if there are such distances and velocities, then in due time, motion over any distance y is possible, even though it is true that any first distance — must be traversed before the second n distance is traversed, and, also, that after any first distance JL n is traversed, the distance, e.g., -^, must be traversed before the 168 METHODS AND PROBLEMS OF METHOD next '~ is traversed, and so on. For, although there is a sum, JL JL. M. — lJI , . . i^ ^ there is also the product ^o n n" n^ n° ^ Zeno's whole difficulty, therefore, was incurred by rationaliz- ing in accordance with an incorrect assumption or principle. It is evident, then, that when one rationalizes, one should use not only correct methods, but also correct material principles or premises. Otherwise it is quite easy to create seemingly real, but actually only artificial difficulties, and to reach seemingly rational conclusions that contradict sense-given facts, as, e.g., the reality of motion. At this point we may advantageously present still another example of an attempt at rational analysis by a false principle rather than by a correct one, of the consequent failure of this attempt, of the conclusions that are derived from such a failure, and, finally, of a consistent and satisfactory analysis of the same complex by a principle that is correct. Ever since Zeno and the other Eleatics, certain philosophers have endeavored to analyze change by the use of the two prin- ciples of identity and contradiction.^ This attempt fails, so that the conclusion is reached, that change is only appearance, and that rest and permanence are alone realities. The analysis that is made may be stated as follows: Under the influence of the traditional logic, with its dominant concept of thing, the problem is stated in the form of the question, How can a thing change? In solution of this, it is found, that the law of identity applies to a thing, i.e., that a thing is identical with itself. Change, then, if it is a fact, seems to mean that a thing ceases to be identical with itself and becomes something else, i.e., that a thing, A, becomes its contradictory, non-A. At a certain instant, therefore, the thing is, or seems to be, both A and non-A, which "condition" violates the principle of con- tradiction, namely, that a thing cannot both be and 7wt be, have and not have, a certain property. Change, therefore, involves this contradiction, or, it may be said to be self -contradictory in this respect, so that, with it tacitly assumed, that that which is self-contradictory cannot he real, it must be concluded that * F. H. Bradley, Appearance and Reality, Chaps. I.-V., especially pp. 45-48; also pp. 231-233. ANALYSIS BY INCORRECT PRINCIPLES 169 change is not real, but only illusory and apparent, while rest and permanence, or, more generally, that which remains identical with itself, is alone reality. Let us now, in contrast, examine the results of the endeavor to analyze change by the use of other principles than those of identity and contradiction, with these latter supplemented, how- ever, and not displaced by such other principles. With our present knowedge of the several specific kinds of relations, of the precise nature of continuity, infinity, and the like, let us assume, at least for the sake of making the experiment, that change is a continuous series, with all that this means by way of those logical principles, entities, and relations that a series involves. The analysis that results not only does not show change to involve any contradiction, but also reveals the opposed analysis to be most inadequate. In the first place, a series is not the mere individuals that are present in it, but is these individuals related ni a very specific^ way, namely, by an asymmetrical and transitive relation.** Cer- tain minor limitations of this statement may be neglected here. And, secondly, a series is continuous, if it is in one-one cor- respondence with the real numbers, namely, the series of positive integers, rational fractions, and irrationals in order of magni- tude.^'^ A series is thus quite consistent with the self-identity of each of its members, while it is also more than these members. In a continuous series no member is next to any other, and there is no finite difference between members, or from any one member to another member. ^^ If, now, we analyze change in accordance with this logic, we limit the use of the principle of identity, and accordingly give up that definition of change which makes it "the ceasing of something to be identical with itself" and the "becoming some- thing else." For by this new logic, there is no such ceasing, although there are individuals, A and B (non-A), that remain identical with themselves. But there are not only these two individuals, but there are in a continuous series an infinite number of individuals betM'een A and B. The change, then, is; the ordered complex or series of these individuals, each of which, like the change itself, is identical with itself, and does not » See Chap. XLIII. " See Chap. XLIII., vii.-x. " /6td. 170 METHODS AND PROBLEMS OF METHOD change. Change, therefore, is a different kind of entity from the individuals that are present in it, &nd is not to be analyzed by the principles that apply to those individuals, any more than the moral situation is to be analyzed by examining those uni- verses of discourse from which morality is absent. In a similar way, "individual" and "change" are entities that belong, each to a distinct universe of discourse, with each capable of con- sistent analysis, unless the individuals are simple, each equally real, and neither to be confused with the other. CHAPTER XXIV MISINTERPRETATIONS OF CORRECT ANALYSIS We now reach the third way in which doubt is thrown upon the reality of certain entities, e.g., space, time, and motion. This is done by misinterpreting actual, correct results obtained by analysis. Misinterpretation is quite excusable, if it is not wilful, but quite unpardonable, if it is intentional. With Zeno it was not intentional when he analyzed, e.g., the motion of the arrow, and interpreted the arrow's being at a point at an instant as rest. From this Zeno reached the conclusion that motion was only a sum of rests, and, therefore, was not real, but only ap- parent. But Zeno also made a misinterpretation. The arrow's occu- pation of a point for an instant, is not rest, — whatever else it may be. To be at rest the arrow must be at a point for at least two instants, and if for two instants, then for an infinite number of instants between the two.^ Zeno's conclusion therefore falls to the ground. Among contemporaneous philosophers Bergson does not hesi- tate to accept Zeno's misinterpretation and to base an anti-intel- lectualistic philosophy upon it.^ Bergson 's argument is, that, because the analysis of motion leads to its contradictory, rest, * See Chap. XLIII., vii.-x. - In Creative Evolution, Matter and Memory, and Time am,d Free Will. MISINTERPRETATIONS OF CORRECT ANALYSIS 171 the analysis falsifies that which is analyzed.^ However, this specific analysis is regarded as typical of all analysis, and there- fore all analysis is held to falsify. Accordingly, the position is arrived at, that, to get at fact, one must not analyze at all, but must rely upon the immediate experience of the (unanalyzed) whole, through intuition, emotion, and the like.* To refute Zeno and Bergson, and to undermine those philo- sophical conclusions which the latter bases on that (false) analysis of motion which he accepts, one has, however, only to state correctly the actual scientific analysis of motion that is ready at hand. This analysis shows that the occupation of a point at an instant is neither rest nor motion. It shows, on the one hand, that rest is the occupation of a point for two and indeed for an infinite number of instants, and, on the other hand, that motion is the one-one correlation of two points and therefore of an infinite number of points with two instants and, therefore, with an infinite number of instants. Or, stated in another way, motion is a series of complexes each of which is itself a one-one correlation of a point with an instant.^ But in order to analyze motion in this way into parts that are them- selves neither motions nor rests, one must accept the two prin- ciples, (1) that a whole can be made up of two or more kinds of parts, and (2) that, even though the parts of one type may be related additively to form the whole, those of certain other types cannot be so related. In anything that is an ordered class or series, this last must be the case. Motion is a series. It consists, in the case of any finite motion, of smaller motions, but it also consists of another type of parts, each of which is the complex, point-correlated-with-instant. These parts, however, are neither rests nor motions; yet, as related non-additively, or, more specifically, as related asym- metrically and transitively, they are that whole which is motion, and which has properties that are different from those of the parts. The results of this analysis furnish, therefore, no oppor- ' Bergson, Creative Evolution, pp. 163, 303-313, and a number of other places. Cf. my " Defense of Analysis " in The New Realism, and H. 3. H. Elliot, Modern Science and the Illusions of Bergson. * See Chap. XV., rv., 2, and Chap. XL., vu.-ix. " See Chap. XLIII., x. 172 METHODS AND PROBLEMS OF METHOD tunity for a valid claim that analysis falsifies, on the ground that parts are reached which are the formal contradictory of, and inconsistent with, the whole. Parts that are different from the whole are indeed reached by analysis, namely, such parts as both instants and points, and also those complex parts each of which is an instant related in a one-one manner to a point. But none of these parts is of such a character that it is pre- cluded from cosubsisting with a whole that is a non-additive result, and that has distinct and peculiar properties of its own. Such a consistent analysis demands, however, the principles that are formulated above, and that are accepted in the new logic, but ignored by the old. All this presentation of the methods and results of the modern analysis of space, time, motion, and change is most important for our purposes. For it shows that, since such entities can be analyzed and rationalized in a manner that is quite free from contradictions and antinomies, we are relieved from attaching any more philosophical importance to them than we attach to the other innumerable facts of science and common sense. Nevertheless a great many influential philosophical systems have been founded in part upon the difficulties and contradictions that have been found in, e.g., the infinity and the continuity of space and time, in motion and in change, and the like. Every phi- losophy must, indeed, consider these problems in connection with the cosmological problem. But today, with a consistent analysis of all these entities at hand, one is left free to consider the fundamental differences between philosophical systems upon some other basis — a procedure that will be adopted in consider- ing, in the later sections of this volume, the solution of philo sophical problems. THE METHODS OF THE NEW LOGIC 173 CHAPTER XXV THE METHODS OF THE NEW LOGIC Summary The foregoing presentation of analyses that are made of such, entities as change and motion, shows that there are logical methods and principles that are quite different from those of the logic of the tradition. Some of the most essential features of contrast between the two doctrines may now be advanta- geously summarized. I. The new logic is opposed both to the psychologizing tend- ency, and to the pragmatic. The standpoint of the new logic is, that logical principles are present in entities, i.e., that they are objective. Toward them one takes the attitude of empirical procedure and of discovery. This means that there may be in this richly endowed universe any number of different logical principles, entities, and situations. It is, therefore, the em- pirical study of entities that extends the field of logical science, and no one should be so brash as to delimit this field to certain logical principles, thus to preclude the possibility of its exten- sion by new discoveries. Indeed, the necessity of maintaining the ''open door'- in this respect, is shown by the fact that it is impossible to solve certain problems by the principles of the old logic, but quite possible to solve these same problems by the new logic. II. The old logic is a logic of substance and qualities, — of things with a core in which qualities inhere. The new logic is, in contrast, one in which these concepts, even if they are not given up entirely, play a minor part, and the concept of rela- tion plays the major role. III. The new logic emphasizes relational propositions, exem- plified by '^A is less than B.'' These propositions cannot be reduced to the subject-predicate propositions of the old logic, in which the predicate is interpreted to be a property of the ;§ubject.^ * Cf. Russell, Principles of Mathematics, in various places, and Royce's Essay, the " Principles of Logic," in the Encyclopedia of the Philosophical kiciencea. tl74 METHODS AND PROBLEMS OF METHOD IV. The new logic consists largely of those principles which are discovered by the analysis of series. This means, again, that the new logic recognizes many types of relations which the old logic quite ignores. The old logic makes no recognition of series, but only of such wholes as are additive, conceptual, causal, organic, thing-like (substance and attribute), syllogistic, and numerically single. The chief relations which the old logic accordingly recognizes are additiveness, similarity and differ- ence, causation, inherence, "member of," inclusion, identity, and contradiction. It therefore omits ynany very fundamental relations, especially such as are involved in series. Some of the most important types of these relations are the fol- lowing: (1) Asymmetrical relations, defined as such relations, R, between a and h, as preclude the identity of the inverse relation, E, with the original: e.g., a for "influences," and ^ — y^— ' for "underlying and mediating." The theory of external relations may then be expressed in the form oi a\R\h, meaning by this, (1) that, if two terms are related, neither term influences the other, (2) that the absence of either term would be ivithout effect on the other, (3) that either term may come into being and into relation with the other term without affecting it, (4) that, accordingly, no terra is complex by virtue of being related, and (5) that no third term, u, underlying a R b in the sense of « — . — - . is necessary U in order to mediate the relationship between a and 6. Briefly, the theory of external relations is, that relaiedness and inde- pendence are quite compatible. The theory of internal relations is a direct denial of these main propositions of the theory of external relations. The "modification aspect" of the internal theory may be expressed by the symbol, a^Rb^, meaning by this, that, if two terms are related, (1) each term influences the other, (2) that related terms are complex. (3) that either terra out of relation with the other would be different from what it is in relation to that other, (4) that terms are what they are by virtue of being related to other terms (the organic view). This modification theory of relations may, or may not be held together with the "underlying reality aspect" of the theory of internal relations. This last theory by itself is expressed by ^ — , — ' , meaning by this, that, if two terms are related, and V whether they modify each other or not, there is an underlying or transcendent reality, U, to mediate this relation, indeed to make it possible at all. Some of the adherents of the theory of external relations regard it as holding without exception for all terras and rela- tions,^ while others maintain that it holds only for some rela- tional complexes.^ In contrast with this, the advocates of the "internal theory," as it may be called, insist, according to that ' I"]. B. Holt in The New Realism and in The Concept of Consciousness. * The writer in the present volume. 178 METHODS AND PROBLEMS OF METHOD aspect to which they are inclined, either that the "modification theory" or the "underlying-reality theory" holds for all rela- tions. II. THE PROOFS OR ARGUMENTS FOR THE THEORIES OP RELATIONS 1. The Theory of External Relations We may first consider the proof of the theory of external relations. This proof is twofold. One part of it depends on the result of an appeal to concrete fact; the other part is the demonstration, that the validity of the external theory is pre- supposed by that very denial which it receives in the internal theory. This last demonstration will be presented first. To prove that there are terms which are related and yet do not affect, modify, or influence one another: — First Proof. Let this proposition be denied, i.e., let us assume that any two related terms do affect each other. Then these related terms are complex.^ But, as complex, they consist of parts, which in turn are related. Therefore, these parts must, by the same hypothesis, also affect one another and be complex, and so on, in an infinite series. Ultimately, therefore, there must be simple terms that make all this complexity possible, but that are themselves not complex. Yet these ultimate, simple terms are related to one another. Therefore, as related, and yet as simple, they do not modify one another, but are independent, — in just this sense, namely, of not modifying one another. Points and instants are examples of such ultimate simple terms, which, though they cannot be isolated or identified by physical experiment, are nevertheless discovered by an analysis in situ. It is also found by the same method that these entities are related, and yet that they do not affect one another, so as to make one another complex, although as related by specific relations they form specific complexes, namely, space and time respectively. The modern analysis of space and time demands, therefore, the theory of external relations/ and accordingly ' Cf. Kussell, " The Basis of Realism," Jour, of Phil., Psych., and Scien- tific Methods, Vol. VIIL, 1911, p. 15811. * See Chap. XLIII., viu.-x. THEORIES OF RELATIONS 179 the thesis is proved, that at least some terms do not, as related, affect or modify one another, and are, in this sense, inde- pendent. This same conclusion can also be established by induction, i.e., we can get instances of related terms that do not affect one another. Thus it is evident that if, as a result of analysis, one accepts genuine points and instants, then these are to be regarded as instances of terms that are both related and independent. But there are, also, other instances. One of the most frequent practices of physical science is that of employing methods by which certain phenomena are isolated, and yet left in situ, i.e., in relation both to one another and to other phenomena. Pur- suing this method, physical science discovers that, although time is related to space, to matter, and to change in general, it is, nevertheless, independent of these. In fact, in all physical science, time is the independent variable. In the case of a great many phenomena it is a leading problem, therefore, to find how "things" are related to, or vary with time. This problem occurs, e.g., in the investigation of the motion of a falling body, in which case it is found that both the body and the motion are related to many other "things," but that the motion, in respect both to itself as motion and to the change of velocity, or acceleration, is related to time as if this were the only referent. The distance traveled by a falling body is the specific function, s = t-, while the velocity is directly propor- tional to the time elapsed, and the acceleration is directly pro- portional to the time increment. Distance traveled, velocity, and acceleration are, therefore, each related to time, but the time is neither modified nor constituted by virtue of these relation- ships, as also conversely, neither the space, the velocity, nor the acceleration are causally affected by the time. These instances are typical. Mechanics, chemistry, and physics are replete with cases of functional relationships between variables, each of which is a series of individuals, just as time is a series of instants. Each variable, also, is related to many "things," of which it is independent. There are, therefore, complex as well as simple entities that furnish data, in respect to the relatonships in which they stand, for a generalization to the theory of external relations. This proof by induction con- 180 METHODS AND PROBLEMS OF METHOD jBrms, therefore, the first, indirect proof of the external theory, and together, both proofs show that the modification theory of relations is one that is at least limited in its range, if, indeed, it is not altogether invalid. A similar conclusion is also reached as a result of the examina- tion of both the argument and the empirical evidence for the underlying-reality theory of relations. This specific theory can be shown to presuppose its contradictory, or contrariwise, the theory of external relations can be demonstrated to be presup- posed by it. To give this proof, let us assume that, in order that any two terms, a and h, may be related, there must be an underlying, unitary reality, U, to mediate the relation. Then, by supposition, this U is simple, and not complex, since, if it were complex, its parts would, by hypothesis, require another V to relate them, and so on indefinitely. Let us assume, there- fore, that V is absolutely simple, and not complex. But even then, as the mediator of the original relation, it is related not only to a, b, and R, but also to the complex, a R h, so that, again, by the original assumption, there is required still another TJ to mediate this relation, and so on in an infinite regress. For every U that is thus reached, since each such TJ is related to that which it mediates, there is implied still another TJ. There- fore each such TJ is only a member of a series, and not such an all-including and all-mediating TJ as is sought. The result is, that no all-relation-mediating TJ is ever arrived at. Even on the basis of the original assumption, which is thus shown to be self-contradictory, it is only the series as a whole that includes every TJ. But an infinite series already subsists in its unity if specific relations subsist to relate its terms. These relations are (1) one-one correlating relations between proper part and whole, and (2) asymmetrical and transitive relations among the individuals of both whole and part. But another term, out- side the series, is, by empirical methods, not found to be neces- sary, in order to give the series unity. The relations already present suffice to give it this. We may conclude, therefore, that, in the case of a being related to b {i.e., a R b) the relation itself is sufficient to give all the unity that there is, even as is the case with the infinite series. No underlying U is needed either to give unity to, or to mediate the relation between, the THEORIES OF RELATIONS 181 related terms. But that the relation is itself thus sufficient, is precisely the position of the theory of external relations. The supplementation of this indirect proof of the external theory by the empirical disproof of the underlying-reality theory is remarkably easy. Strictly empirical procedure, either experimental or otherwise, discloses not a single instance of a one '^ something ," of a TJ, that mediates the relation betweefi two or more terms. Indeed, every so-called instance proves to be only one that is inferred from the tacitly or explicitly as- sumed validity of the underlying-reality theory. Thus, e.g., previous to Locke and Berkeley, the position was commonly taken, that in every physical thing, a suhstance-like sutstratum or core held the qualities together, but Locke was not very certain of the presence of this substratum, and Berkeley denied it entirely for physical things, though he held to an analogous substance for ideas. Hume, however, denied even such a soul, or spirit, and held to the factuality only of impressions and ideas.^ Physics of the present day follows Berkeley's position, and psychology follows Hume's, so that it is disembodied quali- ties, events, and relations that are now studied in these sciences. Indeed both physics and mechanics, in arriving at general laws, disclose functional relations that are instances of the more general theory of external relations. This theory has, therefore, at least some range of application, while the underlying-reality theory seems to have no validity at all. Whether, now, this is the case also for the modification theory we shall shortly con- sider. The basis on which the theory of external relations rests is, accordingly, the twofold one, (1) that it is presupposed by its own denial as this is made in both aspects of the theory of internal relations, and (2) that it is confirmed by induction from positive cases of related terms in which no term modifies others, and no underlying reality is found empirically. There- fore, at least some terms are related in accordance with the theory of external relations. Are all terms so related, or, are some terms related in accordance with the principles of the modification theory ? '^ ' See Chaps. XXX. and XXXI. "The theory of external relations is accepted, and evidence and proof 182 METHODS AND PROBLEMS OF METHOD 2. The Modification Theory of Relations The adherents of this theory usually maintain that it is of universal validity, to the complete exclusion of the theory of external relations, though not of the underlying-reality theory. This last theory may, or may not be held together with the modification theory. The proof that is presented for this modification theory is twofold. One proof is the (attempted) reductio ad absurdum both of the theory of external relations and — for some related terms — of the underlying-reality theory in the form that has just been presented. The other proof seems to be inductive. Let us first consider the argument by which it is attempted to reduce the theory of external relations to an ahsiirdityJ To give this proof, let us assume the external theory to apply to the relational complex, a R h. This means that, though a and b are related, they are also independent. Then, so the argument goes, the absurdity appears, that the terms a and b cannot be related at all, on the ground that, if they are (assumed to be) independent of each other, they are also independent of R (and of it are presented by the following writers: Perry, in The New Realism, in his essay on "Independence"; Russell, Principles of Mathematics, p. 09 If . and p. 221 ff., and in several other places; "The Monistic Theory of Truth," Philosophical Essays ; " The Basis of Realism," Jour, of Phil., Psych., and Scientific Methods, Vol. VIII., p. 158 If. ; "On the Nature of Truth," Proceedings of Aristotelian Society, 1907, N. S., Vol. VII., pp. 28-49; Spaulding, " A Defense of Analysis " in The Keio Realism, p. 155 If.; Marvin, First Book of Metaphysics, Chaps. VII. -XIII. For instances of the independence of related terms and for a discussion of this problem see Chap. II. of this volume; also Perry, "A Realistic Theory of Independence " in The New Realism ; W. H. Sheldon, " Chance," Jour, of Phil., Psych., and Scientific Methods, Vol. IX., 1912, pp. 281-290; E. V. Huntington, " Sets of Independent Postulates for tlie Algebra of Logic," Transactions of the American Mathematical Society, Vol. V., 1904; J. VV. Young, Fundamental Concepts of Algebra and Geometry ; Stout, "Alleged Self-Contradictions in the Concept of Relation," Proc. Aris. Sac, Vol. II., pp. 191-192. ' This is very definitely attempted by Bradley in Appearance and Reality, pp. 1-120, and by Joachim in The Nature of Truth, especially in Chap. III. The position is also accei)tcd essentially without any examination of its grounds and almost as self-evident by Bergaon in Creative Fvolution, pp. 9, 11, 160-16.3, 188, 303, 338-340, and by Wm. James in Pragmatism, p. 134 ff. Royce, in J'he World and the Individual, in the first four chapters, especially Chaps. III. and IV., maintains it in the form of the principle, that relatednrss implies dependence. This is also the position of Lotze, Metaphysics, I., trans., ed. by Bosanquet, Chap. VI., pp. 166-169. Bradley, in Essays on Truth and Reality, 1914, does not depart from his earlier position. THEORIES OF RELATIONS 183 so are not related,).^ Accordingly it is to be inferred that in order to get or to have the terms related — which is the desideratum — there must be other relations to relate the original relation R to a and to h, and also, as alone consistent with this implication, still other relations to relate these relations to one another, and so on, in an infinite series.^ But, it is maintained (though falsely), an infinite series cannot by its very nature ever be completed. Therefore it is inferred that, by the princi- ples of the theory of exter^ial relations, terms are never re- lated. Accordingly it is inferred, conversely, that, in order to have terms related, or to explain how a relation relates, one must accept the "internal theory'' to the effect, that related terms are dependent in the sense that they influence, modify, and affect one another}'^ As a result, all terms hecome, or are com- plex, indeed infinitely so; for, on the one hand, any so-called, simple term is a complex of the effects produced in it through its being related to all other terms, and, on the other hand, since these effects are in turn related, they affect one another, and so are also complex. In criticism of this modification theory of relations, one may attack either the foregoing argument, or the position that the theory is of universal applicability. But that the theory is of limited validity and applicability is shown by the fact, that it leads to the position, that all terms are complex, and thus be- comes self-contradictory. For complexity presupposes at some juncture ultimate simples as the components of all else that is complex, and such simples, though related, must he unmodified hy and independent of one another. The argument for the modification theory thus leads to the limitation of the theory itself. But, quite apart from this outcome, the argument for the theory may itself be refuted as regards its logical procedure. For, at its very beginning, the very question at issue is begged, when it is assumed that the theory of external relations means that, if terms are independent, they cannot he related, and that the relation does not relate them. All the rest of the argument * Royce, ihid. ' Bradley, Appearance and Reality, pp. 32-33. *° Maintained by all the adherents of this position. 184 METHODS AND PROBLEMS OF METHOD proceeds from this unwarranted assumption. Accordingly the argument is 71 ot in the least a disproof of the theory of external relations, but is 07ily a denial, and merely to deny is never to disprove. Is there any proof or evidence at all, therefore, for the modi- fication theory of relations, by which this theory can be shown to hold even for some instances of related terms, if not for all ? The theory certainly does not hold for simple terms, nor for those complex terms which, like time, space, motion, and accelera- tion, are either series or functions in the precise sense of these terms. But for a specific kind of complex term, namely, for so-called organic wholes, it does seem to hold. An example of such wholes is any individual plant or animal. The parts of these wholes are related, and they do interact causally — though, perhaps, not because they are related, but because this is the specific kind of relation between them. Thus, e.g.f the lungs, heart, muscles, and brain of a vertebrate causally influence one another, and develop in mutual causal dependence, in the growth of every individual from a fertilized ovum to maturity. But living beings, both plant and animal, also causally interact with their physical environment. In fact it would seem not only that organic beings, but also that the "things" of the inorganic world are related to and causally influence one another. Yet, if this means that the modification theory of relations is here applicable, it does not mean, how- ever, that this theory applies to every complex of related terms. For some entities, as, e.g., motion-related-to-time, are complexes whose parts are related, yet are causally independent, i.e., whose parts are related in accordance with the theory of external rela- tions. In certain complexes, furthermore, certain terms may be related, and yet be independent, while others are related causally. Thus, e.g., the parts of a shooting sky rocket are in causal (chemical) interaction as the rocket moves, and yet the mass and the changing velocity of the rocket are in a relation of independence to the chemical composition, to the time, and to the "path." This distinction corresponds to that distinction which sub- sists between causal and functional relations. Functional rela- tions subsist by virtue of a specific correlating relation between THEORIES OF RELATIONS 185 the individuals of two series. Thus the changing velocity or the acceleration of a falling body is a function of the time, but it (the acceleration) is also, as are the time and the space, a series. Causal relations, on the other hand, subsist between complexes that are not series, aWiough functional relations, series, and the individuals that are in the series, may be present in these causally related complexes. For example, any living organism is a complex of organs and processes that are causally related, but, within these organs and processes, there are strictly functional relationships of the specific kind that chemistry, espe- cially physical chemistry, is concerned with. This position, namely, that there are certain wholes which consist of complexes which are related dependently and causally, but that also, within these complexes, there are still other com- plexes which are related and yet are independent, agrees with the result previously reached, namely, that the modification theory of relations "rests on" and presupposes the theory of external relations. While for each theory there is therefore a field within which it holds, the theory of external relations is, in this respect, fundamental to the modification theory. 3. The Underlying or Transcendent Reality Theory of Relations The criticism and brief formulation of this specific theory have already been given.^^ No concrete instances can be found, other than hy deduction from the theory itself, of an extra entity that mediates the relations between other entities. Yet the theory is one which, either as explicitly stated or as tacitly presupposed, has had a dominant influence in theology, phi- losophy, and logic down to the present time, and in science during the middle ages. Upon it, indeed, are based, e.g., certain of the proofs of the existence, or subsistence of a deity,' ^ as are also certain doctrines as to the nature of the soul," and much of the traditional Aristotelian logic.'* However, the theory, as a theory, did not receive explicit recognition and formulation '' This chapter, ii., 1. " 8ee Chaps. XXXIV.-XXXVIII. *' In Locke, Berkeley, and Kant; see Part II. " Chap. III. 186 METHODS AND PROBLEMS OF METHOD until the post-Kantian philosophy appeared, but it was then advanced as the very core of what was styled a new logic, namely, the Hegelian.^ ^ Nevertheless, this new logic was really only a development of the old, since it was derived by a specific use of the Aristotelian principle of contradiction. Thus, by the entirely formal use of this principle, there must be formed or thought, for every term without exception, the formal contradictory, i.e., for every a, whatever a may be, there must be thought a non-a. This relation seems to be one of necessary, logical connection, which may be stated in the form of the propositions, that for every a there must he a non-a, or, that a cannot he without non-a, or, that a implies non-a. But^ if a cannot he without non-a, then the two are inseparahle, and, therefore, form a unity. The important problem for the theory therefore is, Where is this unity? or, What is its locus? And the answer is, that the unity cannot be identical with, or be at the "level" of, a and 7ion-a, since these are numerically two. Therefore it must be at a different level, either tran- scendent to or underlying hoth a and non-a, and, also, it must be an absolute unity,^*^ and not a concealed complexity, since, if it were complex, the problem would be repeated in regard to the relatedness of the terms of this complex. This absolute unity may be symbolized by TJ, and, accordingly, the theory itself be expressed by the symbol . . U As an example of the use to which this theory is put, we may consider the demonstration, that change is necessary. This demonstration is not difficult to make, since, if a cannot h& without non-a, and, if change means that a hecomes h, i.e., non-a, then it follows, that change must he. This is, indeed, logically the very demonstration that Hegel himself made of the necessity of change and evolution.^'' It means that for Hegel and his faithful followers, not only must there be change, evolution, " See Chaps. XXXIV. and XXXV. " Among the prominent modern philosophers who hold this position are Fichte and Hegel (see Chaps XXXIV. -XXXVIII. ) ; Bradley, Appear- ance and Reality, p. 520 11'.; Royce, as the outcome of his discussion in The Spirit of Modern Philosophy and The World, and the Individual; E. Caird, Evolution of Religion, Vol. I., p. 67 fl'. ; Calkins, Persistent Problems of Philosophy, p. 418 flf.; T. H. Green, Works, Vol. III., p. 45. ''See Chap. XXXVl. THEORIES OF RELATIONS 187 and progress, but also that these are logical in character, and that, underlying them, there is an absolute unity. Another example of the application of this theory is one in which it is demonstrated that there is an underlying and transcendent Unity for the whole universe. To give this demon- stration, let us select the contradictory terms, self and not-self (or indeed any other pair of formally contradictory terms), and then ask, if everything is not either one's self or not one's self? Then, hy the theory, must there not be One and only One Being that underlies and is transcendent to all else, and that is of a different order from the related terms? ^® Still another example of the application of this theory shows how, by means of it, one can transcend time, and get to the timeless, and perhaps to the eternal. For, if the present be a, all other time, past and future, is, as not-present time, non-a. Therefore, iy the theory, there is a Z7 that is different from both a and non-a, and that is in this respect neither past, present, nor future}^ The underlying-realit}^ theory of relations can be maintained as valid, at the same time that one also holds, that some related terms modify one another, and that others are externally re- lated. Conversely, however, if one accepts the theory of external relations, there is no necessity for accepting the underlying- reality theory, since the former theory means, that the fact that a relation relates its terms accounts for all the unity that there is in the relational situation. Criticism of the Argument The argument for the underlying-reality theory of relations has already been criticized,^*' and need only be referred to here. If a first U is found to mediate the relation between a and non-a, then, since this U is related to the complex, a R non-a, another U is in turn implied to mediate this relation, and so on in infinite series. Therefore, either an ultimate underlying U is never reached, or, if it is, then, although it is related to ** Well illustrated by Bradley's arguments for an Absolute in Appear- ance and Reality. '^^ E.g., Bradley's and Royce's Absolute. "> This chapter, ii., 1. 188 METHODS AND PROBLEMS OF METHOD the complex of the preceding complexes, this relation does not demand an underlying reality to mediate it. But, if there is this one exception, then no relation need demand an underlying entity to mediate it, and the whole theory falls to the ground. The only seemingly possible inductive evidence for the theory is derived from the examination of concepts. Thus if one take either the psychologizing or the pragmatic view of eoncepts,^^ he might go so far as to maintain that the individuals of what we now regard as a class, e.g., the class of living heings, would not be so related as to form this class, if we did not relate them. For relations of similarity between "things" whereby they form classes, are, in accordance with these two positions, either created or invented by having "things" get into relation with a consciousness, or with something, such as an organism that relates them. But if this is the case, then at least these rela- tions, to a consciousness, or to an organism, would not be so created or invented, since they must subsist before other rela- tions could be created or invented. But, if some relations are thus independent, then, clearly, others may also be — especially those relations of similarity by virtue of which there are classes. Classes, therefore, would seem to be independent of a relating consciousness or organism. However, if a relation is, in this manner, ayi objective entity that relates "things," then it is specific relations of similarity that unify individuals into specific classes, so that with the unity of the class accounted for in this way, there is neither the oppor- tunity nor the necessity for a transcendent or underlying unity either to perform the function of mediating the relation, or to give the class unity. Thus, e.g., in the case of the class of living beings, there are (1) the individuals; these are related by a number of specific relations of similarity. Then there is also (2) the class, as a class, whose members are minified objectively by each of these specific relations. But (3) each one of the relations which thus organizes the individuals into a class is distinct both from the class as a whole, and from its individuals ; yet these relations, e.g., similarity in respect to structure, are not, in the usual sense of the term, transcendent, either to the class as a whole, or to its individuals, even as the class and the "Chap. XIII. THEORIES OF RELATIONS 189 individuals are not "outside" of themselves in any sense. The specific relations of similarity which thus organize the indi- viduals into a class form, or are, the objective concept. It goes without saying, perhaps, that this objective concept can be known quite as well as can either the individuals, or the class as a whole, and such knowledge can be called an "abstract idea." Humanity, triangularity, bravery, are exam- ples. On the other hand, the knowledge of the class as a whole is a "general idea," — human being, triangle, brave act being examples. By virtue of abstract ideas we can, without knowing each individual specifically, know about classes as a whole, i.e., we can know that there are individuals of a certain type, because they are related in a specific way. We can know any individual, although, perhaps, no particular one. In fact, in certain instances, not only do we not need to know all the individuals specifically, but, in many cases, we cannot so know them, for one reason or another. For example, because counting is a psychological process requiring for each act of counting a specific time, we cannot, by counting, know specifically all the individuals of an infinite class. Yet we do know that there are infinite classes, and that there are individuals which are mem- bers of these classes, "We thus again discover the important difference between knowing "things" as individuals, i.e., by specification, and knowing them by type, by law, by organizing concepts, or by intension, as it is technically called. That the concept of a class should be that underlying reality which mediates the relation between the members of the class is thus disproved. Yet that the concept performs this function is precisely that view to which the underlying-reality theory has been driven by continued and repeated criticism. The result of this criticism has been, when the adherents of the under- lying-reality theory have desired to get to an idtimate and funda- mental unity underlying the whole physical and mental uni- verse, that they have given up "making" this unity either physical or mental, and have been compelled to make it a bare concept. But, by the foregoing criticism, if this ultimate con- cept were a fact, it would be only that concept or relation of similarity which organizes a universe into a whole, and the universe would have only as inach unity as there is siniilarity. 190 METHODS AND PROBLEMS OF METHOD Unless one could prove, therefore, that any two terms must be similar in order to be related, the universe or totality of entities might consist of related, yet of extremely, perhaps of iiholly dissimilar "things." Or, there might be many kinds of "things," hut no one kind of these kinds, such as, e.g., mind, or matter, or existence. However, one cannot exclusively prove that terms, in order to be related, must be similar. Such a con- clusion follows only from the postulate, in accordance with the modification theory of relations, that related terms affect one another and so cause one another to he similar. But this theory has been shown not to be universally valid. For it presupposes that terms, in order that they may be modified, must first be unmodified and yet related. But such ultimate unmodified, non- complex terms might be absolutely different, and still be related. Yet, if terms can be related and yet be wholly dissimilar, there is no relation of similarity that relates them. We conclude, therefore, that inductive evidence for the valid- ity of the underlying-reality theory of relations cannot be obtained from the examination of concepts. The concept is either the organizing relation, known in an abstract idea, or the class as a whole, known in a general idea, but it is not something more than this relation and this class. There is, therefore, no one concept, which, as outside the universe, also unifies it. Indeed, empirical evidence shows that the universe is not one class, or one kind of "Ihings," but that it is many kinds.^^ CHAPTER XXVII TYPES OF RELATIONS, OF WHOLES, AND OF UNITIES I. TYPES OP RELATIONS Science and philosophy are both concerned with relations between "things," and, therefore, also with wholes, which are identical with parts as related in specific ways. Some of the important types of relations have already been " See Chap. XLIV., n. THEORIES OF RELATIONS 191 presented, but these types may here be advantageously sum- marized, using R for relation, and a, b, c, and d for terms.^ I. Every relation has an inverse. Thus, if a is above b {a R b), there is the inverse relation, R, b below a; also, if a=:b, there is the inverse, b =^ a, where R is the relation of equality. II. Relations are also classified as dyadic, triadic, tetradic, etc. A dyadic relation is expressed by the symbol, a R b; a triadic, hy R (a b c) ; a tetradic, hy R (abed). An example of a triadic relation is the relational complex, sender of a mes- sage — message — recipient. III. Further differences among relations are distinguished by the names symmetrical, non-symmetrical, and asymmetrical, and transitive, non-transitive, and intransitive. These different types may be best considered in the case of dyadic relations. Symmetrical relations are such as are identical with their own inverse; i.e., they subsist, if R is the same as R. Examples: equality, similarity, difference, contradiction, consistency. Asymmetrical relations are such as always preclude the iden- tity of the inverse with the original relation. For example, if a precedes b, it is precluded, that b should precede a. Further instances are: "greater than," before, "ancestor of," and "fa- ther of." Asymmetrical relations are sometimes called totally non-symmetrical. Partially non-symmetrical relations are rec- ognized by Royce and Russell,^ these relations being such as do not always preclude the identity of the inverse with the original relation. Thus, if a is friend of b, it may be that b is friend of a (symmetrical), but it may also be that b is not a friend of a (asymmetrical). Transitive relations are such that, if they hold between a and b, and between b and c, they also hold between a and c. Equal- ity, "ancestor of," and "older than," are examples. Intransi- tive relations are such as are never transitive. Thus, if a is the mother of b, and b is the mother of c, it is precluded that a should be the mother of c. ' Cf. Russell, Hcievtific Methvd in Philosophy, p. 40 ff., and p. 124 ff., iiiid Frinciples of Mathematics in various places (see his index); also Koyce in his essay on The Principles ot Logic"' in the Encyclopedia of the Philosophical iiciences, p. 'J7 ti". '' Ibid. 192 METHODS AND PROBLEMS OF METHOD Non-transitive relations are such as are not transitive in some cases, but are transitive in others. Thus, in the case of men, if a is half-brother of b, and b is half-brother of c, a is not half- brother of c, unless a, b, and c have a common parent, which is not necessary. IV. Relations are also distin fished as one-one, one-many, and many-one. If a relation, B, holds only of a to b, but not of a to c, d, etc., then it is a one-one relation. Thus, if a is the twin of b, a is not the twin of c. One-one relations are present in the case of correlated classes, as, e.g., in the possession of a gun by each man of a regiment; also in correlated series, as, e.g., the occupation, by the center of mass of a moving particle, of one and only one point at each instant. If a relation R holds between a and b, c, d, etc., it is one-many, while the inverse rela- tion of b, c, and (Z to a is many-one. For example, rest is a relational whole that is generated by a one-many relation be- tween one point and an infinity of instants, and, conversely, by a many-one relation between an infinity of instants and one point. Existentially this relational whole is generated, e.g., by the center of mass of a body as it occupies a point for many instants. These several types of relations are found not only among dyadic relations, but also among triadic and tetradie relations. Thus the relation of similarity, which is symmetrical, holds between the members of a class, and the class subsists by virtue of this relation. The class is thus independent of the order of its members; R {a d c b) is the same as R {a b c d) — as a class. If, however, a, b, and c are each a class as, e.g., are Frenchmen, men, and mortals, then the triadic relation, R, of inclusion, a See Chap. I.-III. 203 204. INTRODUCTORY One result was the birth, or rebirth of those empirical methods which have largely created our modern material civilization. But, while the Renaissance was characterized by the adoption of new methods of knowing, it did not apply these to the study of knowing, as itself constituting a problem. This problem first received clear recognition in the investigations of Descartes (1596-1650) and, more especially, of Locke (1632-1704), with the result that, throughout the modern period which follows these philosophers, other philosophical doctrines have, for the most part, been based on epistemologies. Indeed, that characteristic which marks this whole period in philosophy, even to the present, is the domination of the epistemological problem, although it may be, that in the near future, this domination will cease, because it will be proved, that human beings can know without first ascertaining how knowledge is possible, and what is its extent and origin. Science all through this modern period developed with rapid strides, and to a large extent independently of the philosophy of knowledge, both as regards the facts disclosed and the method of their discovery. This development was characterized by the use of new means of knowing which for a long time were not understood in all respects, but which today have become better known, with the result that there is an increased efficiency in scientific method. The new logic, with its emphasis of relations, and the like, is itself a product of the modern study of such methods, and it is to this new logic that we must turn for the solution of many problems in both science and philosophy. With such an extensive scientific development characterizing the modern period, and yet with so little attention given to the epistemological problem by the scientists themselves, the ques- tion arises, why this problem has exercised such a controlling influence over philosophy. The answer to this inquiry is, that such an influence has been due not only to the interest in the knowledge-problem itself, but also to the fact that certain specific solutions of the problem would seem to present a way by which men should be able to prove real that which they would prefer to be real, and also able to prove false or illusory that which they would have of this character. For it is a fact, that, for one reason or another, mast men prefer that, e.g., evil THE PROBLEM ABOUT PROBLEMS 205 were not evil, pain, not pain, hate, not hate, and death, not death, even as they prefer that such "things" as goodness and beauty and life and love should not be illusory, but quite real. All else may be lost, if these but be saved; all else be illusion and appearance, if these but remain the realities. But how, indeed, does epistemology offer opportunity for saving that which men would have saved, and for demonstrating as illusory or as merely apparent that which men perhaps detest and abhor? Why, indeed, should appeal be made in any way to philosophy? Cannot the momentous questions that concern the saving of what men would, in most cases, prefer to have saved, be settled on their own merits, or, at least, by an appeal to science. For does not science reveal to us suns and stars, the depths of space, and the eons of time; does she not pene- trate beneath the surface of "things" to disclose otherwise hidden forces and energies; does she not picture both the macro- cosmically great and the microcosmically small? Then why, also, should not God and soul and immortality, justice and goodness and beauty, come within her realm to lose their secrets too? The answer is, that science, in that it deals with such things as suns and stars, energies and forces, molecules and atoms, has to do with that which is known, hut that, as unknown, ''things'' may be so different from what they are as known, as to be the realities, with the known "things" mere appear- ances or illusions, so that it may be among ''things" as unknown that the science of what is hoped for is to be sought and found. Who can deny that this may not be so? For does not fire make the iron red? Then may not the awareness be to both the fire and the iron, even as the fire is to the glowing and the redness. Epistemology, or rather, certain epistemological the- ories accept this analogy as a principle. For they find, not only that all "things" known are related to the knowing, or to the knower, and that to know what anything would be, or be like, as unknown, is impossible, since this would be again to make the unknown known, but also that knowing makes a difference to "things," even as the fire does to the iron, so that we can never know without making such a difference. How great shall this difference be ? Could it be such a radical difference as to include such characteristics as extension and 4b§ iNTRODUCTdRY duration, hardness and coldr, manifoldness and unity? That ihis is not impossible, is the position that is sometimes insisted upon by those who emphasize epistemology. The situation, that knowing eatinot be elithiriated from the world that we know, is called the "ego-centric predicament"; while the position that knowing makes the world what it is in at least certain respects, is an instance of the application of the modification theory of relations. The outcome of these two premises or postulates is most interesting, and appeals to our hopes and desires. For known ''things" seem in some instances to be evil and unfriendly, hopeless and forlorn, ugly and fore- bidding, rigid and mechanical, and, in general, of little promise. But, iy the premises just mentioned, may not all these unde- sirable "things" be due to the difference that is made hy know- ing? Then enter the realm of the good and the affectionate, the hopeful and the inspiring, the beautiful and the enlightened, the plastic and the free, not by knowledge, but by faith and intuition. These are what one desires, and thus it is that one can argue oneself into the possibility of their attainment. II. THE VALUE-CENTRIC PREDICAMENT ^ If the ego-centric predicament is thus taken advantage of, in order to demonstrate the attainability, or, at least, the reality of that which one would prefer real, the suggestion lies near that an analogous predicament may exist through the fact that our knowing is always related to our desires, our preferences, our yearnings, and, accordingly, perhaps, that our desires and preferences cannot be eliminated from our knowing. Such a situation may be somewhat awkwardly called the value-centric predicament.^ " See, e.g., James' discussion of tough-mindedness and tendsr-mindednesB in Chap. I. of Pragmatism. However, why the pragmatist, who is ad- mittedly a tough-minded individual, should seek to convert the tender- minded philosopher, whose point of view and system satisfy his own vital needs, is a puzzle from the standpoint of Pragmatism. ° N. Kemp Smith, "How Far is Agreement Possible in Philosophy?" Jour, of Phil., Psych., and Scientific Methods, Vol. IX., p. 701 flf. ; see also the report of the twelfth annual meeting of the American PhiU)8ophical Association, J. B. Pratt, Jour, of Phil., Psych., and Scientific Methods, Vol. X., p. 91 ff.; cf. also Marvin, First Book of Metaphysics, Chap. I.; Sir Henry .Jones, Idealism as a Practical Need, 19UU; and J. G. Hibben, Philosophy of the Enlightenment, 1910. THE PROBLEM ABOUT PROBLEMS 207 This predicament — if it is such — lias two forms of which the one concerns us chiefly as individuals, the other, our member- ship in a social group, whether this be narrow in its confines;, or so wide as to include all human beings. The effect of the predicament is, accordingly, that, if you as an individual desire an evil nullified, then do you accept as true only that philosophy which in some way does away with evil; but the effect is also, that, if you and I both have those hopes and longings which are inherited from our forefathers and from our race, then do we endeavor to save whatever is thus valued, by accepting only such a transformation of common sense and of science as will accomplish this result. Yet finally we may become aware of such an influence of our desires and preferences on our knowing, and therefore, in the attempt to eliminate this influence, we may reach that point where ive prefer truth at all costs — no matter what the truth may prove to be. But the question then arises, whether we are not thereby valuing truth itself, and therefore making truth a value, thus to condition it, like other values, by our preferences and our desires. In answer to such an inquiry, it may, however, be further asked, whether, e.g., the fact that I prefer sincerity in all those with whom I have to deal in any way, prevents me from discov- ering that in some cases sincerity is wholly absent? But, if sincerity can be found to be absent, although I prefer its pres- ence, then are not my preference and that which I prefer inde- pendent, although they are r elated f Similarly, does not the fact, that, although I value truth, I may nevertheless fail to find it, prove that my valuing and truth are independent, though related? And finally, if I desire to know, and yet what I desire to know is the truth for its own sake, no matter what the specific truth may be, then may not any specific knowing, with any specific content, be absent, even though I prefer to find such content present? But does not this possible absence prove that any specific knowing — of any specific content — although related to desire and preference, is independent of these? In other words, is there not at least a virtual elimination of desire and preference from any specific knowing — an elimination which means, that, when the desire to know is directed toward getting 20S INTRODUCTORY at the truth for its own sake, irrespective of what the specific truth may turn out to be, the value-centric predicament is solved f Such a solution of this predicament is, as a matter of fact, presupposed all through science in its method of awaiting the outcome of hypotheses and theories, without either believing or dishelieving them, and the situation is not, of necessity, different in philosophy. Accordingly we conclude, that, although many philosophical systems have resulted, at least in part, from the endeavor to save those worths and values which men would prefer to he saved, nevertheless, the disinterested attitude is quite as possible in philosophy as it is elsewhere, and that the logical justification of this attitude is, that, although "truth for its own sake" is related to (this specific) preference, the truth and the preference may, nevertheless, he quite independent. III. THE SOLUTION OP THE EGO-CENTRIC PREDICAMENT The same principles which enable us to solve the value-centric predicament also make it possible to solve the ego-centric pre- dicament. In fact these principles form a most important method for both science and philosophy. In a great many instances of entities which we wish to analyze, it is impossible experimentally to remove the parts which analysis discovers. All the parts must be left in situ, and yet, if possible, we must discover not only the parts, but also the relations between the parts. This method must be pursued, e.g., in his- tory, since we cannot alter the past ; in sociologj'^, since we cannot to any great extent manipulate sociological and economic forces ; in geometry, since we cannot experimentally remove the parts of space; and also, in a great many instances, in such sciences as physics, chemistry, and astronomy. Where we can, we experi- mentally remove a thing, A, that is in relation to B, from its presence and relation to B, in order to discover, whether, thereby, B is altered or removed ; if it is, then we conclude that A influ- ences, or causes B, or that B is functionally related to A; if it is not, then A is not such an influence, or cause, or variable. However, in the fields of research just mentioned, it is im- possible always to determine experimentally the question of influence, cause, or function. Therefore, if we analyze, we must THE PROBLEM ABOUT PROBLEMS 209 leave the parts together, — in situ — to determine their depend- ence or independence.* Such a procedure is successfully prac- tised in a great many cases, especially in science, in order to find specific functional relations. Thus, in the case of a moving projectile, there is the color, the shape, the chemical composition, the mass, the gradually retarded motion (negative accelera- tion), and the explosion that sets the projectile in motion. No projectile is without all these characteristics, with each one of them of some specific (numerical) value, as determined by some scale of measurement; and although any specific value can be substituted by another specific value of the same character, e.g., the mass of 100 lbs. for the mass of 50 lbs., nevertheless no one of these generic characteristics can be experimentally removed from a moving projectile. Rather, each such characteristic must be left in the presence of the others, while their specific relations to one another are, if possible, determined. Analysis shows, however, that, e.g., although the retardation requires time, it does not cause time, nor time cause it, although the two are related. Rather the retardation is found to be a function of the time; related to time, and time to it, time is nevertheless independent of the retardation. The time is the independent variable, the retardation the dependent variable. Thus the time is functionally related to the retardation, but is not an effect of it. In such an instance, therefore, the specific retardation and the specific time must each be left in situ, and yet we discover not only that they are different and distinct, but also that, though related, they are independent. But there are, of course, causes for the retardation, as well as for the motion as a whole and for the initial velocity. Dif- ferent "things" can be distinguished, namely, the distance traveled, the time required, the initial velocity, the final stop- ping, the initial "angle of flight," the mass of the projectile, the force of the explosion, and, finally, the relationships of these entities to one another can be determined, and theij:* dependence or independence be ascertained. Omitting unnecessary details, it may be said, that, by studying various instances of moving projectiles in which we are obliged to leave in situ the several parts, it is discovered, that the motion as a whole, with its *Cf. Chaps. XXII and XXVI. 210 INTRODUCTORY several characteristics, either depends functionally upon, or is caused by, (a) the explosive force, (b) the angle of elevation of the gun, (c) the mass of the projectile, (d) the resistance of the air. Change any one of these, keeping the others constant, and the total motion, with its characteristics of change of velocity and distance covered, is changed. Color, however, makes no difference, nor does the chemical composition of the projectile, provided the same mass is retained. Here, then, analysis in situ reveals two sets of entities that are related to the motion. One set, namely, the explosion, the force of gravita- tion, and the mass, are constituent causes, variables or "ele- ments" in the motion; the other set, namely, the color and the chemical composition of the projectile, are not such causes, elements, or variables. This example illustrates a most important power of achieve- ment of modern scientific analysis. "Things" can be analyzed, parts be discovered and distinguished, and yet left in situ, and relationships be ascertained. Three kinds of relationships ap- pear, namely, (1) functional, in which an independence of re- lated terms is discovered ; i.e., the terms are related in such a way that, if any term were eliminated, the elimination would make no difference to the other terms. There can be only an ideal elimination of such parts. Therefore the analysis must be made in situ. (2) Causal relationships are revealed. In these a specific dependence of specifically related terms is shown. In this case certain terms are what they are by virtue of their relation to other terms; i.e., the relation between them is con- stitutive. (3) Both non-functional and non-causal relationships. In these it is shown, both by actual and by ideal elimination, that there is not only no causal dependence of certain terms, but also no functional connection. In the case of terms thus related, each term is independent, no term is constituted by others, any term can be eliminated without a resulting effect on others, and no term makes a difference to others. For ex- ample, mass and time are thus independent. The ego-centric predicament can be solved, now, by this same method of analyzing in situ, and of thus discovering parts and relations, and the specific character of each. This predicament consists, as we have seen, in the impossibility of experimentally THE PROBLEM ABOUT PROBLEMS 211 eliminating a knowing process as really occurring, or as implied as really occurring, from the world that we know. In other words, the world that we talk about, think about, mention, or know, is a known world. The predicament has most important consequences provided knowing makes a difference to the entity known, but it is of no importance, provided it can be shown, that knowing makes no difference to that world. If this last principle can be established, then it follows that the world as unknown can be quite the same as the world as knoivn, and knowing must be concluded not to be causally related to that world. If, now, it cannot be shown by an experimental elimination and analysis, that knowing is thus related independently to the entity known, nevertheless, an analysis in situ, and an ideal elimination of knowing suffice to furnish this demonstration. Such an analysis and elimination is, in fact, made by every philosopher and scientist who, even in a philosophy that ex- plicitly maintains the opposite, advances any position as a portrayal of the real state of affairs regarding knowing.^ For example, if one is a follower of Kant, and accordingly main- tains, that all knowing makes a difference to the object to be known, i.e., alters it, modifies it, and the like, so that there is a specific and marked difference between the object as known and as unknown, then does not one present this position as the real state of affairs regarding knowing, with this state of affairs nevertheless in relation to a specific knowing as its content or object? But does not one therewith make an exception to the rule that is stated in the position? For does not one tacitly grant and presuppose, that here is one instance, at least, in which knowing is related to its object, and yet does not alter, modify, or constitute that object? And does not one tacitly presuppose, that, *"/ this specific knowing were not taking place, this state of affairs regarding knowing would still persist as the real one? To these questions there seems to be no other answer than "yes." In fact, every philosopher who presents any position in solution of the problem of knowing, tacitly presupposes " See the criticisms of systems opposed to Eealism, Chaps. XXIX.- XXXVIII.; also Chaps. I., II., and III. 212 INTRODUCTORY that the facts which are therewith known are not causally de- pendent upon being known, either by himself or any one else. Every such philosopher thus really solves.the ego-centric predica- ment for himself. Indeed, he solves it, even though in the particular solution which he advances, he may make use of this predicament in order to demonstrate its insolubility, and the consequences that result from this. However, with the ego-centric predicament quite soluble in this way, it should no longer be regarded as serious, or as having important consequences. For if in one typical instance, know- ing can be related to, and yet not cause, alter, or modify, that which is known, so that in this one case knowing is ideally eliminated, then the presumption is, that in all cases of knowing the same state of affairs subsists. To advance any other posi- tion means, that at a certain point an exception is met with that contradicts such a position. Indeed, that knowing makes a difference to its object, is a position that is self -contradictory, while, on the other hand, that knowing is not causally related to and makes no difference to the object knoivn, is a position that can be advanced and maintained quite consistently with itself as a true position. This position is self-consistent, because the proposition, that knowing does not make a difference to its object, itself logically allows one in this very instance to advance this as the real state of affairs concerning all knowing, including, therefore, the specific knowing, that this is the state of affairs concerning all knowing. This self-consistent position is an instance of the validity of the theory of external relations which formulates the fact that terms can be both related and independent. One interesting and important implication of this position, which is presupposed by its own denial, is, that knowing or knower cannot be a thing or substance.^ For, if it were, then it would affect other things. Therefore, in order to understand the real nature of knowing, we must not use the traditional logic of substance and attribute, but the 71CIV logic of relations.'' We must use this logic, because it is empirically discovered to be that logic which is involved in any situation of genuine knowing. For knowing turns out • Cf. Chaps. III., XIII., and XXVII. ' Chap. XXVII. THE PROBLEM ABOUT PROBLEMS 213 to be, not a thing or substance^ but an event, a relation, a dimen- sion, or even a disembodied quality, with the object known entering into and getting out of relation to the knowing, while still maintaining its relations to other objects.^ The critical study of the opposed position, that knowing is in some way related causally and constitutively to its object, shows that this is a conclusion which is derived (1) from the arbitrary, though unconscious, application of the modification theory of relations^ to the specific relational complex, knowing and known object, and (2) from the somewhat surreptitious postulation of the underlying-reality theory of relations to the knowing, or to the knower, whereby the knower is regarded, tacitly at least, as a psychical substance (ego, self, spirit), and, therefore, as a sort of thing with attributes (the knowing states or processes). Either of these two postulates has carried with it the other postulate, and the reason why one or the other postulate has been made, is, that the model of the particular physical thing, with the two derivative concepts of substance and of cause, has for the most part dominated philosophical and even some scientific thinking from the time of Aristotle to the present." For in this tradition "things" are regarded not only as groups of qualities that inhere in a substance, but also as entities that causally act on, influence, and modify one another, with the effect dependent not only on the thing acting, but also on the thing acted upon. Thus the effect cf melting produced by a red-hot cannon ball an inch from a candle is as much dependent on the candle as upon the cannon ball. Substitute an iron bar for the candle, and the effect is different. It is clear, then, that, if the principle thus illustrated is generalized and applied to certain problems or situations, certain specific con- clusions by way of solutions to these problems are deducible. But it is precisely this generalization and this application that have been made, at least tacitly, in the reasoning out of a number of the great philosophical systems of history, especially those that are based on a prior solution of the problem of knowledge. The generalization and the application have taken place pari passu. The generalization has been made on the tacit or unconscious assumption (1) that the type or model for all, " See Chaps. XLIII., iii. and xi. ' Chap. XXVI., ii., 2. '" Chap. III. 214 INTRODUCTORY or for most entities, is that of a thing and its qualities, with the qualities inhering in the substance of the thing; and (2) that the most important relation between "things" is the causal. Thus, in philosophy such entities as matter, soul, God, per- sonality, the universe, ideas, concepts, and percepts, and, in science, atom, force, energy, have been made things with attri- butes, while in logic the result has been, that reasoning has concerned itself (1) with substance-like individual things and their identity with themselves, (2) with kinds or classes of things, and the relationship of inclusion, complete, partial, or negative, of these kinds, (3) with the causal relationship between things, and (4) with the kinds of causation. Aristotle, with substance as his leading category, illustrates one phase of this influence, as does Descartes with his two substances, mind and matter, and Spinoza, with his one sub- stance, God, of which mind and matter are attributes. Modern Objective Idealism, or Psychism, with its doctrine of one spirit- ual substance, of which everything else is manifestation or attribute, exemplifies the same controlling influence," as do also Locke, Berkeley, and Kant in their respective doctrines of a mind, a perceiving spirit, and a transcendental ego}- Science also shows the same influence in its older mechanistic theory, that all matter and all physical events consist of the motion of minute extended things or particles. On the other hand, as illustrating the other main phase of the influence of this great dominating tendency and tradition, we have, e.g., the Phenomenalism of Kant, and the Idealism of Berkeley, with their common position, that we can know only the (causal) effects of "something" that acts on our "minds." But also Naturalism (developing out of Hume's Positivism), Materialism, Pragmatism, and Komanticism are examples of positions that are developed from the postulate of universal causal interaction. The two principles which have thus been used as postulates from which such specific philosophies have been deduced as derivative results are respectively, as logically formulated, the underlying-reality theory of relations, for the substance phi- ^^ E.g., Bradley, Appearance and Reality, pp. 141, 143. »* Chaps. XXIX. and XXX. THE PROBLEM ABOUT PROBLEMS 215 losophies, and the modification theory of relations, for the causation philosophies. Both theories, however, can be present, in any one philosophy, as applying to different situations. These two theories together form what we have previously called the two aspects of the theory of internal relations. Ac- cordingly, with the problem of knowing the pivotal point for most modern philosophical systems, it is this theory of relations, with its two aspects, that has been applied to the several phases of the relational complex, knowing and known object. From such an application, or postulation, specific philo- sophical systems have been derived. This postulation as made historically, has been, in most cases, unconscious and uncritical, since it has been due to the influence of the tradition of which the two aspects of the theory of internal relations form the logical core. However, at the present time, with the logical character of the tradition itself come to consciousness, and with the opposed theory of external relations, as instanced in science, also known, it is possible to derive the several chief systems of philosophy in a purely logical manner by freely postulating one or another of the three theories of relations as applying to the complex, knowing and known object, in its several aspects, and by then deducing the logical consequences of these postulates as so applied. This method will be pursued in the sections that follow. Solutions of the other major problems of philosophy will then be derived logically from these same postulates, or from those solutions to the epistemological problems which are derived from such postulates, in a manner that in general corresponds to the historical dependence of the solution of these other problems on the prior solution of the problem of knowing. SECTION II CAUSATION PHILOSOPHIES CHAPTER XXIX PHENOMENALISM Phenomenalism may be defined briefly as that philosophical position which maintains, that, by the very nature of the know- ing situation, it is possible to know only phenomena or appear- ances, but not "things" as they really are; or, more briefly still, that "things" as they really are, are unknoivahle, and not merely unknown. This position is identified historically with the name of Immanuel Kant (1724-1804). We shall present this position, not as it was consciously developed, temporally and historically, by Kant and other phe- nomenalists, but logically, according to those principles that were unconsciously and uncritically assumed by Kant, and that, as postulates, form a sufficient basis from which to deduce the phenomenalistic philosophy. Thus we shall examine this position much as a modern geometer examines the geometry of Euclid, namely, not in the sequence in which Euclid developed it, but critically in regard to the postulates upon which it depends, and the logical sequence of propositions that result from such postu- lates. I. THE LOGICAL DERIVATION OP PHENOMENALISM In order to make such a logical derivation of Phenomenalism, let us assume, as Kant really did under the influence of the Aristotelian tradition, (1) that the knoiving self is a psychical "thing" with attributes (categories, percepts, concepts, and the like), i.e., an absolutely unitary being (ego) in which there 'in- here," or which holds together, certain specific mental attri- butes * called categories, concepts, percepts, and the like. Let us symbolize such a self by K8 (knowing self). ' Although in his discussion of the Paralogisms (see, e.g., Watson's Selections from Kant, pp. 145-155) Kant denies that the concept of suh- 216 PHENOMENALISM 217 Let us also assume (2) that, as numerically distinct from such a self, there is a "thing" or entity, X,' that is to be known, if possible. In thus assuming both KS and X to be thing-like entities, it may be that the modificatmi theory of relations is also already assumed for the relational situation ES R X (object-to-be- known-related-to-the-self-that-knows-that-object), for, in accord- ance with the traditional logic, things interact; but, if this assumption is not therewith made, then (3) let it be made explicitly. From these three assumptions the consequence can be de- duced, that KS and X, as in relation to each other, interact, so that a twofold effect is produced. X acting on KS produces an effect called sensation, which we will express by KS^,^ while stance is applicable to the transcendental ego, nevertheless it can be shown that throughout his entire philosophy Lie regards the knowing self, not as a process, quality, or relation, but as a substratum-like entity in which both a priori concepts (categories) and empirical experiences (sensations and ideas) inhere. ^ Kant's " thing-in-itself," all through his Critique of Pure Reason. ' See Miiller's translation, Transcendental Esthetic, ed. 1896, pp. 16-17. As here translated, Kant says: — " Whatever the process and the means may be by which knowledge reaches its objects, there is one that reaches them directly, and forma the ultimate material of all thought, viz., intuition (Anschauung) . This is possible only when the object is given, and the object can be given only (to human beings at least) through a certain affection of the mind ( Gemiith ) ." " This faculty (receptivity) of receiving representations (Vorstellungen), according to the manner in which we are affected by objects, is called sensibility (Sinnlichkeit) ." " Objects therefore are given to us through our sensibility. Sensibility alone supplies us with intuitions ( Anschauungen) . These intuitions be- come thought through the understanding (Verstand), and hence arise conceptions (Begriffe). AH thought therefore must, directly or indirectly, go back to intuitions (Anschauungen), i.e., to our sensibility, because in no other way can objects he given to us." " The effect produced by an object upon the faculty of representation ( Vorstellungsfahigkeit), so far as we are affected by it, is called sensation (Empfindung). An intuition (Anschauung) of an object, by means of sensation, is called empirical. The imdefined object of such an empirical intuition is called phenomenon (Erscheinung) ." " In a phenomenon I call that which corresponds to the sensation its matter; but that which causes the manifold matter of the phenomenon to be perceived as arranged in a certain order, I call its form." " Now it is clear that it cannot be sensation again through which sensations are arranged and placed in certain forms. The matter only of all phenomena is given us a posteriori ; but their form, must be ready for them in the mind (Gemiith) a priori, and must therefore be capable of being considered as separate from all sensations." (Italics mine.) $18 CAUSATION PHILOSOPHIES K8 acting on X produces an effect, X^^, the known object "over against" the sensation as psychical "attribute."* In other words, with it necessary, in order to know, that K8 should be related to X, it follows, on the assumption or postu- late, that relatedness means dependence, and dependence, modi- fication, that both KS^ and X^^ are of necessity produced in the act of knowing. Neither is produced without the other, and each is produced with the other. If there were no K8 to be in relation to X, there would be only X, but no X^^^; so, likewise, with no X in relation to KS, there would be no E8^. But, KS and X are, or, at least, knowing and object known are. For knowing, as Descartes showed, seems to be implied by its own attempted denial. Doubt knowing, and there still is cogitans. Also, to know without knowing something (an object), seems to be impossible. Indeed, to think of a knowing without an object known is again to reinstate an object. If, then, both K8 and X are, and if, being, they are related, and also if, being related, they interact, then there are, also, K8^ and X^^. K8^ and X^^ as effects imply K8 and X as causes.^ Not only is X^^ different from X, but, since KS^ is the effect of X acting on KS, it is also different from KS. KS is the original thing-self, while KS^ is the stream of sensations, and the like, which constitute the "empirical self" and which we get at by introspection and memory. X, on the other hand, is the original thing -in-it self , the "thing" as it really is, while X^^ is the thing of the material or physical world, known in sensation, and in all that knowledge which depends on and is derived from sensation. With X and Z^«, and KS and K8^, respectively, dif- fering and, in some respects, distinct from each other, it is important to ask. How different are they in each case, i.e., how does KS differ from KS^, and X from X^^f In order to determine this, it is evident that one must, if possible, get at or know X by itself, i.e., as X is unrelated to and unmodified by KS, in order to contrast X with X^^, and also get at or know KS, in order to contrast it with KS-^. * Cf. C. N. Broad. Perception, Phpsics, and Reality, 1014, Chap. V. on the Causal Theory of Perception, especially pp. 18()-187 and 204-206. • Pointed out, e.g., by G. E. Schulze in his JEnesidemus, 1792. PHENOMENALISM 219 Otherwise one must rest content with KS^ and X^^, knowing only that they are different from KS and X, but not how dif- ferent. However, to succeed in such an attempt to know X by itself is impossible for the reason, that success would mean again to relate X to KS, and, therefore, to make it X^^. Thus it results that it is only X^^ that we can know. In other words, the very attempt to know what "the world" would be like if it were not known, only again brings in the knowing, and so defeats itself, since, by assumption, knowing makes a difference to that which is known. Here, it is evident, the ego-centric predicament * appears, but it is also evident that certain specific consequences result from this, because it is also assumed, that knowing makes a difference to the object known. Accordingly, with this assumption actu- ally made, as it was, e.g., by Kant, because of the influence of tradition, it follows, that, unless the knowing can be eliminated in some way, such as by the method of analyzing in situ, then that difference which knowing makes cannot he eliminated from the known world — which is the only world that we know. Such an outcome means, however, that our world is one that is made, at least in part, by knowing, and that it is in just this sense a world of phenomena or appearances.'' Another world — of things- in-themselves — of X's is, of course, implied, as standing in con- trast with these phenomena, but such a world can never be known — unless to discover that which is implied is to know. But, if this should be the case, then it must be granted either that such knowing modifies its object, thereby making that object mere appearance; or that the object that is known — hy heing found to he implied — is known as it really is. But, if this last be the case, then the proposition — basic for Phenomenal- ism — that ttvo related terms (in this instance, knowing and object known hy implication) causally influence each other, ia contradicted, and Phenomenalism as a position becomes self- contradictory. The position that is derived logically in this relatively simple ' The writer assumes that this predicament is now understood by the reader. See Chaps. X., XXVIII., XXXIX., XLI. ^ Terms also used all through the Critique. 220 CAUSATION PHILOSOPHIES manner is tlie essence of the phenomenalistic philosophy. The presuppositions or postulates from which the position is derived are (1) the modification theory of relations, namely, that related terms as related modify or influence one another; (2) that the known object and the knowing are (of course) an instance of related terms; and (3) the ego-centric "situation," to the effect, that knowing is always present to the (only) world that we know, and cannot be eliminated in any way — even by an analysis in situ. The further development of the position results from the making of further postulates, one of the important details of such a development being the conclusion or result, that, although things-in-themselves, X's, cannot be known (except by implica- tion), nevertheless the "original" self, K8, can be known in its real and genuine character.^ To present the logical development of such an outcome, let us examine the postulates already made, and, if necessary, also ^Critique, Milller's translation, ed. 1896, p. 41; here Kant says: " We call sensibility the receptivity of our soul, or its power of receiving representations whenever it is in any wise afl'ected, while the understand- ing, on the contrary, is with us the power of producing representations, or the spontaneity of knowledge. We are so constituted that our intuition must always be sensuous, and consist of the mode in which we are affected by objects. What enables us to think the objects of our sensuous intuition is the understanding. Neither of these qualities or faculties is preferable to the other. Without sensibility objects would not be given to us, without understanding they would not be thought by us. ' Thoughts without contents are empty, intuitions without concepts are blind.* There- fore it is equally necessary to make our concepts sensuous, i.e., to add to them their object in intuition, as to make out intuitions intelligible, i.e., to bring them under concepts. These two powers or faculties cannot exchange their functions. The understanding cannot see, the senses cannot think. By their union only can knowledge be produced. But this is no reason for confounding the share which belongs to each in the production of knowledge. On the contrary, they should always be carefully separated and distinguished." Also, Kant says (Miiller'a trans., ed. 1896, pp. 4-5-46) : " On the supposition therefore that there may be concepts, having an a priori reference to objects, not as pure or sensuous intuitions, but as acts of pure thought, being concepts in fact, but neither of empirical nor aesthetic origin, we form by anticipation an idea of a science of that knowledge trhich belongs to the pure understanding and reason, and bp which ice may think objects entirely a priori. Such a science, which has to determine the origin, the extent, and the objective validity of such knowledge, might be called Transcendental Logic, having to deal with the laws of the understanding and reason in so far only as they refer to objects a prion, and not, as general logic, in so far iis they refer promiscu- ously to the empirical as well as to the pure knowledge of reason." (Italics mine.) PHENOMENALISM 221 make other postulates. Proceeding in this way we find, that the postulates already made mean not only that KS and X are distinct, but also that they are each active. Let us next set up the two further postulates, (4) that that which is self-evident is true, and (5) that that whose opposite is inconceivable is true. We then find hy hoth these tests that it is true (6) that any active thing, or, that a thing, if it acts, must act in accord- ance with its own nature. From this last proposition, as conjoined with postulate (1), it follows that KS, the knowing self, must, whenever there is knowing, act in accordance with its own nature — whatever this nature may be. Accordingly, the problem becomes one of find- ing, if possible, i.e., of knowing what the nature of KS is. But this problem is solved by finding and enumerating all those most generic ways in or by which we must think or know. For, on the one hand, if a "thing" must act in accordance with its own nature, and cannot act in contradiction to this nature, then, on the other hand, and conversely, those ways in which KS must act or think or know will constitute its nature, and to discover what those ways are will be to discover and to know what the nature of KS is. But what those ways are in accord- ance with which KS must act, is shown by finding what princi- ples are such that they are either (7) self-evident, or (8) are presupposed by the very attempt not to use them, or (9) are of such a character that their opposite is inconceivable.'* For, if there is revealed in this way a specific compulsion on KS to use certain principles when it acts or thinks, then by postulate (6) this compulsion is explainable by the hypothesis, that such principles make up the nature of KS, so that to know these principles is to know KS. With this the method by which there are ascertained those principles which are apodictic or necessary for thinking and for * Cf. Chap. XI., v.-vii. ; see the Critique, Miiller's translation, p. 24, for this principle. Here Kant says: — " Space is a necessary representation a priori, forming the very founda- tion of all external intuitions. It is impossible to imagine that there should be no space, though one might very well imagine that there should be space without objects to fill it. Space is therefore regarded as a condition of the possibility of phenomena, not as a determination produced by them; it is a representation a priori which necessarily precedes all external phenomena." 222 CAUSATION PHILOSOPHIES knowing, and which constitute the nature of the '' transcendental self," K8, it is evident that the particular list of principles that one may find, is dependent upon the outcome of applying the criteria by which one determines what one must think. These criteria are, respectively, as we have seen, self-evidence, the inconceivability of the opposite, and presupposition hy denial. But since the first two of these criteria are, as we have previ- ously discovered, distinctly psychological tests, and the third, although logical in character, is open to error in its application, the results obtained by using these criteria vary from individual to individual, differing with differences in temperament, train- ing, and intellectual environment and influences. Indeed, only a meager inquiry shows that what is self-evident to one person is not self-evident to another, and that that which cannot be conceived by one is readily conceivable by another. We should, therefore, expect to find a considerable variation in the lists of those principles which the several adherents of Phenomenalism present as categories, or laws of thinking, and such a variation is found. For Kant, however, the list of such principles included space, time, unity, plurality, totality, substance and attribute, cause and effect, actuality, possibility, necessity, quantity, quality, relation, modality. If, now, there are such "laws of thinking," as the attributes of a thing-like transcendental self, certain interesting conse- quences follow. First, it follows, that these principles are not derived from the residts of the seeming action of ordinary things, X^^'s, on our sense organs (which are also X^^'s) ; i.e., they are not derived from our sensations, K8^, but, rather, they are in some manner "in" the self, KS, and so are prior to ordinary "things" and sensations. Ordinary "things" and sensations are constituted by the interaction of KS and X. But these laws are already in K8 prior to this interaction. Accord- ingly there can be certain sciences such as those of number, of space, of time, of space related to time, i.e., of motion, and these sciences (1) are independent of sense experience, so that (2) they cannot be contradicted by sense experience, and (3) are necessarily true. Secondly, the interesting consequence follows, that these prin- PHENOMENALISM 228 ciples and all that is rigorously derivable from them are con- stitutive of the world that we live in and know through our sensations. For, if that world is the partial effect of the know- ing self, KS, as it acts on unknowable X's, then the effects so produced are dependent on that self's nature or attributes. But some of the more important of these attributes were (for Kant) space, time, cause, and substance. Therefore the world which we know is spatial, temporal, causal, and substantial, because it is made so by being known. In contrast with this world, how- ever, the unknowable world of X's does not of necessity possess these characteristics, although it may possess them. It is evident, therefore, that Phenomenalism allows not only for two distinct kinds of objects, namely, for things-in-them- selves, X's, and for phj^sical objects, X^^'s, but also for two distinct kinds of selves, both of which are, however, known. Thus, on the one hand, there is the original transcendental thing-self, KS, with its attributes, namely, tJie principles of knowing. The traditional definition of a thing, as a unitary substance in which attributes inhere, is, however, the model for this conception. This self is sometimes called by Kant the "transcendental unity of apperception," meaning by this that knowing in its several forms and in its manifoldness belongs to a numerically single knower. And, on the other hand, there is the empirical psychological self, KS^, that consists of the stream of sensations, memories, concepts, emotions, and the like, and that is the effect of things-in-themselves, X's, acting on tran- scendental selves, KS's. Kant in developing his Phenomenalism explicitly stated that the laws of the transcendental self, the categories, were applica- ble only to phenomena, meaning by this, that phenomena must bear their impress, i.e., that phenomena must be causal, spatial, temporal, substance-like, etc., because of the effect which knowing produces on the thing (to be) known. What, then, about the psychological phenomena of the em- pirical self that are given by introspection, memory, and the like? Do the categories apply to them also? Or, just as know- ing imposes its laws on things-in-themselves to produce physical phenomena, do, conversely, things-in-themselves, X's, impose their nature on the transcendental selves in producing the KS^'s, 224 CAUSATION PHILOSOPHIES so that KS^'s are different from X^^'s, and have different cate- gories applying to them? Yet again it may be asked, whether, as known — by a knower — the empirical self should not bear the impress of all the knowing principles that reside in the tran- scendental knower, and, therefore, be spatial, causal, temporal, substance-like, etc.? Such questions indicate certain inconsistencies in the phe- nomenalistic philosophy — and Kant himself did not remove them. But the reason why he did not do so may well be, that they are inherent in the position and, indeed, irremovable, even as irremovable as the inconsistency of the Critique of Pure Reason itself, in, on the one hand, portraying and maintaining it to be the real and quite knowahle state of affairs concerning the know- ing situation that, on the other hand, the reality of '^ things" is unknowable and that our knowledge is limited to appearances. II. phenomenalism's solution of problems It is not our purpose, however, to present the m