Digitized by the Internet Archive ' in 2007 with funding from Microsoft Corporation http://www.archive.org/details/elementsoflogicoOOboydrich ELEMENTS OF LOGIC ON THE BASIS OF LECTURES BY WILLIAM BARRON, F.RS.E. PROFESSOR OF BELLES-LETTRES AND LOGIC IN THE UNIVERSITY 01 ST. ANDREWS. LARGE SUPPLEMENTARY ADDITIONS, CliJEFIA FROM WATTS, ABEECEOMBIE, BEOWN, WHATELY, MILl-, AND THOMSON. EDITED AND COMPILED BY Pkof. JAMES E. BOYD, D.D., AUTHOR OF ELEMENTS OF RHETORIC, EDITOR OF KAMEs' CRITICISE AND OF ENGLISH POETS WITH NOTES, ETC. °f THC university , t cond (revised) edition. OF A. S. 13AKNES & COMPANY, NEW YORK AND CHICAGO. "A "Well of English Undented.' LITERATURE AND BELLES LETTRES. PROFESSOR CLEVELAND'S WORKS. A WHOLE LIBRARY IN FOUR VOLUMES. COMPENDiraiiLITERATIE. CLEVELAND'S COMPLETE MILTON, WITH VERBAL INDEX. One Hundred and Twenty Thousand of these Volumes have heen sold, and they are the acknowledged Standard wherever this refining study is pursued. PROF. JAMES R. BOYD'S WORKS. EMBBACING COMPOSITION, LOGIC, LITERATURE, RHETORIC, CRITICISM, BIOGRAPHY ;— POETRY, AND PROSE. BOYD'S COMPOSITION AND RHETORIC. Remarkable for the space and attention given to grammatical principles, to af- ford a substantial groundwork ; also for the admirable treatment of synonyms, figurative language, and the sources of argument and illustration, with notable ex- ercises for preparing the way to poetic composition. BOYD'S ELEMENTS OF LOGIC explains, first, the conditions and processes by which the mind receives ideas, and then unfolds the art of reasoning, with clear directions for the establishment and confirmation of sound judgment. A thoroughly practical treatise, being a system- atic and philosophical condensation of all that is known of the subject. BOYD'S KAMES' CRITICISM. This standard work, as is well known, treats of the faculty of perception, and the result of its exercise upon the tastes and emotions. It may therefore be termed a Compendium of Aesthetics and Natural Morals ; »ad its use in refining the mind and heart has made it a standard text-book. BOYD'S ANNOTATED ENGLISH CLASSICS. Milton's Paradise Lost. I Thomson's Seasons. Young's Night Thoughts. Pollok's Course of Time. Cowper's Task, Table Talk, &c. I ' Lord Bacon's Essays. In six cheap volumes. The service done to literature, by Prof. Boyd's Annota- tions upon these standard writers, can with difficulty be estimated. Line by line their expressions and ideas are analyzed and discussed, until the best compre- hension of the powerful use of language is obtained by the learner. Entered according to Act of Congress in the year 1856, by A. S. BARNES & COMPANY, In the Clerk's Office of the District Court of the United States for the Southern District of New York. B'S E. OP L. INTRODUCTORY JBSERVATIONS. The Lectures which constitute the basis of the present work were read by the learned author, during twenty-five sessions, in the University of St. Andrews, and may consequently be pre- sumed to have been elaborated with great care, and to be wor- thy of the attentive study of all who desire to become ac- quainted with the science and the art of Reasoning. As the Lectures are few and concise, there seemed to be occasion, in fitting them the better for a text-book in schools, or even for private perusal, to supplement them occasionally, from the works of distinguished writers on Logic, on points where, for practical utility, a more full discussion of the subject is needed ; and also to introduce various important topics upon which Professor Barron had neglected to offer observations. As stated in the title-page, the work* to which the compiler lias had recourse for this purpose, are, chiefly, those of Dr. Isaac Watts, Dr. Abercrombie, Archbishop Whately, Dr. Thom- as Brown, John Stuart Mill, and William Thomson. The con- tributions gained from these standard sources will be found at /east equal in value, and nearly also in amount, to the Lec- tures. It is hoped, therefore, that a work "has thus been con- structed which will be found to possess some advantages over the text-books now most generally used. One peculiar feature of it, is the omission of a great deal of perplexing and useless matter relating to the Syllogism ; and yet it presents a full dis- cussion of the value and functions of that ancient form of rea- . 215268 4 INTRODUCTORY OBSERVATIONS. soning. The opinions and views of distinguished authors on this interesting branch of the subject are largely quoted, that the student may be led to a discovery of the true state of the case. He is not, moreover, here subjected to the irksome task of learning a huge mass of intricate and unprofitable details about syllogistic Moods and Figures, such as are found in most treatises on the science of Logic. The author of " The Philosophy of Rhetoric," Dr. George Campbell, not a mean reasoner, nor an indifferent critic in mat- ters of this kind, in that celebrated work observes : " It is long since I was convinced, by what Mr. Locke hath said on the subject, that the syllogistic art, with its figures and moods, serves more to display the ingenuity of the inventor, and to exercise the address and fluency of the learner, than to assist the diligent inquirer in his researches after truth. The method of proving by syllogism appears, even on a superficial review, both unnatural and prolix. The rules laid down for distin- guishing the conclusive from the inconclusive forms of argu- ment, the true syllogism from the various kinds of sophism, are at once cumbersome to the memory and unnecessary in practice. No person, one may venture to pronounce, will ever be made a reasoner who stands in need of them. In a word, the whole bears the manifest indications of an artful and osten- tatious parade of learning, calculated for giving the appearance of great profundity to what in fact is very shallow. Such, I acknowledge, have been, of a long time, my sentiments on the subject. On a nearer inspection, I cannot say I have found reason to alter them, though I think I have seen a little further into the nature of the disputative science, and consequently into the. grounds of its futility." After a series of observations made in vindication of these criticisms upon what he calls the scholastic art of disputation, Dr. Campbell concludes in the following terms : " When all erudition consisted more in an acquaintance with words, and INTRODUCTORY OBSERVATIONS. 5 address in using them, than in the knowledge of things, dex- terity in this exercitation conferred as much lustre on the scholar as agility in the tilts and tournaments added glory to the knight. In proportion as the attention of mankind has been drawn off to the study of Nature, the honors of this con- tentious art have faded, and it is now almost forgotten. There is no reason to wish its revival, as eloquence seems to have been very little benefited by it, and philosophy still less. Kay, there is but too good rea'son to affirm that there are two evils, at least, which it has gendered. These are, first, an itch of dis- puting on every subject, however incontrovertible ; the other, a sort of philosophic pride, which will not permit us to think that we believe any thing, even a self-evident principle, without a previous reason or argument. In order to gratify this passion, we invariably recur to words, and are at immense pains to lose ourselves in clouds of our own raising. We imagine we are advancing and making wonderful progress, while the mist of words in which we have involved our intellect hinders us from discerning that we are moving in a circle all the time" — [Philosophy of Rhetoric, p. 92.) Of the ancient Logic (which Archbishop Whately and others have endeavored to revive), the same views were entertained substantially by Dr. Thomas Reid and Dr. Adam Smith, Pro- fessors of Moral Philosophy in the University of Glasgow, and by Professor Dugald Stewart, of the University of Edinburgh. One of the pupils of Dr. Adam Smith, and who was ranked among his most valued friends during life, makes the following significant statement : " In the Professorship of Logic, to which Mr. Smith was appointed on his first introduction into the University of Glasgow, he soon saw the necessity of departing widely from the plan that had been followed by his predeces- sors, and of directing the attention of his pupils to studies of a more interesting and useful nature than the logic and meta- physics of the schools. Accordingly, after exhibiting a gen- INTRODUCTORY OBSERVATIONS. eral view of the powers of the mind, and explaining so much of the ancient logic as was requisite to gratify curiosity with respect to an artificial method of reasoning, which had once occupied the universal attention of the learned, he dedicated all the rest of his time to the delivery of a system of rhet- oric and belles-lettres." — (Dugald Stewart's Account of the Life and Writings of Adam Smith, Works, vol. vii. pp. 8, 9.) The same view of the subject was expressed by Lord Karnes, in his " Progress of Reason :" — " Aristotle," he observes, " has done hurt to the reasoning faculty, by drawing it out of its natural course into devious paths. His artificial mode of rea- soning is no less superficial than intricate. I say superficial ; for in none of his logical works is a single truth attempted to be proved by syllogism that requires a proof. The propositions he un- dertakes to prove by syllogism, are all of them self-evident. Take, for instance, the following proposition : That man has a power of self-motion. To prove this, he assumes the following axiom, upon which, indeed, every one of his syllogisms is founded, viz. : That whatever is true of a number of particulars, holds true of every one separately ; which is thus expressed in logical terms : Whatever is true of the genus, holds true of every spe- cies. Founding upon that axiom, he reasons thus : ' All ani- mals have a power of self-motion : man is an animal : ergo, man has a power of self-motion.' Now, if all animals have a power of self-motion, it requires no argument to prove that man, an animal, has that power ; and, therefore, what he gives as a conclusion, or a consequence, is not really so : it is not inferred from the fundamental pr6position, but is included in it. At the same time, the self-motive power of man is more clearly ascertained by experience than that of any other animal ; and, in attempting to prove man to be a self-motive animal, is it not absurd to found the argument on a proposition less certain than that undertaken to be demonstrated ? What is here observed, • INTRODUCTORY OBSERVATIONS. 7 will be found applicable to the bulk, if not the whole, of his syllogisms." The views of Dr. Thomas Brown, of the University of Edin burgh, correspond substantially with those above given, and will be found in the latter part of this volume. These are fol- lowed by a more profound discussion of the subject by Mr. Mill, who in part sustains, and in part dissents from, the statements and reasonings both of the writers just referred to and of our author. Yet on the whole, perhaps, he has present- ed the most satisfactory explanation of the exact value and lim- ited functions of the famous Syllogistic Process. Other por- tions, also, of this work have been greatly enriched by contribu- tions derived from the same author. The method of treating the general subject, which Professor Barron has in the following Lectures pursued, seems to be phil- osophical, and well adapted to secure all the most valuable ends of Logic, in a large and 'popular sense of that term. He first discusses every topic introductory to the art of reasoning. He explains the manner in which we receive Ideas, the sources from which they are derived, and the methods we must employ to render them clear, adequate, and conclusive. He then ex- plains the nature of the propositions into which they may be formed, and the judgments which we must pass on these prop- ositions. He delineates the prejudices which pervert our judg- ments, and lays down some rules which we must follow, in order to form them with accuracy and justness. He then treats of Reasoning, or the method of ascertaining, propositions by means of intermediate ideas, or proofs, whether demonstrative or probable. He explains the different -methods, in common use, of distributing or arranging ideas in different processes of reasoning. The principal kinds of Sophistry, or False Reason- ing, are subsequently brought to view (which, however, are more fully considered in the pages we have drawn from Dr. Abercrombie). The author concludes with an exposition of the 8 INTRODUCTORY OBSERVATIONS. nature of the Syllogistic Process, and of its great want of utili- ty, for all the legitimate purposes of reasoning in common life. From the treatise of the learned Dr. Watts have been drawn some valuable observations ou Prejudices, and on Fallacies in Reasoning ; also, some important Principles and Rules of Judg- ment, in matters of Reason and Speculation, of Morality and Religion, of Human Prudence, of Human Testimony, and of Divine Testimony. He has supplied us, also, with some ex- cellent Rules of Method in Reasoning. The pages drawn from the work of Dr. Abercrombie (on the Intellectual Powers) are regarded as possessing uncommon value. They instruct us how we may examine and test the validity of a process of reasoning : they expose the most com- mon fallacies that are practised in reasoning : they enable us to distinguish the sound exercise of judgment from the art of ingenious disputation ; and they contain some admirable re- marks upon the due culture and regulation of the judgment, showing its important applications, alike to the formation of opinions and the regulation of conduct. While some of these topics do not fall within the narrow limits of the Ancient Logic, they possess an admirable fitness to prepare the mind for logical investigations, and deductions, and communications, as well as for a rational course of action. To Archbishop Whately this volume is much indebted, not for what has been taken from his Logic, but from the First Part of his work on Rhetoric, which, for all the practical pur poses of life, in matters of reasoning, is far more valuable than the other work. The best thoughts which he has therein com- municated on the subject of reasoning have been selected, and introduced into the present work, and will be acknowledged to be worthy of diligent study and attention. To the additions already named has been appended, as in- teresting, and not inappropriate, a brief illustration of the Socratic method of Reasoning. INTRODUCTORY OBSERVATIONS. 9 These additions, which are either distributed through the Lectures or appended, may readily be distinguished from them by being included in brackets, or by a distinct announcement being made. The last three Lectures of the original work of Professor Barron, embracing a general view of human knowledge, or of the sciences and arts which are proper objects of investigation, have been omitted in this volume, as not peculiarly appro- priate to a work on Logic. Some portions of the other Lec- tures, also, of a local character, or of not sufficient pertinency and importance, have been omitted, and occasionally a verbal correction has been made. The Editor has, further, taken the liberty of indicating by the Italic character the prominent top- ics — has prepared running titles at the top of the page, and arranged the matter of the Lectures under two forms of type, that the illustrative and also the less important parts might be more readily discerned, — thus adapting the Lectures to more convenient use in the class-room, or for private reading. What Mr. Thomson has so well said in the conclusion of his able w T ork on the Laws of Thought, the compiler of the present work would here introduce, as conveying an important admoni- tion to those who would derive from it the greatest amount of ben- efit which it is designed and suited to confer. He says : " If this little work is hastily examined and cast aside, of course the reader will not have become a logician ; he will have learned the unimportant fact that upon this or that disputed doctrine the author held this or that opinion, and his knowledge will go no further. Instead of learning Logic, he will know an insig- nificant fact in logical history. The mistake is not uncom- mon : — we inquire what Aristotle and Bishop Butler said on morality, and think that we have studied Moral Philosophy ; we read the Organon, and call ourselves logicians. History presides over these and other facts : we are in her domain when we use our books in this narrow spirit. Philosophy does not v 1« 10 INTRODUCTORY OBSERVATIONS. exist until the mind of the student begins to work for itself with the principles it receives historically ; to decompose and to compose anew, to criticise the arguments employed, to essay at least to push the confines of Truth further into the wilds of error and ignorance, and to leave her a wider territory." u If Grammar is learnt by speaking and writing ; if a man cannot become an orator without repeated efforts to speak v* public, nor a poet without practising the mechanism of verse, till he can use it with ease, it seems absurd to expect that a course of lectures heard, with a string of definitions learnt, will make a logician. Let those who wish to possess the intel- lect they have received from above in the depth and clearness, the sober composure, the calm activity which a high degree of culture can alone bestow, venture to study Logic in a larger spirit than the merely historical." Having thus stated the general design, and glanced at the more prominent topics considered in this volume, and having noticed some of the various enlargements and improvements, which have been attached to the original Lectures that form the basis of the present work, the Editor sends it forth on a mis- sion of usefulness among the Academies, Female Seminaries, and Colleges of this Western Hemisphere, with the earnest de- sire that it may be found eminently serviceable in forwarding the cause of Truth, and in promoting a sound and useful edu- cation. r J. R. B. NOTE TO THE SECOND EDITION. The value of the work has been increased by some verbal correc- tions ; but especially by adding a section on Induction and Deduction, from Thomson's Laws of Thought. CONTENTS. fAOK. Introduction, by Professor Barron 13 LECTURE I. Object of Logic — Its utility — Operations of the mind — Ideas — simple and complex — distinct and obscure 15 LECTURE II. Ideas, adequate and inadequate — particular and abstract — Genera and Species — Extension and Intension — Rules for acquiring and examining Ideas 23 LECTURE III. Rules to prevent ambiguity — Division — Description — Definition. . 37 LECTURE IV. Knowledge and truth, what ? — The result of Intuition or of Rea- soning — Propositions— constituent parts — Various kinds of propositions — Propositions, expressive of relations — Sources whence propositions are derived. 5 i LECTURE V. Propositions derived from Consciousness — from Intuition — from Reasoning — from Testimony — Inference, or Reasoning in gen- eral — Prejudices 6-2 LECTURE VI. Prejudices 81 LECTURE VII. Rules to prevent Prejudices — Principles and Rules of Judgment, in matters of Reason and Speculation — in matters of Morality and Religion — of Human Prudence — of Divine Testimony. . . 90 1V< CONTENTS. LECTURE VIII. ,m Reasoning — mathematical — moral — political — prudential — Proba- ble Reasoning 113 LECTURE IX. Different processes of Reasoning — Examination of the validity of a process of Reasoning — Different kinds of Sophistry — The various use and order of several kinds of Propositions and of Arguments in different cases — The exercise of a sound Judg- ment 127 LECTURE X. Syllogism 187 LECTURE XL Syllogism — Its merits as a mode of reasoning 202 CONCLUDING CHAPTER. Dr. Brown's Analysis of the Scholastic Logic — Mr. Mill on Syllo- gism — Induction and Deduction — The Socratic Method of Rea- soning — Thomson's Division of the Sciences 218 INTRODUCTION. BY PROFESSOR BARRON. Some people imagine that Logic is a frivolous, an os- tentatious, at best an unnecessary art, which may serve to puzzle and perplex, hut can be of little utility in business or philosophy. Others are perhaps of opinion, though it were more useful than it is, yet it requires a study so dry and uninteresting, so abstract and difficult, that few inquirers have patience to make any progress in it, or to convert it to any advantage. Were the system I have to lay before you composed of the idle syllogism of the schools, which till lately was the only system taught in our colleges, I should not have confidence to maintain, that there was not a great deal of foundation for the first objection. In the short account of that system which I have to advance, I be- lieve it will appear, that it is a vain and unavailing in strument of truth and knowledge. But, though the syllogism of the schools, and the old art of logic, be admitted to be idle systems, yet we surely have more candor than to infer, that there is no art at all in reasoning ; that there is no such thing as good reasoning ; or that it is of little~use to be a good reasoner. I, on the contrary, will take for granted, that there is no accomplishment or qualification any man can acquire more important. Whether, then, you be come in life men of speculation, or men of business, in every step you take, your rational faculty must be con- 14 INTRODUCTION. stantly exerted ; and the following lectures are calcula- ted entirely to render you expert and successful in that exercise. As to the second objection, that the study is uninter- esting, dry, and difficult, the proper answer is, that it is no more so than every exercise of the understanding naturally is, and must be. There is nothing in it either so uninteresting, so dry, or so difficult, which any per- son possessed of ordinary capacity may not easily sur- mount, and which every person must surmount, who expects to acquire, either in philosophy, literature, or business, as much use of his understanding as to attend to any train of thought. It is by the proper use of his understanding that man attains his eminent character- istic of being rational. It is by the proper use of his understanding that he can make any progress in knowl- edge. It is by the same means only that he can ob- tain the flattering distinctions claimed by superior judgment, and by which he can avoid the disgrace at- tached to ignorance and stupidity. In a word, to all orders of men, true logic pretends to lend the most salutary aid. Her pretensions are at least commend- able, and her efforts are entitled to the most patient re- flection and candid examination.* [* Whatever has at anytime been concluded justly, whatever knowl- edge has been acquired otherwise than by immediate intuition, depended upon the observance of the laws which it is the province of logic to in- vestigate. If the conclusions are just, and the knowledge sound, those laws have actually been observed. We need not, therefore, seek any fur- ther for a solution of the question, so often agitated, respecting the utility of logic. If a science of logic exists, or is capable of existing, it must be useful. If there be rules to which every mind conforms in every instance in which it judges rightly, there seems little necessity for discussion whether a person is more likely to observe those rules, when he knows the ruiot», than when he is unacquainted with them. — MiU's Logic. ELEMENTS OF LOGIC. LECTURE I. OBJECT OF LOGIC OPERATIONS OF THE MIND IDEAS SIMPLE AND COMPLEX DISTINCT AND OBSCURE. The object of education is to increase knowledge, to refine imagination, to improve taste, and to prepare us for acting a part in life, respectable and useful in itself, as well as advantageous and honorable to the public. The professed purpose of logic is to teach the right use of reason, both in the investigation and in the com- munication of truth ; to inform us how to introduce clearness and good order among our ideas ; to explain the operations of the mind, which are conversant about them ; and to guard us, in performing these operations, against falling into error.* The understanding is occupied entirely about knowl- edge. The end of all science is to instruct us in knowledge ; and the same end is pursued by all study, whether prudential, political, moral, or mechanical. In whatever way we exert our understanding, it is to obtain some information we did not possess before; [* Logic, accurately defined, is the art of thinking and reasoning justly: it traces the progress of our knowledge from our first and most simple conceptions through all their different combinations, and all those nu- merous deductions that result from variously comparing them with one another. — London Oyc] 16 OBJECT OF LOGIC. and the design of the art of logic is to hold forth the manner of attaining that knowledge with most ease and expedition. From these views of the nature and end of logic, it is apparent that it is one of the first arts to which we should apply our attention in our progress towards knowledge, as affording the best means of fortifying and improving our understanding. The more acute the understanding is, it will be more successful in the investigations of science. The less it is liable to err, the more certain and expeditious will be its progress. The more we are acquainted with those prejudices and partialities whi-ch have misled other reasoners, the less danger of mistake will there be. The better we un- derstand the nature of the instrument we employ, the more expert and successful may we reasonably expect to be in the use of it. Every thing, then, in logic, that, does not contribute to improve the understanding, and to promote our progress in useful knowledge, I shall not hesitate to pronounce unworthy of attention ; but every thing, on the other hand, that promotes these ends, cannot obtain more attention than it deserves. I am well aware that no art ever gave occasion to so much idle research, and fanciful refinement, as that of which I now speak. No art has so much bewildered and repressed every useful exertion of the understand ing, as that which pretended to enlighten and improve this faculty, and to guide it in the road to truth. All the efforts of human genius, all the learning which foi many centuries prevailed in Europe, were subtle dis quisitions and puzzling distinctions about the method of investigating knowledge, without applying that method to any important inquiry. ( All the syllogism of the schools, after the thousands of volumes that have been written upon it, and after the employment of a UTILITY OF LOGIC. 17 aeries of ages to bring it to perfection, never enriched science or business with one useful discovery. Let us not, however, rashly conclude, that these abu- ses furnish a proof of the general inutility or insignifi- cance of the art to which I now call your attention. It is curious even to survey the ingenuity with which so many men have gone wrong, with the endless per- plexities in which they have involved themselves. To point out these is one of the purposes of this work ; but it is of more substantial utility to learn the nature of truth, and the operations of the human mind, which are concerned in the discovery and extension of knowl- edge. As the sophistry, then, and absurdity, with which logic has been disgraced, are no valid objections against the use of it, so neither is the argument, that many men reason often very justly without any acquaintance with its rules. There is in all mankind some natural logic, for it is one of those arts which may be learned by practice, without the knowledge of theory. One of the best methods of making progress in the art of rea- soning, is actual practice, or the acquisition of the habit of examining a train of ideas that constitute an argu- ment; and of this branch of the art all men acquire some share by experience ; many men acquire a great deal. But, though long experience in sound reasoning may render us expert logicians, in the same manner as practice, without the knowledge of principles, may form eminent practitioners in any other art ; yet this success will not justify any inference against the utility, or even the propriety of theory. The end of all theory in the arts is to render us more methodical and reputa ble performers, and it can scarcely fail to produce this effect, when properly applied. What is the theory of an art ? It is a philosophical 18 UTILITY OF LOGIC. delineation of the principles on which the art is found* ed, of the end it has in view, and of the means by which it proposes to accomplish that end. From this delineation are deduced the rules of the best practice, which are commonly illustrated from the experience of the most successful practitioners. A theory of an art, then, is a collection of all the knowledge which can be obtained concerning that art, from the combined infor- mation of all preceding theorists and practitioners. It points out the most patent and direct road to success, and it marks all the corners and obstructions, at which improper deviations are most likely to be committed ; so that, after having learned the theory, nothing re- mains but to obtain the habit of ready and accurate practice, in order to render us able and successful per- formers. Although, then, many men are good reasoners who never learned logic, yet the knowledge of that art may be neither superfluous nor nugatory; because an ac- quaintance with it may either facilitate our progress in becoming good reasoners, or may enable us to reach greater eminence in that line, than those wh« have not enjoyed the advantages we possess ; and if we acquire by it either of these emoluments, it is of too much im- portance not to attract our serious attention.* [* Logic has its use in improving the condition of men: it teaches, or may be made to teach, them to think. The active intellect has two parts, one of which originates our thoughts, and may be called the suggestive, whilst the other checks and judges thoughts as they arise, and may be called the critical power. Thoughts are continually suggested without the consent of the will. The suggestive' power may be educated as certainly as, though more gradually than, the critical. The discovery which we call a flash of genius, a happy thought, really depends as much upon previoua acquirements, as the power of stating a case or applying a rule does. All discipline of /he suggestive must proceed from the critical power: it is by u long, careful, patient analysis of the reasonings by which others have at- tained their results, that we learn to think more correctly ourselves. He ivho reads over a work on logic probably thinks no better when he rwe» THEORY OF LOGIC. 19 As the object of logic is to teach the best use of our rational faculty, both in investigating and in communi- cating truth, the theory of it, and the materials of which that theory consists, are deduced from this end. That theory, accordingly, consists of two parts / the na- ture of ideas, which are the materials on which we rea- son, and the nature of the faculties or operations of the mind which are concerned in reasoning. Before we can reason, we must have ideas ; and before we can reason rightly, we must understand what kind of opera- tion reasoning is. The explication of both compre- hends the whole of logic which is of any use. In explaining the nature of ideas, and of the opera tions employed about them, one of two methods must be adopted. We must either treat them separately, or in conjunction. We must either first discuss the ideas, and then the operations, or we must carry on the ac- count of both at the same time. The latter is the bet- ter method, because one of the chief means of explain- ing the nature of ideas is, to point out the operations of which they are the objects ; and one of the chief means of illustrating the operations is, to present the single ideas, or the clusters of ideas, about which the opera- tions are exerted. This latter method we cannot hesi- tate to follow ; and, in adopting it, all we have to do is, to specify and illustrate the operations from experi ence, and then to explain the single ideas, or the collec- tions of ideas, about which each operation is conversant. up than when he sat down ; but if any of the principles there unfolded cleave to his memory, and he afterwards, perhaps unconsciously, shapes and corrects his thoughts by them, no doubt his whole powers of reason- ing gradually receive benefit. In a word, every art, from reasoning dowa to riding and rowing, is learnt by assiduous practice, and if principles do Huy good, it is proportioned to the readiness with which they can be con- verted into rules, and the patient constancy with which they are applied in all our attempts to excel.— Thomson.} 20 CLASSIFICATION OF IDEAS. The operations employed in the investigation of truth are commonly reckoned three — perception, judgment, and reasoning. By perception is understood that ope- ration by which the mind sees and becomes acquainted with every single idea it possesses. By judgment is understood that operation by which the mind discovers the agreement or the disagreement of any two ideas it may have occasion to compare, in order to discover truth and knowledge. By reasoning is understood that operation in which the mind compares two ideas by means of one or more intermediate ideas, in order to discover the amount of what is commonly called a de- monstration or an argument. This short account of these operations must at present suffice ; for, as they comprehend the whole theory of logic, I am afterwards to resume and consider them separately.* Ideas are arranged into classes, and different names assigned, according as they are simple or complex, dis- tinct or confused, adequate or inadequate, particular or abstract. A simple idea, as its name insinuates, can be contem- plated only in one view. It cannot be divided or taken to pieces, because it does not consist of parts, being naturally indivisible. Most of our ideas of the qualities of bodies are of this clas hard, soft, round, smooth, white, black, cold, hot; all ideas, per haps, of tastes, smells, sounds — as bitter, sweet, low, loud; and many of our ideas of the feelings and operations of the mind — as of desire, aversion, hunger, pain, thinking, willing, discerning, reasoning. [* Mr. Thomson distributes the subject into three parts, the first treat- ing of conception, or the power of forming general notions ; the second o' judgment, or the power of deciding whether two notions agree or not, and the third of syllogism, or the power of drawing one judgment from another. To these a fourth part, in which method, or the power of using the other three functions in the discovery of truth, is explained, has bee»; usually added, which answers to applied logic] CLASSES OF IDEAS. 21 We cannot divide them, even in imagination ; they are perfectly uniform, and void of parts. A complex idea contains two or more simple or subordinate ideas, into which it may be divided, and which subordinate ideas, when divided, may be consid- ed separately. All our ideas of substances are com- plex, as of animals, vegetables, and the inanimate par's of nature. The idea of a tree, for instance, includes a great variety of subor- dinate ideas — those of wood, stock, roots, branches, vegetable life, shape, leaves, bark, blossoms, fruit ; several of which subordinate ideas may be subdivided into other ideas. All ideas of figures — as of circles, squares, triangles, cubes, cylinders, pyramids ; most of the ideas of virtues and vices — as of justice, fortitude, veracity, theft, ingratitude, falsehood, deceit. The second division of ideas was, into distinct ana confused, or, which is much the same thing, into clear and obscure. Distinct or clear ideas are those of which we have full and perfect comprehension, and which we can readily separate or distinguish from all other ideas. Confused or obscure ideas are those of which we have not full and perfect comprehension, and which we can- not easily separate or distinguish from all other ideas. Distinct and clear ideas are perceived with a perspicacity and energy similar to that by which the mind contem- plates figures in mathematics, or numbers in arithmetic ; all their boundaries and their differences are completely discernible. Confused or obscure ideas are like the colors of a rainbow, they run into one another, and the mind neither perceives fully their nature nor their limits. The acquisition of clear and distinct ideas is of the utmost consequence in the investigation of knowledge ; for the degree of conviction with which it is presented to the mind, is- always in proportion to the degree of 22 IMPORTANCE OF CLEAR IDEAS. clearness and distinctness which we have introduced among our ideas. Were all our ideas clear, all our knowledge would be demonstrative, a quality which belongs only to our scientific knowledge. Obscurity, more or less, adheres to all our other ideas, and leaves us only greater or less degrees of probable evidence, corresponding to the less or greater obscurity of our ideas. In the mathematical sciences, and in arithmetic, the evidence is demonstrative, because our ideas of all the figures and numbers about which we reason are perfectly clear and distinct, and be- cause, in comparing them, we perceive accurately whether they agree or disagree ; and if they disagree, how great the excess of one is above another, so that we can affirm, either that they are equal, or that the one exceeds the other by a certain quantity. In morals, in politics, in arts, and in business, almost all our ideas are more or less obscure ; hence, in comparing them, we can- not precisely pronounce whether they agree or disagree; and though we were sure that they disagree, yet we cannot accurately ascertain the difference. The necessary consequence is, that in all these branches of knowledge, we can obtain no demonstrative evi- dence for truth. We must be satisfied with probable evidence, and we should be attentive to procure ideas as clear and distinct as possible, that we may reach the highest degree of probability. I shall not at present pursue farther the doctrine of distinct and obscure ideas ; a future opportunity will occur of discussing more completely this important subject. I shall then have occasion to point out the caution with which we should proceed in the examina- tion of our ideas, the prejudices by which they are obscured, but particularly the attention we must em- ploy to prevent the confusion which may be introduced among them by the improper use of words. From these views, the important and extensive utility of logic will appear, and how deeply its rules and principles enter into all our inquiries and knowledge. IDEAS — ADEQUATE AND INADEQUATE. 23 LECTURE II. IDEAS ADEQUATE AND INADEQUATE PARTICULAR AND AB- STRACT RULES CONCERNING IDEAS. The third division of ideas related to their being adequate or inadequate. An adequate idea is a perfect picture of its archetype, or contains a representation of all the parts of which the archetype (or object) consists. It is different from a distinct idea, because an idea may be distinct and not adequate ; that is, we may have a clear perception of all the parts of an idea, as far as these parts extend, though these parts may not consti- tute a complete collection of those of the archetype. We may have, for example, a distinct idea of a triangle, and yeu not possess an adequate idea of a right-angled triangle, an isoscele c , or scalenum — which, besides the general ideas of three sides and three angles, require that the sides and angles should be of a par- ticular species. An inadequate idea is not a perfect picture of its archetype, or contains not a complete representation of the parts of which the archetype consists. Almost all simple ideas are adequate, as those of colors, tastes, or qualities ; all ideas of mathematical figures, and of numbers, as triangles, squares, cubes, cylinders, fifty, a hundred, a thousand, ten thousand But although, when we examine archetypes with atten- tion, ideas will be as adequate as we can make them ; and when knowledge is either demonstrative or even highly probable, ideas must really, or very nearly, be adequate ; yet if we compare ideas, not only with what we know of their archetypes, but with what may be lviown of them, and perhaps is known of them by supe- 24 IDEAS PARTICULAR OR ABSTRACT. rior beings, few of our ideas, except those of mathe- matics and arithmetic, will be found to be adequate. There is hardly any other thing in nature, of which our knowledge is complete. We are acquainted with a few only of the properties of animals, vegetables, and inanimate matter ; what substance is, whether of matter or spirit, is totally beyond our comprehension. The whole system of the transmutation, or the assimilation of nature, by which the nutriment of animals is converted into the different parts of which their bodies consist, bones, flesh, sinews, blood, hair, horn, &c, and by which inanimate nature is converted into the numerous parts of vegetables and metals, seemingly so different from one another, as trees, shrubs, leaves, bark, blossoms, fruit, gold, silver, mercury, &c, is to us altogether unintelligible. In all these cases, and in many others which might be mentioned, our ideas are unavoidably inadequate. But fortunate would it be if our ideas were always ade- quate, or as near to adequate as possible, when it is in our power, by industry and attention, to make them so. They are less adequate than they might be, chiefly from two causes — first, carelessness in the examination of archetypes, which overlooks some of their properties or parts ; and, secondly, inattention in ascertaining the meaning of the words employed to denote them, which words often do not express the same parts, or all the parts, in our minds, which they do in the minds of others. In both cases, our knowledge cannot be so complete as that of a person who has taken care to prevent these errors or defects ; and in every discourse or controversy with that person, we must misunderstand him when these words occur. The last distinction of ideas considers them as par- ticular or abstract This is the most important distinc- tion, as it enters deep into the constitution both of language and knowledge. All things exist in nature IDEAS PARTICULAR OR ABSTRACT. 25 as individuals or particulars. Every substance is that of some particular animal, vegetable, or inanimate piece of matter. Every material quality, as bard, smooth, rough, black, white, belongs to some substance or body, without which the quality cannot subsist. Every virtue or vice has always relation to some agent; and though we may speak, speculate, or reason con- cerning them separated from this agent, yet we must admit that, independent of him, they have no actual existence, nor any existence except in idea. Particular ideas represent individuals as they exist in nature, as a house, a horse, a man, a tree, for which, perhaps, we have no names, or to which we give the names of St. James's, Bucephalus, Alexander, or the Royal Oak. Ideas, however, would be in number infi- nite, and communication, of course, would be impracti- cable, if every individual thing with which we are acquainted were to require an idea and a name to de- note it. To surmount this obstacle, the mind is very fortunately endowed with the faculty called abstraction, by which it arranges into classes all the individuals which have any common qualities, or which have any thing similar, either in their figure, existence, or action. It assigns a general idea and name to each class, and takes the trouble, only when compelled so to do, to specify individuals, to distinguish them in the mind by ideas, and in language by names.* Ideas and lan- guage, by this expedient, are rendered exceedingly manageable an 1 convenient; for the individuals of [* A general name is one which is capable of being truly affirmed, in the lame sense, of each of an indefinite number of things. An individual or singular name is a name which is capable of being truly ifiirmed, in tbe same sense, only of one thing. A class is the indefinite multitude of individuals denoted by a general aame. — Mill's Logic, p. 18.] 2f) GENERAL OR ABSTRACT IDEAS. which it is necessary to form ideas and fabricate names are not very numerous, being limited chiefly to the hu- man race. It was much more necessary to assign ideas and names to the individuals of this class, than to assign ideas and names to all the individuals of all the classes in nature, while the expedient of giving a general name is equally convenient for the purposes of communication.* This power of forming an idea of a class of objects, is called abstraction, for the following reason : The idea of a class contains only those parts or qualities which are common to all the individuals of the class ; while the qualities peculiar to any individual are left out, or abstracted from those which constitute the general idea of the class. The general or abstract idea, for example, of the class of vegeta- bles called trees, contains the following parts : a plant of considera- ble height, which sets out large branches, is clothed with bark, and in summer bears leaves and seeds. All the plants that can be called trees have these qualities ; and in forming an idea of these qualities, the mind abstracts its attention from all the qualities which are peculiar to any particular tree, such as the size and di- rection of the branches, the nature of the wood, the color, surface, and shape of the bark, and of the leaves, and the nature and prop- erties of the seeds, such as berries, acorns, apples, pears, &c Again, the general idea of a horse contains the idea of a large and beautiful quadruped, of cylindrical body, high-set neck, taper limbs, swift, strong, useful, docile ; but it includes not the ideas of shape, color, size, pleasure, or utility, which distinguish -individuals, the race-horse, the hunter, the. war-horse, or the horse of the plough. [* The notions formed in the mind from things offered to it, are cither of single objects, as of " this pain, that man, Westminster Abbey;" or of many objects gathered into one, as " pain, man, abbey." Notions of single objects are called intuitions, as being such as the mind receives when it simply attends to or inspects (intuetur) the object. Notion, formed from several objects are called, conceptions, as being produced by the power which the mind possesses of taking several things togethei (concipere, i. e., capere hoc cum Mo). They are also called general notions — Thomson,'] CLASSES OF OBJECTS. Zi The mind is not satisfied with forming one grade of classes, which may comprehend individuals. It gener- alizes much further, with the same view of simplifying and facilitating the means of communication and knowl- edge, and of abridging the number of ideas and words. It constitutes classes above classes. Accordingly, it forms a second class, containing the properties which one first class has in common with other first classes, so that the first class is now considered as making only one of the constituent parts of the second class. The class of creatures called men, for example, comprehends what qualities are common to all its individuals, Romulus, Alexan- der, Julius Caesar. But the class of men has many common quali- ties with other classes of living creatures, horses, dogs, sheep, fishes, fowls, &c, namely, life, motion, shape, color ; and hence, of these common properties is framed a higher class, called that of animal*, which contains the qualities common to all living creatures.* The mind sometimes ascends higher, and forms another class more general, of all the properties which this second class has in common with other classes in nature. For example, animals have several properties, in common with vegetables, as shape, color, growth, decay, circulation of juices; of these is formed a third class, called animated nature. We may proceed farther still to form & fourth class, which will contain all things, [* By observing John, Thomas, and Peter, and abstracting from their accidents the essential marks, we get the notion of man ; but again, by comparing the conception man with other conceptions, cow, sheep, wolf, whale, and observing the mark common to all, that-they suckle their young, we form the wider conception mammalia, — wider, because it includes man and many other conceptions. We may carry the process further still ; and, with writers on Natural History, compare the mammalia with aves, amphibia, pisces, insectae, and vermes, when we shall discover that all these, however different, agree in having life and sensation, from which marks we gain the new conception animal, wider thar any of the formei, as including them all, — higher, as requiring a second step in the abstrac- tive process to reach it.— T homs on. Of THf 28 STEPS OF GENERALIZING. animate and inanimate. The properties, however, of it are very few, and scarcely amount to more than ex- istence and figure. Though all these steps of generalizing are sometimes necessary or useful, yet knowledge and language sel- dom require attention to more than three of them ; namely, the individual, the first class, and the second. The first class is called the species, the second the genus. Thus, Alexander is the individual, man is the species, and animal is the genus ; the royal oak is the individ- ual, tree is the species, and vegetable is the genus ; St. James's is the individual, dwelling-house is the species, edifice is the genus.J The third and fourth classes are also denominated genera. The second class, or the one immediately above the species, is called the proximate genus, the third and fourth classes are called transcen- dent genera. The proximate genus of the species man is animal ; existence is the transcendent genus. The proximate genus of tree is vegetable; the transcendent may be animated nature, or existence.* It is to be observed, though general or abstract ideas are more comprehensive, or extend to more objects, than particular ideas, yet that they are less complex, or con- tain fewer parts, and that the more general they are, the less complex they are, or contain fewer parts in pro- [* The same class which is a genus with reference to the suh-classes or species included in it, may he itself a species with reference to a more comprehensive, or superior, genus. Man is a species with reference to an- imal, but a genus with reference to the species, mathematician. Animal is a genus, divided into two species, man and brute ; but animal is also a species, which, with another species, vegetable, makes up the genus, or- ganized being. Biped is a genus with reference to man and bird, but a species with respect to the superior genus, animal. Taste is a genus, of which, sweet taste, sour taste, &c, are species ; but taste is a species of the genus, sensation. Virtue, a genus with reference to justice, temper- ance, &c, is one of the species of the genus, mental quality.— Afill's Logi\ p. 82.1 EXTENSION AND INTENSION. 29 portion. The reason is exceedingly obvious. A genns contains only the few properties which are common to the several species which it includes, and which are not nearly so numerous as those that belong to each species. The species, again, contains the properties which are common to all the individuals it includes, and which are not so numerous as those that pertain to each indi vidual. The genus animal, for instance, includes few properties, life, shape, color, motion, growth, decay. The species man contains all these properties of the ge- nus, besides those of the species, namely, power oi speech, thinking, acting with design, and many others. The individual contains all these qualities I have enu- merated, both of the genus and of the species, together with those peculiar to the individual, wise or prudent, knowing or ignorant, rich, poor, fortunate, unfortunate, — all these qualities, however variable, and in a particu- lar degree corresponding to the nature or character of the individual.* [* Extension and Intension. When we compare a vague and general conception with a narrower and more definite one, we find that the former contains far more objects in it than the latter. Comparing plant with ge- ranium, for example, we see that plant includes ten thousand times more objects, since the oak, and fir, and lichen, and rose, and countless others, including geranium itself, are implied in it. This capacity of a conception we call its extension. The extension oi 'plant is greater than that of gera- nium, because it includes more objects. But conceptions have another capacity. Whilst plant has more objects under it than geranium, it has fewer marks in it — fewer properties by which we assign it a place under some appropriate conception. I can describe the leaves petals, stamina, and pistils oi geranium, but oi 'plant no such de- scription is possible. 1 cannot say that every plant has a stem, for there are the lichens to contradict me ; nor a flower, for ferns have none, and so on. I can say little more about plant, than that all plants have growth and vegetable life. The logical expression of this defect is, that its intens'on is very limited. The greater the extension, the less the intension ; the more objects a conception embraces, the more slender the knowledge which it conveys oi any of those objects ; and vice versa. With the help of the important distinction between extension and inter 30 UTILITY OF ABSTRACT IDEAS. The power of abstraction is one of the most important belonging to the understanding, and the practice of it in ccience and in business is of the npst extensive use. £lt will afterwards be explained, thaftr all definitions are regulated by the arrangements ot abstraction, and that they consist entirely in referring an individual to its species, with the addition of some quality which distin- guishes it from the other individuals of its species; or in referring a species to its genus, with the addition of some quality which characterizes it as a species. To evince the exceedingly extensive utility of abstrac- tion, I must observe, that all science, almost all reason- ing, indeed almost alLthe words of language, are con- versant about abstract ideas. You will readily appre- hend, that the two sciences of quantity, mathematics and arithmetic, are occupied entirely about abstract ideas. No property is demonstrated of any triangle in the elements of geometry, that is not true of all triangles, at least all triangles of the same kind. The figure delineated on the board of the mathemati- cian is not particular or local ; it represents every figure of the same species, and the demonstration is equally extensive in its applica- tion, namely, to all figures of the species. Were not this the case, sci- ence would have no existence, and the mind of man could make no progress in knowledge. "Were not this the case, the mathematician would be obliged to demonstrate the properties of every particular figure he should employ, and all progress in knowledge would be suspended, because the new figures of the same species which may occur are infinite. All the operations in arithmetic, the objects of which are dis- sion, or as others express it, the sphere and matter of the conception, we can understand the meaning of the saying, that the subject of a judgment is in the predicate, and the predicate in the subject. " Man is an animal :" this conveys two notions, that man is contained in animal, as a species in a genus ; and that whatever makes up our notion of animal — all the marks of animal — are contained in man. So they are mutually contained. In- stead of "man is an animal," Aristotle would say "animal inheres in man. 1 ' — Thomson.] UTILITY OF ABSTRACT IDEAS. 31 creted quantity, or quantity divided into parts, are of a general na- ture, and all the truths they establish are of the same denomination. The capital operations of addition and subtraction, into which all others in arithmetic are resolvable, however apparently removed from them, respect not the comparison of any two individual parts of divisible quantity; the conjunction of both in one total, which is the object of addition, or the disjunction of the quantity by which the greater exceeds the lesser, which is the object of subtraction They are of a general nature, and are applicable to all cases what- ever, in which quantity is divisible and separable. In like manner, inquiries in morals, concerning vir- tues and vices ; in politics, concerning legislation, and the happiness of communities; in arts, concerning beauty and utility ; in business, concerning propriety, decency, wisdom, and interest ; are all of an abstract nature, and are theories established by argumentation and experience, which every individual applies to his particular case, according to his best judgment. /We must not, however, conclude, that no reasoning is competent about particular ideas or individuals. The agreement or disagreement of ideas, in which knowledge consists, is equally perceptible in particular ideas as in general ones ; and we can reason as well about one man, one tree, or one triangle, as about the species or genus of these individuals. But all particu- lar reasonings are confined to the cases to which they are applied ; and, of course, as they are of very limited use, we avoid them as much as possible, and rathe* seek for general theories, in which particular cases may be included. In a word, all the appellative nouns of language are significant only of abstract ideas, so that there is hardly a topic about which we can either speak or write, that is not the offspring of abstraction. As abstraction is the capital operation by which ideas are prepared for reasoning, and by which reason- ings become of extensive use, so it is the operation by 32 RULES FOR ACQUIRING IDEAS. which man is most eminently distinguished above the inferior animals. "We cannot doubt that the inferior animals possess particular ideas, and that they even deduce inferences from them ; that they are endowed with a power of recalling them, and of forming asso- ciations among them. The horse recollects, and discovers a mani- fest inclination to revisit the house where he has formerly been well used ; but he forms the same opinion of no other house, where his opinion has not been supported by experience, that is, he draws no general conclusion concerning the probability of similar good usage in similar houses. The pointer that has frequently been beaten for starting heath-game or partridge before the fowler was ready to take aim, learns in time to connect correction with such rashness, and consequently forbears the latter from fear of the former ; but his associations extend not beyond his experience, and his primitive rashness remains with regard to a hare or a snipe. I have now explained those classes of ideas which appear to be of consequence sufficient to attract atten- tion ; but, as I intend this course to be an introduction, not to the idle syllogism of the schools, but to sound reasoning in the sciences, in arts, and in business, and as ideas are the materials of a|l reasoning, before I re- linquish this subject I shall point out the most frequent causes of their imperfections, and endeavor to suggest the best means of preventing or removing these imper- ections. I shall not, however, treat of these topics separately, because they are necessarily^ conjoined. When we know the causes of errors, the road to truth is to avoid them. When the imperfections of ideas are removed, they become clear and distinct of -course. I shall therefore comprehend both these views in the fob lowing rules concerning the acquisition and examina- tion of ideas. 1. Replenish the mind with as great variety of im- portant ideas as possible^ The end of all science, of reading, of observation, of ACQUISITION OF NEW IDEAS. 33 the study of nature and arts, of useful conversation, and of education, is to replenish the mind with ideas, in or- der to extend our knowledge, and to improve our facul- ties, to render us happy in ourselves, serviceable to so- ciety and our friends, and respectable in life. Human knowledge, it must be confessed, is in many articles extremely limited. The business, the avocations, even the necessary amusements and refreshments of life, em- ploy a great part of our time. But, notwithstanding these disadvantages, much might be done, much im- portant information might be obtained, were we to spend, in searching for new ideas, what portion of time may still remain unoccupied. Industry, properly direct- ed, w T ould be attended with signal acquisitions, and in this field nothing but industry can avail. Genius can- not begin to operate with advantage, till the mind has procured materials, numerous, valuable, and various. The end of education is to direct us in making these acquisitions ; but it is not to be expected, considering the immensity of the field we traverse, at a time of life when our heads are giddy, and our faculties unaccus- tomed to investigation, that we should make very much progress in appropriating what we learn. The acquisi- tion of new ideas should be the business of the best part of life, and no man ever accumulated a large trea- sure of them, who derived them not from his own ap- plication. Obtain, therefore, all the knowledge you can of science, of arts, of nature, of society, of manners, laws, and customs. Endeavor to gain great and com- prehensive views of men and things -in all your re- searches and inquiries, and let these views serve as foundations of your judgments and reasonings in all your particular pursuits.* [* " The way of attaining such an extensive treasure of ideas" (says Dr. Watts), " is, with diligence to apply yourself to read the best books ; oou- 2» 34 IMPORTANCE OF ACCURACY OF IDEAS. 2. Endeavor to attain accurate ideas of the informa- tion you receive, which requires two operations, first, to compare ideas with their archetypes ; second, to com- pare them with the established meaning of the words by which they are denoted. I need not employ much time to evince the necessity and utility of this rule. Unless accuracy be obtained, all our labor and search are in a great measure thrown away. If the foundation be not properly prepared and secured, the superstructure can never be finished with beauty and strength. Inaccurate ideas are little better than no ideas ; they are sometimes worse. In respect of every deduction resulting from them, they are not preferable to ignorance, because such deduction cannot be legitimate. But this is not their only inconvenience ; they lead us to suppose ourselves well-informed when verse with the most knowing and the wisest of men ; and endeavor to im- prove by every person in whose company you are : suffer no hour to pass Rway in a lazy idleness, in impertinent chattering, or useless trifles : visit other cities and countries when you have seen your own, under the care of one who can teach you to profit by travelling, and to make wise obser- vations : indulge a just curiosity in seeing the wonders of art and nature : search into things yourselves, as well as learn them from others : be ac- quainted with men as well as books : learn all things as much as you can at first hand; and let as many of your ideas as possible be the representa- tions of things, and not merely the representations of other men's ideas : thus your soul, like some noble building, shall be richly furnished with original paintings, and not with mere copies." " In order to preserve your treasure of ideas, pursue the following ad- vice : — " (1.) Recollect every day the things you have seen, or heard, or read, which may have made any addition to your understanding : read the wri- tings of God and men with diligence and perpetual reviews : be not fond of hastening to a new book, or a new chapter, till you have well fixed in your mind what was useful in the last. " (2.) Talk over the things which you have seen, heard, or learned, with some proper acquaintance. "(3.) Commit to writing some of the most considerable improvements which you daily make, at least such hints as may recall them to youi mind, when perhaps they are vanished and lost." J IMPORTANCE OF ACCURACY OF IDEAS. 35 we are not so, and, of course, expose us to all the mor- tification which attends the detection of error, ard to all those irksome contentions which arise from contro- versies about the meaning of words. In comparing ideas with their archetypes, nothing more is requisite than patience and attention ; for, by the exercise of these qualities, we shall render our ideas as adequate and accurate as it is in our power to make them. We should, for this purpose, carefully and re- peatedly make comparison, particularly of ideas which lead to consequences of importance, or which relate to topics of ambiguity or difficulty. Of the three kingdoms of nature — animals, vegetables, and in- animate matter, the objects generally remain as long as we pleasa under our examination, and we have sufficient time to attend to every particular necessary to be known. In the demonstrative sciences, also, mathematics and arithmetic, our ideas of princip^s at least will be accurate ; and it is seldom that our conceptions, even of proofs and conclusions, are liable to ambiguity. The pre- cise and defined nature of the subjects of these sciences, the simple and perspicuous language in which most writers have agreed to communicate them, render it almost impossible for a reader en- dowed with ordinary attention not to comprehend distinctly the sense intended to be communicated. ^It is, then, in the sciences susceptible only of proba- ble proof, in morals, in politics, in metaphysics, in writings which convey miscellaneous truth, as history, criticism, but particularly in controversial writings, and in conversation, that the hazard of inaccurate ideas is very considerable, and the probability of avoiding them altogether is exceedingly small. One great source of ambiguity, in all these cases, is the indefinite nature of the subjects, and the different aspects under which they appear to different inquirers ; but the greatest source is the unavoidable ambiguity of language, and the diffi 36 IMPORT OF WORDS SHOULD BE UNDERSTOOD. culty of ascertaining exactly the meaning of words.* This double indistinctness, both of the subjects and of the means of communication, cannot fail to produce important consequences in all our opinions and reason- ings; 'and the subject is of too much moment not to obtain a little more of our attention. [* Since reasoning, or inference, the principal subject of logic, is an oper- ation which usually takes place by means of words, and in all complicated cases can take place in no other way, those who have not a thorough in- sight into the signification and purposes of words, will be under almost a necessity of reasoning or inferring incorrectly. And logicians have gener- ally felt that unless in the very first stage they removed this fertile source of error, the pupil would not be in a condition to practise the remaining part of their discipline with any prospect of advantage. Therefore it is that an inquiry into language, so far as is needful to guard against the er- rors to which it gives rise, has at all times been deemed a necessary pre- liminary to the science of logic. But there is another reason why the import of words should be the earliest subject of the logician's consideration ; because without it he can- not examine into the import of propositions. Now this is a subject which stands on the very threshold of logic. — Mill' 9 Logic, pp. 11, 12.1 SIMPLE IDEAS. 37 LECTURE III. IDEAS, SIMPLE AND COMPLEX TO PREVENT AMBIGUITY — DIVISION RULES DESCRIPTION DEFINITION. To penetrate to the bottom of the doctrine of ambi- guity, as it relates both to thoughts and language, and to provide every possible preservative against it, I begin with observing, that, in respect of simple ideas, all mankind are nearly agreed, both about the arche- types and the expression of them, as soon as they are acquainted with the objects that suggest them, and understand the language of which the expression makes a part. Simple ideas are not very numerous, and they are called simple, partly because they admit no divis- ions into parts, but chiefly because, in receiving them, the mind is perfectly passive, and cannot acquire them without an actual survey of the external objects which suggest them, or an actual feeling of the mental opera- tions which produce them. The chief simple ideas are those of the qualities of external objects, shape, colors, tastes, smells, sounds ; those of the operations of the mind, perception, judgment, reasoning, willing; and those of pleasure and pain, power, extension, unity, ex- istence, which are derived partly from the senses, and partly from reflection. There is no method of conveying any knowledge of these ideas but by presenting their archetypes to the external or internal per- cipients ; and if a person be deprived of any of the senses which should convey the knowledge of them, no words, no signs, no known mode of communication can supply that defect ; he must 38 COMPLEX IDEAS. forever remain in ignorance. If a person be deprived of sight, foi example, he must be destitute of all conceptions of light and colors. If he require an account of thinking or willing, of pleasure or pain, we can only refer him to experience. About these ideas, then, no controversy can exist ; because, as all men must receive them from their archetypes, and, of course, all men must receive either the same impressions, and must have these impressions constantly suggested by the words allotted to denote them, or even if they receive somewhat diiferent impres- sions, they must speak and reason about them as if they were the same — for every person can speak and reason only about the simple ideas in his own mind. For example, it is reasonable to believe that the idea of the color denoted by the word green is the same in the minds of all men; but though there were some difference of idea in different men, yet it could not perhaps be detected, for every person must speak and reason concerning that color from the idea of it he possesses. The next class of ideas about which, and the words that denote them, little difference or ambiguity can take place, consists of those complex ideas, which result from collections of simple ideas of the same hind. These are the first remove from simple ideas; and as simple ideas are clear and intelligible, the compositions made out of them partake of the nature of their constit- uent parts, and are likewise clear and intelligible. The two sciences susceptible of demonstration present collec- tions of such ideas, and on this account, among others, they are capable of that high species of evidence. All the operations in arithmetic, however complex, never exhibit any collections of ideas, which result not from different combina- tions or fractions of the simple idea of unity. All the enunciations and demonstrations of mathematics, however compounded and re- fined, contain no ideas which are not formed from combinations of the simple idea of extension. All the triangles, circles, squares, and parallelograms, about which the mathematician is conversant, ex- hibit only different views and combinations of the same simple idea of quantity. About simple ideas, of course, and those sciences which involve combinations of them, men have differed very little, COMPLEX IDEAS. 39 either in the conceptions of them, or in the language that denotes them. Thus far our path is luminous and patent; here, however, the field of perfect light terminates, and the next step lands us in some degree of darkness and ob- scurity. When we enter the confines of the othei sciences, morals, politics, criticism ; when we contem- plate the subjects of miscellaneous knowledge, oratory, poetry, history, essays, or attend to the business of arts and common life, we immediately encounter complex ideas, comprehending large groups of subordinate ideas, and these groups composed not of combinations of the same simple idea, but of combinations of differ- ent ideas, partly simple and partly complex, and we find it almost impossible to avoid mistakes. When we examine, for example, the ideas denoted by the word beauty, a word in everybody's mouth, when speaking of truth, arts, and animals, we are amazed at the multiplicity it includes, and the combinations it exhibits. When applied to truth, it de- notes some important proposition, established by a clear but a refined train of proof — as when we speak of a beautiful theorem, or a beautiful discovery. When applied to animals, it includes the ideas of shape, color, utility, sensibility, acquired bodily and mental accomplishments, youth, health, gracefulness. When applied to arts, it includes uniformity, variety, high polish, convenience, utility — as when we speak of a beautiful woman, or a beautiful picture. Taste is another word in frequent use among men of genius and lovers of the fine arts, and it also will serve to illustrate to what ambiguity communication is in many cases unavoidably exposed. It signifies that sensibility to the beauties of nature, genius, and art, which results from a sound state of the imagination and the under- standing, and which leads us to distinguish and properly prize these beauties. It is plain that much ground of difference is laid in the nature of the objects of this internal sense, because every man must judge from the state of his own faculties, and the cultivation of the faculties of no two men, perhaps, is, entirely equal. Their ideas of the objects of taste must share a similar difference, and must cor* 40 RULES AGAINST AMBIGUITY. respond to the state of their respective faculties. It were easy to multiply examples ; but it will appear from those I have adduced, that a double source of ambiguity prevails with respect to the ideaa and words I have mentioned, and many more similar ideas and words, which every day occur in books and in business. The ideas which compose a complex idea may really be different in different men's minds, according to the improvement of their faculties or powers of perception ; but the greatest hazard of error results from the inattention with which the complex idea may be formed. Thus, one man may omit some of the ideas which compose the complex ones of beauty and taste ; others may add to them more ideas than they naturally and justly contain. Another great source of ambiguity in every inquiry where body or spirit is concerned, is the nature of sub- stances, whether corporeal or spiritual. What substance is, we are utterly ignorant. All we can conceive of it s, that it supports qualities ; and, of course, all our .deas of substances are nothing more than collections cf the qualities we have found to belong to them re- spectively. Now, if any person form not the same conception with us of any of these qualities, or if he either add to or diminish their number, it is plain that his complex idea of the substance can never agree with ours, and that in all communication concerning it, we and he must misunderstand one another. From these observations, the following important practical rules will be allowed to result, as the best preservatives against ambiguity. 1. In all cases when complex ideas come under our consideration, we should employ every precaution to render our collection of the constituent ideas as com- plete and accurate as possible; and whenever we dis- cover that our reasonings and conclusions disagree with the reasonings and conclusions of those with whom we converse, or whose books we read, we should stop and re-examine both the constituent ideas and the expres ORIGin OF DISPUTES. 11 sion of them, because it is a thousand to one tha in the re-examination we shall discover the cause of Jie difference. The propriety and utility of every part of this *ule appears so obvious as hardly to need any illustration. Happy had it been for the peace of society, fortunate had it been for the progress of knowledge, if it had al- ways been punctually practised. All those irritating and frivolous disputes which pester conversation, almost all those controversies which have disturbed and dis- tracted the world, would have been prevented. Consult the controversies which have involved, not individuals only, but classes and periods of learned men, and you will find that they have originated chiefly from misap- prehensions of the ideas and terms which furnish the ground of the difference, and that, if the parties had ex- ercised any patience and pains to understand one another, before they began to dispute, they might have prevented much trouble and vexation to themselves, and much contention and disturbance to society. The famous controversy concerning the superior merit of ancient or modern learning, which interested and divided almost all the learned men of Europe in the end of the seventeenth and the begin- ning of the eighteenth century, and which still interests, and some- times divides, learned men, appears a pertinent illustration. It is a controversy about the meaning of words, and affords very little ground of difference of opinion when the terms are fully ascer- tained. The parties have never considered, that no comparison of authors can exist, except in circumstances perfectly similar. If the state of ancient society gave encouragement to some efforts of genius and industry, which are not now prompted by similar incitements, can we wonder that these efforts should be more brilliant in the former situation, than they are found to be in the latter ? If ora- tory, statuary, architecture, and perhaps poetry, received superior countenance and patronage in Greece, than they found even in Kome, and much more than they have found in modern times, iai 4:2 ENUMERATION, OR DIVISION. it not natural to expect that their exhibitions should be more de- serving of applause ? If, on the other hand, the moderns possess superior knowledge of the system of nature, from the advantages which the progress of science has thrown into their hands; if the improvements of gov- ernment, and the extension of refinement and knowledge, have led them to excel in politics, in moral researches, and in the greater part of the useful arts, can we be surprised at their superiority 8 It was impossible that the moderns could rival the ancients in the former case ; it is equally impossible that they should equal us in the latter. The superiority in the one case, or the inferiority in the other, is no compliment to, or impeachment of, the genius of either ; it is the natural consequence of the different situations of human affairs, and could not, without a miracle, have been otherwise. Had the keen combatants in this controversy attended to this nat- ural state of the case, they would have forborne their ill-founded and injurious recriminations. The patrons of modern literary merit unjustly measure the merits of ancient genius by a scale adopted from modern ideas and manners ; the patrons of ancient genius re- taliate the same game, and pretend to determine the eminence of modern genius by a scale derived from the ideas and manners of ancient times. Let these reasonable limitations be admitted, and the shadow of a controversy, I believe, would vanish ; the differ- ence would at least be found to be so frivolous, as to satisfy every- body of the absurdity of the contest. 2. After ascertaining the amount of a co?nplex term by enumeration, by description, or by definition, 6m- ploy it ahvays in the same sense, without adding to, diminishing, or changing the ideas it denotes. Enumeration, commonly called division t>y logicians, is a recapitulation of the subordinate ideas of which a complex idea consists, and forms a very satisfactory method of explaining or ascertaining that complex idea. For example, the term gratitude includes the following subordi- nate ideas : a consciousness of favor received, a disposition to ac- knowledge it on every proper occasion, and a resolution to seize the first opportunity of returning a similar favor to the benefactor. DIVISION DESCRIPTION. 43 Honor, in like manner, includes an unalterable regard to truth in words, humanity and generosity in actions, candor and forgiveness in thoughts, and resentment of insult or affront, [Division of a conception enumerates all the objects or classes that are included under it, and so deals with the extent of the no- tion ; or it is the enumeration of the various co-ordinate species of which a proximate genus is composed. The rules for conducting the process correctly are — (1.) The constituent species, called the dividing members, mast exclude one another. (2.) The constituent species must be equal, together, to the ge- nus divided. (3.) The division must be made according to one principle or ground. The first rule is to secure that the classes and sub-classes shall be distinct from each other. Exceptions to this rule are often un- avoidable, especially in subjects that do not belong to strict sci- ence: thus, in enumerating the species of imaginative writers, one would probably mention poets, dramatists, and writers of tales; yet some poets are dramatists, and some tales are poems. The second rule provides that no class shall be omitted, and se- cures completeness. The principle of division mentioned in the third rule, is some new conception, for the marks of which we seek in the conception to be divided. Thus man may be divided into European, African, Asi- atic, American, and Australian ; and again into Christian, Mobam medan, Jew, and Pagan ; and again into just and unjust. The separation of the parts of any individual object, as of a sword into blade and hilt, is termed partition. An individual is thai which cannot be divided without ceasing to be what it is : its parts can- not have the name of the whole. When a genus is divided, every part of it remains unchanged, and may have the name of the genus. The trunk and limbs of a man cannot be severally called a man ; but a European is a man, and an Asiatic, and an American.— Thomson.'] Description, also, is a sort of enumeration, but is ap- plicable chiefly to objects of sight. It is used often to distinguish objects of sight, which have not obtained names, or of which the names are unknown. We de- scribe a landscape, a river, a house, a town, a ship, a 44 DEFINITION. horse, a tree, a robber, in order to communicate ideas of these objects to those who have not seen them, or tc enable those to distinguish them when they do see them. Description is a recapitulation of the parts or properties of the object described. A landscape, for instance, contains corn-fields, plantations, water running or stagnating, hills, houses, villages, animals, situate in such a manner as diversify it from all other landscapes. The color, shape, strength, gentleness, fleetness, and easy motion, which con- stitute the description of my horse, discriminate him from all other horses. A deserter, or a robber, is described by his stature, figure, complexion, features, and dress ; or, in other words, by a recital of the particulars which form his appearance, and which mark him out among other men. Definition is the last method of ascertaining complex ideas or general terms, and differs not essentially from the preceding methods. The chief difference is the use of it on different occasions. It may be employed in fix- ing complex ideas of all sorts, whether their archetypes are objects of the external senses, or are the creatures of reflection, that is, whether they exist in matter or in mind. It is used, however, chiefly to ascertain species, whose archetypes exist in the mind. A good definition -.consists of two parts ; by one part are marked those objects with which the thing defined has any common qualities ; by the other part are marked those qualities which characterize the thing defined alone. Nothing more can be done to ascertain the nature of any object^ than to point out those objects with which it has any common qualities, and next to enumerate the qualities peculiar to itself. Hence the logical rule, that every definition* should consist of a genus and a specific dif- [* As division ascertains the various classes of objects united under one conception, so does definition ascertain those common marks which all the objects possess, or that common nature represented by the conception KULES OF DEFINITION. 45 ference, the genus denoting the common qualities, and the specific difference the characteristic or peculiar ones. Suppose, for example, it were required to define what the mathe- maticians call a square, or a parallelogram, these most accurate ut all logicians will tell us, that " a square is a figure which has four equal sides, and four right angles," and that " a parallelogram is a figure that has four angles, and four sides, the opposite angles and sides only being equal." The things defined are species, that is, the square and the paral- lelogram are not a square and parallelogram which exist in some book, or are delineated on a particular board ; they stand for the en- tire species of squares and parallelograms, and mark the properties common to all the individuals of these species. The first part of the The rules of definition may be stated, as a help to understanding the pro- cess itself. (1.) A definition must recount the essential attributes of the thing defined. Thus, in defining " words" as u the articulate signs of thoughts," we are not to introduce such a superfluous mark as " words are the articulate signs by which an orator expresses his thoughts ;" for whilst this is true, it is not necessarily found in the conception in our mind, and consequently has no place in the act of analyzing it. (2.) The definition mvst not contain the name of the thing defined; as this is precisely the word we are bound to explain. Thus, if " life" is defined to be "the sum of the vital functions," we have not logically defined " life," as the word "vital," which implies it, stands unexplained in the defi- nition. (3.) A definition must be precisely adequate to the species defined. If it explain a species below, it is said to be too narrow, as where "triangle" is defined " a rectilinear figure with three equal sides and angles." If it is applicable to the genus above, it is too wide, as when we define u words" as the " sign of thoughts," whereas there are other signs also. (4.) A definition must not be expressed in obscure, or figurative, or am- biguous language. The Divine Nature has been represented as " a circle whose centre is everywhere, and whose circumference is nowhere;" but this bold figure cannot for a moment be accounted a definition. (5.) A definition must not be negative. "Evil is that which is not good." " A point is that which has no parts and no magnitude." These definitions are to be judged according to our view of the possibility of find- ing others of the positive form. Some conceptions are in their nature negative, as indivisibility, blindness, and must be defined negatively.— Thomson .1 4:0 DEFINITION EXAMPLES. definition refers them to their genus, or characterizes them by the name of figures, by which it is signified that they have something in common with all other mathematical species, circles, triangles, rhombuses, ellipses, namely, they include space, and are bounded by lines. The second part of the definition exhibits their specific difference, or enumerates the peculiar properties which distinguish them from all the other species of the same genus; squares have four right angles, and four equal sides ; parallelograms have also four angles and four sides, the opposite angles and sides only being equal, which no other species have but themselves. If I define eloquence to be the art of speaking or writing well, logic the art of reasoning well, statuary the art of forming an exact resemblance of the human shape in marble, painting the art of de- lineating a resemblance of the same shape on canvas by means of oil colors, I refer all these species to their genus, and mark proper- ties in which they all agree, namely, in being arts, or something acquired by industry and practice, and then I mention the proper- ties which distinguish these arts from all other arts, and from one another ; eloquence by speaking or writing well, logic by reasoning well, statuary by forming a resemblance of the human shape in marble, painting by delineating a similar resemblance on canvas. If, again, I define morality to be the science which teaches to be wise, virtuous, and happy ; politics the science which teaches to provide for the prosperity of communities, or large bodies of men ; mathematics the science which teaches to compute quantity ; pneu- matics the science which teaches the properties of spirits, or the doctrine of fluids ; optics the science which teaches the theory oi vision and colors : I refer, first, all these branches of knowledge to their next genus, science, by which I signify, that they all agree in presenting some useful truths to the mind, and that they are sup- ported by satisfactory evidence. In the second place, I distinguish each science from the rest, and from all other sciences not men- tioned, by specifying as above the particular truths which it incul- cates. Definition might certainly be employed to discrimi- nate complex ideas on every occasion, and might su- persede both enumeration and description ; but in all such cases, the specific difference would become either an enumeration or a description. Indeed, there is no ma- terial difference between these methods of ascertaining SPECIFIC DIFFERENCE. *7 ideas, except in the length of the specific difference. An enumeration, or a description, either includes or supposes a genus, to which the idea explained refers ; and the specific difference of every definition is either an enumeration or a description. For example, the enumeration formerly advanced, of the ideas expressed by the word honor, may easily be converted into a defi- nition, of which the specific difference will become the enumeration itself. " Honor is a disposition which prompts us to regard truth in our words, generosity in our actions, candor in our thoughts, and to entertain resentment of insult or affront." In like manner, I may convert the description of a horse into a definition, of which the description will constitute the specific difference. I may call him an animal of a cylindrical body, long and taper legs, high neck, beautiful head, of a bay color, gentle temper, easy motion, and fit for riding. It is to be observed, however, when the spe- cific difference resolves itself into an enumeration, or a description, it is of little consequence to distinguish the genus. On the other hand, when it is of consequence to distinguish the genus, the spe- cific difference seldom consists of more than one or two properties. Definition is always used in the last case, and enumeration or de- scription in the two first. Enumeration is commonly employed to explain complex ideas, of which it is of little consequence to men- tion the genus ; description, to ascertain complex ideas, the arche- types of which are objects of sight ; and definition, to ascertain. the abstract ideas of species. With respect to definition, it is proper further to ob- serve, that we must never attempt to apply it to simple ideas, because they are immediately derived from per- ception, prompted by the objects or operations which suggest them ; and no definition or explication can ren- der them more distinct or intelligible than they are. Even the mathematicians have not always been suffi- ciently attentive to this remark. The word ratio denotes the idea of equality or inequality, which results from the comparison of two magnitudes of the same kind in point of quantity ; as when one of the magnitudes h said to be 48 SIMPLE IDEAS NOT TO BE DEFINED. equal to, greater or less than the other, or to hold to it some fixed proportion. The idea appears to be simple, at least no words can make it plainer than the actual comparison of the magnitudes by which it is prompted. Yet all the editions of Euclid I have seen, previous to the one published by Dr. Simpson of Glasgow, present definitions of it. " Ratio," we are told, " is a habitude of magni- tudes of the same kind, according to quantity." Habitude is a word at least as unintelligible as ratio ; yet it seems no plainer word could be found. The truth is, the definition should not have been attempted, and Simpson has accordingly expunged it. Motion is another simple idea, on which Aristotle, and the schoolmen after him, have exercised their ingenuity, and have pro- duced the following famous specimen of jargon. They tell us, that motion is " actus entis in potentia, quatenus in potentia," the act of a being in energy, as far as it is in energy. Even later and bet- ter philosophers, who define motion by " a passage from one place to another," do not make the matter much plainer. They only substitute one word for another, and it is difficult to decide whe- ther motion is better explained by passage, or passage by motion. As, then, complex ideas only are susceptible of ex- plication in any of the ways I have mentioned, if we would preserve perspicuity, careful attention must be paid that the same meaning, thus settled, shall be in- variably retained. The determination of this point is simple and easy, and may always be accomplished by substituting the explication in the place of the term de- fined. "If this be practicable, and the sense be pre- served, we may be confident we have not changed the meaning of the term. Before I relinquish this branch of the subject I must observe, that although, in compliance with the exam- ple of all logical writers, I have hitherto considered, and shall through the whole of this course continue to consider, all knowledge as composed of ideas, and shall call every impression made on the mind, whether de- rived from an external or an internal archetype, by this name : yet that some- late writers of eminence have DEFINITIONS OF NAMES AND OF THINGS. 49 called these impressions by other names than that of ideas. All impressions, then, prompted by archetypes, which have a real existence without the mind, they distinguish by the name of perceptions. All impres- sions, of w T hich the archetypes have no real existence, but are the creatures of the imagination, as a mountain of gold, a sea of milk, they denominate coyiceptions. Those impressions only they call ideas, which have been formerly received into the mind, and are again recalled by memory. You will find this explanation useful in reading some metaphysical, and even some critical writers ; but it is more convenient for our pur- pose to give the name of idea to every impression, whether simple or complex, and from whatever source it may be derived. [Definitions have been divided into those of names and those of things : the former explain the meaning of a term, the latter the nature of a thing, the last being the most important. The distinction between nominal and real definitions, between definitions of words and what are called definitions of things, though conformable to the ideas of most of the Aristotelian logi- cians, cannot be maintained. We apprehend that no definition is ever intended to " explain and unfold the nature of the thing." No definition can unfold its whole nature; and every proposition in which any quality whatever is predicated of the thing, unfolds some part of its nature. The true state of the case we take to be this. All definitions are of names and of names only : but in some definitions it is clearly apparent, that nothing is intended except to explain the meaning of the word ; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing corre- sponding to the word. Whether tins be or be not implied in any given case, cannot be collected from the mere form of the expres- sion. a A centaur is an animal, with the upper parts of a man and the lower parts of a horse," and u A triangle is a rectilineal figure with three sides," are, in form, expressions precisely similar; although in the former it is not implied that any thing, conforma- able to the term, really exists, while in the latter it is, as may be 3 50 DEFINITION AND FUSTULATE. seen by substituting in both definitions the word means for Is. Id the first expression, " A centaur means an animal, &c," the sense would remain unchanged : in the second, " A triangle means, &c," the meaning would be altered, since it would be obviously impos- sible to deduce any of the truths of geometry from a proposition expressive only of the manner in which we intend to employ a par- ticular sign. There are, therefore, expressions, commonly passing for defini- tions, which include in themselves more than the mere explanation of the meaning of a term. But it is not correct to call an expres- sion of this sort a peculiar kind of definition. Its difference from the other kind consists in this — that it is not a definition, but a definition and something more. The definition above given of a triangle, obviously comprises not one but two propositions, perfect- ly distinguishable. The one is, u There may exist a figure, bound- ed by three straight lines :" the other, " And this figure may be termed a triangle." The former of these propositions is not a defi- nition at all : the latter is a mere nominal definition, or explanation of the use and application of a term. The first is susceptible of truth or falsehood, and may therefore be made the foundation of a train of reasoning. The latter can neither be true nor false : the only character it is susceptible of, is that of conformity or discon- formity to the ordinary usage of language. There is a real distinction, then, between definitions of names and what are erroneously called definitions of things; but it is, that the latter, along with the meaning of a name, covertly asserts a matter of fact. This covert assertion is not a definition, but a postulate. The definition is a mere identical proposition, which gives information only about the use of language, and from which no conclusions affecting matters of fact can possibly be drawn. The accompanying postulate, on the other hand, affirms a fact, which may lead to consequences of every degree of importance. Tt affirms the real existence of things possessing the combination of attributes set forth in the definition ; and this, if true, may be a foundation sufficient on which to build a whole fabric of scientific truth.— MilVs Logic, pp. 98, 99.] INVESTIGATION OF TRUTH AND KNOWLEDGE. 51 LECTURE IV. KNOWLEDGE AND TRUTH, WHAT? THE RESULT OF INTUITION OK OF REASONING DIFFERENT KINDS OF PROPOSITIONS SOUR- CES WHENCE DERIVED. In former lectures I have considered ideas as simple, as complex, distinct or confused, adequate or inade- quate, particular or abstract ; and I have illustrated at considerable length the pains we must take, and the rules we must follow, in order to have them in the most perfect state, and to obtain over them the most com- plete command. All, however, I have hitherto ad- vanced, is a mere preparation of the materials of logic ; we have not yet taken the least step towards applying them to any use in the investigation of truth and knowl- edge. To this application I am now to proceed. The investigation of truth and knowledge consists of two operations. The first compares two ideas, in order to perceive in them agreement or disagreement; the second compares two ideas, by the help of one or more intermediate ideas. The truth or knowledge acquired by the first operation is said to result from judgment ;* the truth or knowledge acquired by the second opera- tion is said to result from reasoning. I begin with [*It is hardly necessary to remark, that judgment enters as an element into almost all our mental acts. We think in judgments; that is, we are always affirming one thing of another, and we do not consider any thing else to be thinking. To conceive of things without forming judgments, is to make no progress. We can only be said to think when we fcrm a judg- ment respecting two conceptions, in which one is affirmed of the other.— Dr. Wayland.] v . 52 KNOWLEDGE — TRUTH. judgment, and the truth and knowledge which are at- tainable by its means. Two preliminary questions occur : what is knowl- edge ? and, what is truth ? We are familiarized with these words, and we are not disposed to suspect there is any mystery in their meaning. But it is not, per- haps, so obvious as is generally supposed ; and it is of bo much importance in our present inquiries, that we must not proceed without attempting to ascertain it. Knowledge, then, I assert, is the perception of the agreement of ideas with one another; truth, is the agreement of ideas with words. But what, it will again be asked, perhaps, is the signification of these words, agreement and disagreement? I reply, that the signifi- cation of these words is not always the same, but varies according to the nature of the science, art, or subject, about which the ideas are conversant. A few examples will be the best illustration. In arithmetic and mathematics, the only comparison of ideas which can take place relates to the equality or inequality of the quantities; agreement denotes equality — disagreement, inequality. When I compare the quantities four and five, I perceive that they are unequal, or that the ideas of them disagree. I perceive further, if I add one to four, that these two together will form a compound quantity, which will be exactly equal to five, or that the ideas tour and one conjoined will agree with the idea five. My knowledge, then, that four is not equal to five, but that four and one are equal to five, is the intuitive perception I have that the idea of four disa- grees with the idea of five, while the idea of four and one together agrees with the idea of five. In like manner, from the ideas I have of a right angle, or half a light angle, or from the ideas I have of an acre, and half an acre, 1 know certainly that the half right angle disagrees with, or is a less quantity than the whole right angle — that the half acre disagrees with, or is a less quantity than the whole acre; and that if I double the half right angle and the half acre, I shall form two compound quantities, the ideas of which will agree respectively with those of UNIVERSITY Of KNOWLEDGE CERTAIN OR PROBABLE. 53 the whole right angle and the whole acre. The perception of the agreement or disagreement of ideas, in all these cases, is the same thing with the knowledge of the equality or inequality of the quan- tities compared. If, in natural philosophy, I compare body or matter with divisi- bility, I immediately discover that divisibility applies to, or is a property of, matter ; in other words, I find that the ideas of matter and divisibility agree together, and I know that matter is divisible. Agreement, in this case, signifies property or relation, not equality, as in the preceding cases. If I maintain, in morals, that a good man is happy ; or in politics, that a wise king is a blessing to his people ; or in arts, that industry is commonly attended with suc- cess, my knowledge of all these maxims is perfectly the same thing with the agreement I perceive between the ideas of a good man and happiness, of a wise king and the happiness of his people, of industry and the acquisition of wealth. Truth relates to the enunciation of knowledge, and is the agreement of ideas with words. If I assert that the British is a free government, and that the English are more industrious than any other nation in Europe, I maintain truth, because my words actually correspond to accurate ideas of the fact3. If, again, I say that the three angles of a triangle are equal to two right angles, I express a truth, because it is demonstrable that my words and ideas agree. Falsehood, on the other hand, is the disagreement of words with ideas [i. e., with ac- curate ideas of the facts of the case] ; as when it is asserted that the British government is despotic, or that the three angles of a triangle are equal to three right angles. A mistake, is the actual disagreement of words with ideas, when we suppose that they agree. The ignominious falsehood called a lie, is the disa- greement of words with ideas, uttered with an intention to deceive. Knowledge, further, is of two kinds, certain and prob- able. Certain knowledge takes place when the mind is perfectly satisfied of the agreement or disagreement of 64 PROPOSITIONS- -FOUNDED ON INTUITION. its ideas.* Probable knowledge takes place when the agreement or disagreement of ideas is not so clear as to afford perfect satisfaction, and the degrees of proba- bility are greater or less, according as the satisfaction is more or less perfect. In judging of the agreement or disagreement of ideas, we must examine them in pairs, and the words in which we express that judgment form a sentence, called a proposition. For example, if the idea of a whole be compared with the idea of a part, it is immediately found that they disagree; and this judgment is ex- pressed by the following proposition: "The whole is greater than any of its parts." But, if the idea of the whole be compared with the idea of all its parts taken together, it is found that they agree; and this judg- ment is expressed by the following proposition : " The whole is equal to all its parts taken together." If the agreement or disagreement be perceived by bare juxtaposition of the ideas, without the intervention of any intermediate idea, the evidence of the proposition is said to be intuitive. But, if the agreement or disa- greement be perceived by means of some intermediate idea, or train of ideas, the mind then must proceed by steps. It must compare the first idea of the proposition with the first intermediate idea, and pass a judgment on their agreement or disagreement. It must next com- pare the first intermediate idea with the second inter- [* Knowledge is a clear and certain conception of that which is true, and implies three things: firm belief — of what is true — on sufficient grounds. Our knowledge is of two kinds: 6f facts, and of truths. A fact is any thing that has been, or is. We derive our knowledge of facts through the medium of the senses. Truth is an exact accordance with what has been, is, or shall be. There tte two methods of ascertaining truth : (1) by comparing known facta with each other; (2) by comparing known truths with each other. Hence, truths are inferences, either from facts or other truths. — Davit? Logic nj Mathematics.] PROPOSITIONS — FOUNDED ON REASONING. 55 mediate idea, and pass a similar judgment. It must proceed, in like manner, through all the intermediate ideas, and pass similar judgments, till it comes to com- pare the last intermediate idea with the latter idea of the proposition ; and from all these intermediate judg- ments the conclusive judgment is deduced, concerning the agreement or disagreement cf the two primary ideas of the proposition. In this case the evidence of the proposition, declarative of the agreement or disagree- ment of the two primary ideas, is said to be founded on reasoning. Hence it appears that all knowledge, whether it he the offspring of intuition or the result of reasoning, is denoted by propositions, which express the agreement or disagreement of ideas ; that each proposition con- tains two ideas, simple or complex, besides the assertion of agreement or disagreement ; and that the proposition which denotes agreement may be called affirmative, that which denotes disagreement may be called nega- tive. u That the three angles of a triangle are equal to two right angles," is an affirmative proposition; "that a part is not equal to the whole," is a negative one. The two capital ideas constitute two parts of a propo- sition. The first idea, or sometimes several ideas con- sidered as one, is that of which something is affirmed or denied, and is therefore called the subject of the proposition ; the second idea, or sometimes several ideas considered as one, is the property, or quality, or attri- bute, which is either affirmed or denied to belong to, or to agree with, the first idea, and is therefore called the predicate of the proposition. " The three angles of a triangle are equal to two right angles," is a proposi- tion, of which the idea of the three angles forms the subject, and the idea of equality to two right angles forms the predicate. The affirmation contained in the 56 SUBJECT PREDICATE COPULA. word are is commonly called by logicians the copula 01 connective of the proposition.* [Mr. Thomson more briefly thus defines these several parts of a proposition or judgment : Every judgment has three parts: the subject, or notion about which the judgment is; the predicate, or notion with which the subject is compared ; and the copula, or nexus, which expresses the mode of connection between them. The subject and predicate are called the terms of the judgment, i. e., the extremes or boundaries (termini) which it brings together.] [The subject (Dr. "Wayland remarks) may be either an individual or a species, — the predicate must be a genus ; that is, it must designate a larger class than the subject. In a proposition, we therefore affirm that a particular individual is included within a particular [* The copula is the sign denoting that there is an affirmation or denial. and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. Thus, in the proposition, " The earth is round," the predicate is the word round, which denotes the quality affirmed, or (as the phrase is) predicated ; the earth, words denoting the object which that quality is affirmed of, compose the subject; the word is, which serves as the connecting mark between the subject and predicate, to show that one of them is affirmed of the other, is called the copula. A predication is sometimes distinguished from every other kind of dis- course, by a slight alteration in one of the words, called an inflection ; as when we say, Fire burns ; the change of the second word from burn to burns, showing that we mean to affirm the predicate burn of the subject fire. But this function is more commonly fulfilled by the word is, when an affirmation is intended ; is not, when a negative ; or by some other part of the verb to be. It is apt to be supposed that the copula is much more than a mere sign of predication ; that it also signifies existence. In the proposition, "Soc- rates is just," it may seem to be implied that not only the quality just can be affirmed of Socrates, but moreover that Socrates is, that is to say, exists. This, however, only shows that there is an ambiguity in the word is ; a word which not only performs the function of the copula in affirmations, but has also a meaning of its own, in virtue of which it may itself be made the predicate of a proposition. That the employment of it as a copula. does not necessarily include the affirmation of existence, appears from such a proposition astnin, " A centaur is a fiction of the poets ;" where it cannot pos- sibly be implied, that a centaur exists, since the proposition itself expressly asserts that the thing has no real existence.— rMill's Look, pp. 12, 53.] DIFFERENT KINDS OF PROPOSITIONS. 57 class. Hence every proposition must be either true or false. The subject is either included within the class designated by the predicate, or it is not. It cannot be neither within nor without it.] [Judgments (or propositions), according to the com- mon account of relation, are divided into three classes : the categorical, the hypothetical, and the disjunctive. The categorical judgment is one in which one con- ception is affirmed to belong or not to belong to another, as, " Men are endowed with conscience ;" " An enslaved people cannot be happy." The hypothetical expresses seemingly a relation be- tween two judgments, as cause and effect, as condition and conditioned ; for example, " If the autumn is very dry, the turnip crop is scanty ;" " If the heart is right, so will the actions be." The disjunctive judgment expresses the relation (ap- parently) of two or more judgments which cannot be true together, and one or other of which must be true ; as, " Either the Bible is false, or holiness ought to be followed ;" or the proverb, " A man is either a fool or a physician at forty." — Thomson.'] Propositions, further , are distinguished by different names, according to the clearness of the evidence by which the agreement or disagreement of the subject and predicate is evinced. If the evidence be perfectly sat- isfactory, the proposition is denominated certain. If the evidence be not perfectly satisfactory, it is denomi- nated probable ; and it is more or less probable, accord- ing as the evidence is more or less satisfactory. If the evidence for the agreement of the subject and predicate balance the evidence for their disagreement, the propo- sition is called doubtful. If the evidence be stronger on the side of disagreement, it gets the name of im~ probable ; and the improbability will be the greater, ad 8« 58 DIFFERENT KINDS OF PROPOSITIONS. the evidence of disagreement shall increase. If the proposition bear an affirmation contrary to [accurate] ideas, it obtains the name of false. If the affirmation be conformable to [such] ideas, it is denominated true. Propositions, also, are divided into universal, par- ticular, singular, and indefinite. A proposition is universal, when the subject of it comprehends an en- tire genus or species. Thus, " All animals are endowed with life and organization," is a universal proposition, because the subject of it includes, and the predicate ap- plies to, all living creatures, or to a whole genus. " All men are liable to err," is another universal proposition, because the subject includes, and the predicate applies to, a whole species, or every individual of the human race. A particular proposition denotes a limited 01 partial meaning of the subject, or signifies that it does not include an entire genus or species; and, in this case, the restricting words, some, few, many, &c, usu- ally precede the subject of the proposition. For exam- ple : " Few men spend all their time to the best advan- tage ;" " Many men repent of their folly when it is too late ;" are both particular propositions, because they include a part only of the human species to which they refer. A singular proposition has an individual for its sub- ject ; as when we say, " Alexander conquered Persia ;" u Caesar was assassinated in the senate-house." An in- definite proposition relates to one individual among many, and is commonly introduced by the indefinite article : " A wise man guides his affairs with discre- tion ;" "A fool is perpetually betraying his ignorance and impudence." Propositions likewise are denomi- nated conditional, when they express condition or de- pendence, " If people break the laws, they will be pun- ished ;" or relative, if they denote consequence or con- PROPOSITIONS, EXPRESSIVE OF RELATIONS. 59 nection, "Though he fall, yet will he rise again." But distinctions of this kind seem to belong more to gram mar than to logic. [Propositions are nothing more than expressions of relations of one kind or another which we have previously recognized : there are the relations of position, resemblance or difference, proportion, degree, and comprehension. I judge that A is actually higher than B, though at first sight it might appear to be lower ; i. e., I recognize the relation of position which they bear to each other. 1 judge that this picture resembles my friend, in certain respects, and that it is entirely unlike him in others : i. e., I am impressed with the relations of resemblance and dissimilarity, which exist between the picture and my friend. I judge that two is to four, as this latter number is to eight ; i. e., I feel the relation of proportion which the numbers bear to one another. I judge that a house consists of its foundation, roof, differ- ent apartments, mt A £b, I also contradictories. All A is B, "J Some A is B, and \ respectively subalternate. No A is B, Some A is not B, I INDUCTION. i -> axioms of logic are on a level with those of mathe- matics. § 2. Having noticed, in order to exclude from the province of reasoning, or inference properly so called, the cases in which the progress from one truth to another is only apparent, the logical consequent being a mere repetition of the logical antecedent ; we now pass to those which are cases of inference in the proper acceptation of the term, those in which we set out from known truths, to arrive at others really distinct from them. Reasoning, in the extended sense in which I use the term, and in which it is synonymous with inference, is popularly said to be of two kinds : — reasoning from particulars to generals, and reasoning from generals to particulars ; the former being called induction, the latter, ratiocination, or syllogism. It will presently be shown that there is a third species of reasoning, which falls under neither of these descriptions, and which, nevertheless, is not only valid, but the foundation of both the others. The meaning intended by the above expressions is, that induction is inferring a proposition from proposi- tions less gmeral than itself; and ratiocination is in- ferring a proposition from propositions equally or more general. When, from the observation of a number of individual instances, we ascend to a general proposi- tion; or when, by combining a number of general propositions, we conclude from them another proposi- tion still more general, the process, which is substan- tially the same in both instances, is called induction. When from a general proposition, not alone (for from a single proposition nothing can be concluded which is not involved in the terms), but by combining it with other propositions, we infer a proposition of the same 76 INDUCTION. degree of generality with itself, or a less general propo- sition, or a proposition merely individual, the process is ratiocination. When, in short, the conclusion is more general than the largest of the premises, the argument is commonly called induction ; when less general, or equally general, it is ratiocination. Induction is, without doubt, a process of real infer- ence. The conclusion in an induction embraces more than is contained in the premises. The principle or law collected from particular instances, the general proposition in which we embody the result of our ex- perience, covers a much larger extent of ground than the individual experiments which are said to form its basis. A principle ascertained by experience is more than a mere summing up of what we have specifically observed in the individual cases that we have examined ; it is a generalization grounded on those cases, and ex- pressive of our belief, that what we there found true, is true in an indefinite number of cases which we have not examined, and are never likely to examine. In every induction we proceed from truths which we know, to truths which we did not know; from facts certified by observation, to facts which we have not observed, and even to facts not capable of being now observed ; future facts, for example, but which we do not hesitate to believe upon the sole evidence of the induction itself. —MilVs Logic, pp. 108-112.] [We return now to Professor Barron's Lecture.*] I have now explained the nature of propositions; I have specified the different kinds into which they may be divided ; and I have enumerated the principal sorts of evidence by which they are supported. From what 1 have advanced, it has appeared that all the proposi [* For some excellent remarks on Induction and Deduction, from Thomson's Lawi of Thought, refer to the concluding chapter of this volume J ' THE PROPER FUNCTIONS OF JUDGMENT. 77 tions into which knowledge may be formed, are resolva- ble into an affirmation or negation of the agreement of the two terms or ideas of w T hich they consist ; and that the judgment the mind passes on this agreement or dis- agreement, is then proper and just, when it corresponds to the degree of evidence by which the proposition is supported. The perfection of judgment is, to compare our ideas fairly and candidly, either by juxtaposition, as in the case of intuitive propositions, or by the inter- vention of intermediate ideas, when proof is requisite, and to pass a decision on that comparison, according to truth and justice, unbiased by partiality or prejudice, unseduced by fallacious appearances in things, ambi- guities in words, or any disposition to deceive, or to be deceived. As, then, the purpose of all our inquiries is, to dis- cover truth and knowledge, and as the completion of this discovery consists in discerning the agreement or disagreement of our ideas, it is plain that we cannot proceed one step without having constant recourse to the operation of judgment. We exert it immediately in cases of intuition ; we exert it at the conclusion of every process of reasoning, in determining whether two principal ideas agree or disagree; and we exert it in every step of that process, in deciding concerning the agreement or disagreement of each couple of interme- diate ideas. The candid inquirer, therefore, should study to preserve his mind in a state fitted to perform this operation in a proper manner, and to divest it of all obstructions or incumbrances which may interfere with its success. Without this precaution, it is vain to pre- tend to discover truth, because we shall only perplex and discompose our minds, spend our time in irksomeness to ourselves, in disturbance to others, and sink deeper in falsehood and in error. After all the candor and 78 patience we can exercise, the investigation of knowl edge is a painful and laborious task ; but our labor and time are totally thrown away, without a legitimate ex- ertion of judgment. It is, therefore ^ a matter of the highest importance, in searching for truth, to hriow those impediments which obstruct the rectitude of our judgments, and to learn the rules we m,ust observe, in order to conduct them with justice and expedition. This is a subject deserving most serious attention, and must not be forgotten in a system of logic. Erroneous judgments are denominated prejudices, or rash judgments / that is, judgments passed before we have duly examined all the circumstances of the case on which we intend to decide. Prejudices generally relate to opinions ; prepossessions, to attachments : the former refer chiefly to things, the latter to persons. But I intend here that prejudices should comprehend all the impediments w T hich interfere w T ith our forming [right] judgments of every sort, whether respecting things or persons. Prejudices are arranged by Lord Bacon under four heads, w r hich he calls, in the lan- guage of the schools, Idola Tribus, the prejudices of the species ; Idola Fori, the prejudices of language ; Idola Specus, the prejudices of the individual ; and Idola Theatri, the prejudices of authority. These terms, though scholastic, are extremely significant. It is seldom we find the language of the schoolmen so re- plete with meaning. Prejudices are not improperly distinguished by the title of Idola ; because they occupy the place of truth in the mind, in the same manner as the idol attracts in the temple the devotion which be- longs to the Author of nature. The Idola Tribus are the. prejudices common to all mankind, and arise from the natural imbecility and vanity of the mind, or from *iie influence which imagina- PREJUDICES OF THE SPECIES. TO tion, passion, affection, and attachment have upon the operations of the understanding. The Idola Fcn % i in- clude the erroneous judgments into which we are led by the inaccuracy or the abuse of language. The Idola Sjoecns comprehend those prejudices which result from peculiar circumstances, from constitution of mind or body, from education, from habit, or from accident. The Idola Theatri are the errors into which we are de- coyed by public opinion, by authority, by custom, by fashion, or by any other means which mankind employ to pervert the judgments of one another. These divi- sions contain, if not all, at least the chief materials of our prejudices. I shall therefore resume them, and point out the particulars contained under each. I begin with the Prejudices of the species. Though the human understanding, assiduously em- ployed and properly directed, might have proceeded much farther than it has done in the investigation of knowledge, yet, so limited are its powers, that there is much reason to apprehend its progress, in the most fa- vorable circumstances, cannot be very great. Thousands of subjects daily occur, concerning which we are totally ignorant, and concerning which any industry we can exert cannot be supposed to remove that ignorance. The substance and many of the operations of all existences, cor- poreal and spiritual, are now, and perhaps will remain, altogether unknown. We comprehend nothing of either, but a few of their qualities. All the assimilating powers of nature, by which animals are produced, and reared, and live, and act, by instinct or design ; by which plants grow to various sizes, cpnsist of texture so differ- ent, display colors so beautiful %id so numerous ; and by which minerals so precious, and so dissimilar, are formed in the bowels of the earth ; constitute an immense field of inquiry, in a great meas- ure beyond our reach. All investigations which involve the idea of infinity, whether with regard to excellence, space, or time, exceed our comprehension ; because of infinity we have no adequate con- 80 PHILOSOPHY OF THE SCHOOLMEN. ception, and can only approach it negatively by discovering whnt it is not. All inquiries, also, about futurity, however anxiously pursued by men in all ages and situations, surpass the human powers of research, if we except the very short progress which the sagacity of some men may make, guided by the imperfect and falli- ble aid of experience and analogy. Limited, then, as the mind of man is in. its inquiries, by the nature of many subjects themselves, and numer- ous as still are the fields of accessible knowledge, un- touched or unexplored ; such, notwithstanding, is its vanity, its folly, or its presumption, that more perhaps of its time and its industry has been employed in searching for what is not to be found, than in investiga- ting what is useful and intelligible. Is it not deplorable, that so much ingenuity should have been thrown away, even in enlightened times, on skeptical and useless in- quiries concerning the nature and existence of matter and spirit, without attending to what is of real importance, the qualities and operations of both, from which useful knowledge concerning them might have been deduced ? Is it not equally lamentable, that the true method of prosecuting the study of nature should have been unknown till the days of Lord Bacon ? and that philosophers should have been so misled, or so absurd, as to retire to their closets, and to form theories to account for the phenomena of the heavens and the earth, without consulting the facts which they every day beheld ? But all the abuses and misapplications of human ingenuity com- bined, furnish nothing equal to those of the schools for near five hundred years, from the middle of the eleventh century to the re- vival of learning in the sixteenth. Never did any set of philosophers labor so strenuously and successfully to enlighten the mind of man, and to promote the discovery of truth, as the schoolmen did to confound all human inquiry, and to interrupt all progress in knowl- edge. Never were subtilty and ingenuity employed so preposter- ously, in pretending to teach the method of investigating truth, and exposing error, without communicating any useful information.* [* " The works of Aristotle, translated into barbarous Latin, formed the groundwork of what has been called the philosophy of the schoolmen ; who THE SCHOOL-LOOrC. : 81- LECTURE VI. PREJUDICES. "Vanity and presumption have not been engaged more successfully in obstructing the progress of general knowledge, than the imagination, the passions, and self-interest, have been employed in clouding the mind with prejudices respecting society, business, arts, and social intercourse. National partialities are so insuper- able in the most enlightened and civilized periods, that it seems impossible for the people in general of any nation, to do justice in the judgments they form, of the capacity, the ingenuity, the courage, or the integrity of their rivals. The proud Jews of old treated all the rest of mankind with con- tempt ; and if they admitted them to be creatures of the Author of nature, they accounted them unworthy of his care, inonopo- never rightly understood Aristotle, and enlarged and disfigured his logio by endless and insignificant commentaries. The school-logic was taught in all universities before the Reformation, and in not a few of them since. It was, indeed, almost the only thing that was then taught in those semi- naries ; and so eagerly was it run after, that Duns Scotus, a great teacher of it at Oxford, is said to have had at one time twenty thousand scholars. This is not probable; and, if true, can be accounted for in no other way than by supposing that, in an ignorant age, the man who could dispute, or speak fluently, would be admired as a prodigy, and might acquire among the common people what influence he pleased. It is to be observed, too, that the school-logic was found to be a good support to the Romish religion, and was by the Church of Rome patronized accordingly. For th's log c, by t x)t)fiuing men's minds within the narrow circle of its own rules, and making them more attentive to words than to things, and totally regardless of na- ture, checked all freedom of inquiry ; and, by promoting a habit of arguing against one's belief, as well as for it, had a tendency to prevent serious thinking, to harden the heart, to pervert the understanding, and to make tuerrmdifferent about the Uuth. v '— -Beatti&s Moral Science,-^. 55&-6«] - - 4» 82 NATIONAL PARTIALITIES. lizing his attention and his providence to themselves. The Greeks, vain of their enterprise, their learning, and their arts, considered all other nations, even the refined and luxurious Persians, as bar- barians, and held in little estimation their manners, their arts, and their fidelity. The Athenians represented their rivals, the Spar- tans, as ignorant, rude, ambitious, and as destitute of every quality except stratagem and patience. The Spartans retaliated the op- probrious epithets of fickle, factious, sophistical, impertinent; of restless, loquacious, turbulent, and ostentatious. The Romans, like the Greeks, stigmatized with the appellation of barbarous the rest of the world. They vilified the military character of the Car- thaginians and Macedonians. They ridiculed the mercantile spirit of the former, converted their national faith into a proverb of re- proach, and scarcely left them a single civil virtue. But, though superior liberality of sentiment certainly prevails in modern times ; and nations, having much more intercourse, survey their neighbors with less aver- sion and suspicion ; yet there is scarcely to be found, even among men of letters, that candor and generosity which, disdaining all partial and local attachments, constitute the philosopher the citizen of the world. All the civilized nations, I believe, of modern Europe, discover among their countrymen knowledge, genius, and industry, superior to what are to be found in simi- lar circumstances among any of their neighbors. The French, the English, the Italians, will not, I conceive, readily yield to one another precedency in science or arts. In private life, the prevalence of imagination, of passion, and of attachment, extinguishes almost every ray of impartiality and justice in the judgments of men. The power of imagination is so prevalent in some minds as to render them altogether impatient under the irksome operation of comparing ideas ; and they hasten to any judgment, however erroneous, rather than con- tinue in a state of suspense. The greater part of man- kind are guided more by their imagination and feeling THE JUDGMENT PERVERTED BY THE PASSIONS. 88 than by reason. An analogy or a figure influences them more than an argument. They will go with the multitude, however misguided, rather than stand single on the side of justice and truth. The passions pervert judgment still more than the imagination, and there is hardly any thing we wish to think right and reasonable, which we will not quickly find arguments for judging to be so. The spirit of party, and the passions it prompts, appear on many oc- casions to eradicate every idea of equity, candor, and consistency. Men oppose to-day what they supported yesterday ; they reprobate measures as void of faith, honor, and integrity, which they formerly maintained to be the result of wisdom and discernment, and the source of the most important public good. When our own interest comes in competition with that of others, it is almost impossible to survey the subject of dispute with an impartial eye. In all such cases, men of can dor, conscious of their imperfection, renounce judgment altogether, or endeavor to contemplate their situation and attachments in the light they could view those ot neutral persons. It is, indeed, exceedingly difficult to emancipate the mind entirely from these causes of erro- neous judgment ; but every inquirer should make the attempt, as he may be assured his researches otherwise will never be attended with pleasure or success. [Some important suggestions on this subject we here subjoin, from Dr. Watts. Logic, Part ii., chap. iii. The various passions or affections of the mind lead the judgment astray from truth. It is love that makes the mother think her qwn child the fairest, and will sometimes persuade us that a blemish is a beauty. Hope and desire make an hour of delay seem as long as two or three hours. Hope inclines us to think there is nothing too difficult to be at- tempted. Despair tells us that a brave attempt is mere rashness, and that every difficulty is insurmountable. What could persuade the wise men and philosophers of a popish country to believe the 31 JUDGMENT WARPED BY THE FEELINGS. gross absurdities of the Romish Church, but the fear of torture or death, the galleys or the Inquisition ? The fondness we have for self and the relation which othei per sons bear to ourselves, furnish us with another long list of preju- dices. We are generally ready to fancy that every tiling of our own has something peculiarly valuable in it, when indeed there is no other reason but because it is our own. We entertain the best opinion of the persons of our own party, and easily believe evil reports of persons of a different sect or faction. We set up our own opinions in religion and philosophy as the tests of orthodoxy and truth. We are thus tempted to pervert even the sacred books of Scripture to make them speak our own sense. When our own inclination, or ease, or honor, or profit tempt us to the practice o f any thing, how do we strain our thoughts to find arguments for it and persuade ourselves it is lawful ! In matters of equity between man and man, our Saviour has taught us to put my neighbor in place of myself, and myself in place of my neighbor, rather than be bribed by this corrupt princi pie of self-love to do injury to my neighbor. Again, the peculiar tempers and humors of the mind influence the judgment and occasion many mistakes. The credulous man is ready to receive every thing for truth that has but a shadow of evidence ; he is ready to resign his own opinion to the first objec- tion which he hears, and to receive any sentiments of another that are asserted with a positive air and with much assurance. The man of contradiction stands ready to oppose every thing that is said. He gives but slight attention to the reasons of other men, from an inward scornful presumption that they have no strength in them. Again, the dogmatist is sure of every thing, and the skeptic be- lieves nothing. The former adopts his opinions hastily and on in- sufficient grounds, and then will hear no arguments- to the con- trary : the latter will not take pains to search things to the bot- tom, but when he sees difficulties on both sides, resolves to believe neither of them. Some men believe a doctrine merely because it is ancient, others because it is new : some will not believe a proposition in theology if it is mysterious, while others would on that account receive it more readily.] The Idola Fori, which originate from language, the ^reat instrument of social communication, form the. IDOLA SPECUS. • 85 second class of prejudices. The principal inconvenien- ces they occasion, result from the use of words which have no meaning, or which bear, in our apprehension, a meaning more or less extensive than they ought to have. I am, however, fortunately relieved from the necessity of recapitulating and exposing them, by what I advanced in a former lecture concerning the ambigui- ties of general terms, and the manner of ascertaining them by enumeration. What I there observed refers, indeed, to the enunciation of single ideas ; but no more is necessary to obtain a distinct and just judgment. If language exhibit single ideas perspicuously and fully, it has done all that can be expected from it. If an er- roneous judgment shall still be passed, the understand- ing must bear the blame, while the expression will de- serve no censure. The next class of prejudices, denominated Idola Specus, include all those errors in judgment into which men are seduced from circumstances peculiar to them- selves, from the constitution of their minds or bodies, rank in life, education, or course of study. Infinite, almost, is the variety of the external appear- ance of the human race, and no less various, perhaps, are the constitutions of the minds of men.* For this reason unanimity is nut to be looked for, even concern- ing business and the common intercourse of life, far less concerning speculative tenets of difficult conception, probably in some cases of exceptionable evidence. If judgments are formed by candid men on such topics, [* Some men have a native obscurity of conception whereby they are hindered from attaining clear and distinct ideas. Some bave a defect of memory, so that they are not capable of comparing their present ideas with a great variety of others, in order to secure themselves .Sm incon- sistency in judgment. Others scarcely ever take a survey of things wide enough to judge wisely and consistently. See Waits, part ii. obap. iihl 86 JUDGMENT BIASED BY EDUCATION. they will be different, suitable to the different aspects in which the objects appear to their respective appre- hensions. No inconvenience ensues from these differ- ent judgments, either in affairs or in speculation, if men are animated by charity and proper respect for the opinions of their neighbors as well as for their own. They add variety to conversation and to action, corre- spondent to the difference which nature has established in the individuals of the species. They inspire patience and toleration, which afford exercise for several of the most amiable and social virtues. If any nation, then, or large society of men, pretend to be unanimous about tenets speculative in their na- ture and remote from vulgar comprehension, those of religion itself not excepted, the whole almost of the judgments from which that unanimity springs must be indigested if not inadequate; that is, they must be the judgments of teachers or leaders, adopted without ex- amination. Their followers are generally incapable of forming opinions for themselves, on account either of the imbecility of their faculties or the abstract nature of the topics ; and of course their assent, founded on pretended judgment, is no better than acquiescence in the judgments of those they revere, concerning subjects which they do not fully understand. Education, the professed purpose of which is to lead us to the temple of truth by the easiest and shortest road, will not readily be supposed to retard or embar- rass our progress in that course in which it pretends to be a guide. It is, however, certain, that no station we can occupy, no discipline we can undergo, is more fre- quently prolific of partial judgments* [* How many fooleries are instilled into us by our nurses, our fellow- children ; by servants or unskilful teachers, which are maintained through life! We choose our particular sect and party iu the civil, the xeligiou* ERROR OF EDUCATION. 87 In all periods of society, teachers have too commonly been more concerned to inculcate the philosophy of their sect, or the religion of their church, than the pure doctrines of truth ; and the inexpe- rience of youth, with the respect they naturally entertain for ad- vanced years and superior wisdom, cannot often fail to render such education a hot-bed of errors and prejudices. History and experi- ence teem with examples of the fertility of this soil, and teach, in the strongest language, the necessity of the most assiduous atten- tion, to prevent or eradicate the plentiful crop of noxious plants with which it is in hazard of being overrun. The fundamental error, perhaps, of education, has consisted in addressing truth, whether prudential, moral, or philosophical, to the memory rather than to the un- derstanding. It is commonly supposed, if a great deal of information be lodged in the mind, and committed to the custody of faithful recollection, that it will prove a plentiful and useful magazine, from which the pupil may draw with facility and advantage every supply he may need in the conduct of life. But it is unfortunate- ly forgotten, that accumulation of truth is only half the business of instruction, and is not even the more im- portant half. The more important part is to acquire the habit of employing to some good purpose the ac- quisitions of memory, by the exercise of the understand- ing about them ; and, till this habit be acquired, these acquisitions will not be found of very great use. With regard to prudential truth, or the conduct of a pupil respecting his instructors, his parents, his friends, his equals, his attachments and amusements, the great fundamental rule seems to be, that good behavior is both his duty and his interest, and that upon his ob- and the learned life, by the influence of education. The Turks are taught early to believe in Mahomet, the Jews in Moses ; the heathens worship a multitude of gods, under the force of their education, and it would be well if there were not millions of Christians, who have little more to say for their religion than that they were born and bred up in it. — Watts.] 88" PREJUDICES RESULTING FROM EDUCATION. servation of it his treatment and gratifications will de pend. If the uniform and discreet conduct of the teacher, or the parent, makes him consider what his behavior is, and forces him to reason about the practice of it, he will be happy and satisfied, he will be attentive and civil to others, and he will be prepared to judge for himself in the conduct of life, when he shall be obliged to think and act without direction. But if he have no rule of conduct but the dictates of every sudden whim which may arise in his own fantas- tic imagination, or which the occasional indulgence or severity of an indiscreet superintendent may suggest, his conduct will be the re- sult of foolish attachments or aversions, of caprice, or of passion. His wants will be multiplied beyond the bounds of nature, and the circumstances of his situation ; he will be miserable himself, dis- gusting to others. Advice and instruction will have with him no useful influence. His subjection to authority will be his utter aversion, because it interferes with his gratifications. His applica- tion to study will be disagreeable, because he has no conception of the utility of knowledge. From such a train of unfortunate preju- dices, what other conduct can ensue than we often survey? .Namely, a headlong career of the most unlimited gratification, as soon as he is emancipated from that mortifying restraint from which he has long wished so ardently to disengage himself; and an in- surmountable aversion to every path of inquiry and truth, into which it had been the purpose of education to lead him. Though these fatal consequences of improper instruc- tion are fortunately not very frequent, yet numerous examples occur of prejudices implanted by the author- ity of teachers, relative to philosophical, political, and prudential truth, which have produced effects not a little detrimental. The lectures of philosophy in ancient Greece, tended more to inculcate the particular tenets of the Epicureans, the Stoics, and the Academics, than the science of human nature, and the doctrines of wis- dom. Aristotle was perhaps, more anxious to excite admiration, than to extend useful knowledge; to consti- tute a new sect of inquirers, than to promote the influ EXAMPLES FROM ENGLISH HISTORY. 89 ence of 'ruth. From the abuse, at least of his logic, flowed a corruption of the education of Europe, which for many centuries not only did not point out, but ob- structed every avenue to improvement. That no ray of useful information should have transpired amid all the industry, and acuteness, and even ingenuity of the scholastic doctors, can only be explained from the vanity and futility of the learning they inculcated. When the art of reasoning itself was converted into an engine of sophistry and deceit, when the educa- tion of the most learned and elevated members of society consisted in subtle wrangling and syllogistic disputation, can we wonder that the understandings of men should be debased and disgraced by the admission of the most palpable inconsistencies, and that the stupen- dous fabric of Popish superstition, the most presumptuous system that ever insulted human reason, should have been then received and established? The history of Great Britain presents two striking ex- amples of the pernicious effects of the prejudices of edit cation, one political, and the other religious. Charles the First lost his life and his crown by the arbitrary maxims of government he had received from his ances- tors. James the Second lost his crown by the Popish education he had received in France. Though Charles the First is commonly called a martyr to the doctrine and worship of the Church of England, and is accounted by the vulgar to have sacrificed his life in defending her against the bigotry and violence of sectaries, whose hatred to her and him was insatiable; yet it is well known, that his attachment to that church was neither the first nor the chief cause of the discontents which generated and prolonged the civil war. Religious jealousies and fears were then employed, as they have often been, to rouse, and 'rritate, and alienate the people. But the 1 encroachments on prop- erty contrary to law, and the levying of money without consent ot Parliament, alarmed all wise men, and excited that tremendous spirit of resistance which terminated in the lamentable fate of the monarch, and the destruction of the constitution, evils that seem tc have exceeded in magnitude every wish or conception of the pat- 90 EFFECTS OF PARTY SPIRIT. riots who first opposed the arbitrary measures of the crown. That Charles knew the constitution reprobated the levying of money b\ his own authority, we have no reason to doubt ; but he had been fatally educated in principles which suggested, that cases of neces- sity, or the wants of princes, were superior to the constitution or the laws ; and that, if Parliament refused to grant what supplies he thought necessary, a case of necessity took place, and he was at liberty to exert his sovereign power, to provide for the salvation of the state. The education of James the Second in France, and his attach- ment to Popery, were the springs of the Revolution, and of the ejection of the family of Stuart from the throne of their ancestors. Nothing perhaps but the bigotry of that prince could have saved the liberties of this country from extinction. Could he have relin- quished his attachment to Popery, could he have suspended or moderated that attachment, he might have reigned without a par- liament, and trampled on the laws and religion of his subjects. His finances, by economy and good management, were in perfect order, and nearly adequate to the annual expenses of government. The calamities and disasters of the late civil wars were fresh in the memories of men, and all ranks were reluctant to renew them. The enthusiastic spirit which had inflamed the body of the nation against his father, had now nearly spent its force, and nothing seemed wanting to success but to allow the minds of men to cool, and to habituate them to the slavery that was preparing for them. The blind zeal, however, of the king, and his intemperate attach- ment to his religion, for the happiness of this land of liberty, hastened every event to a crisis. They so completely disgusted friends and enemies, that the people, with the most unprecedented unanimity, pushed from a throne, without violence or convulsion, a monarch and a family, who would have sacrificed the happiness and peace of a great nation to an absurd system of foreign super- stition. The Idola Theatri constitute the last class of preju- dices of which I have to speak. They generate all those erroneous judgments which result from the malignant influence of society, and which may be comprehended under the effects of party spirit, of fashion, and of an thority. Party spirit has in all ages been the most formida EFFECTS OF PARTY SPIRIT. 91 ble enemy to sound judgment in philosophy, in politics and in affairs. No man, it would seem, ever retained either discernment or candor to withstand its seduction, after allowing it to get possession of his breast. The only safety for the impartiality of the mind, the only means of preserving the solidity and equity of its deci- sions, is to fly from the evil, and to avoid the infection. If we advance within the sphere of its attraction, we are undone. It would be endless to enumerate the examples of the baneful influence of this spirit, which history and ex- perience so plentifully supply. Numerous and violent are the contentions it has produced in science, in re- ligion, and in business. When engaged in a party, w T e retain no rule of judgment but the opinion of the people with whom we associate. Every thing they think, or say, or do, is right, proceeds from honorable and useful motives, and is directed to the accomplishment of some important end. All our friends are men of discern- ment, of integrity, of generosity, of liberal minds, of impartial views, and of great virtues. The case of our antagonists, their motives, qualities, and conduct, are directly the reverse. Their designs are the result of imprudence, folly, or iniquity. Weakness, wickedness, or selfishness, mark all their plans, and disfigure all their operations. They inherit no spark of discretion, enterprise, or public spirit. Truth is thus suppressed or misrepresented ; and in all the subjects of contest, there will not be found, on either side, a single sound or im- partial judgment. , Religious party spirit, in former ages, chiefly misled and agitated the minds of men. Happily for the honor and peace of the present age, the influence of this most malignant disposition is now nearly extinguished. The progress of truth and knowledge has not been a little 02 PRWUDICES OF FASHION. - extended and accelerated by this fortunate event. Po- litical party spirit, however, still keeps strong hold ot the minds of men ; and the misrepresentations and falsehoods witli which it corrupts their hearts, and mis- leads their judgments, are sufficiently discernible. Did not attachment to party blind the understanding, and obliterate the feelings of modesty and candor, men would be ashamed of the contempt or neglect with which they receive the plainest truths. On some occa- sions, indeed, this spirit appears to prompt suc^ par- tiality, as not only despises the dictates of truth and reason, but disregards even the most important inter- ests of society, provided it may accomplish its favorite objects of ambition. The prejudices of fashion seduce and pervert a-11 mankind. Every thing feels its influence. All ranks are subjected to its power. Manners, arts, language, dress, amusements, studies, science, even laws and reli- gion, are not exempted from its sway. Fashion is, on many occasions, the opinion of the majority of society, or of the more illustrious part of it; and so ductile are the minds of many men, that they consider its dictates as of superior authority to those of reason itself. Of all our prejudices, however, those supported by fashion are perhaps the most justifiable, at least they are often the most difficult to surmount. In all matters of indiffer- ence, it would seem, we should submit to fashion ; and as we would not choose to follow any authority in j udg- ing of right and wrong, so it appears unreasonable to be singular in cases where neither is concerned. [Fashion has a most powerful influence on our judg- ments, for it employs those two strong engines of fear and shame to operate upon our understanding with unhappy success. We are ashamed to believe or tc profess an unfashionable opinion in philosophy, and a PREJUDICES OF AUTHORITY. 93 cowardly soul dares not so much as indulge a thought contrary to the established or fashionable faith, nor act in opposition to custom, though it be according to the dictates of reason. I confess there is a respect due to mankind which should incline even the wisest of men to follow the innocent customs of their country in the outward practices of civil life, and in some measure to submit to fashion in all indifferent affairs, where reason and Scripture make no remonstrance. But the judg- ments of the mind ought to be forever free, and not biased by the customs and fashions of any age or na- tion whatsoever. — Watts^] The prejudices of fashion are nearly allied to those of authority. They differ only in the extent of the source from which they are derived. Under the former, we are guided by the practice or opinion of the great body of the people ; under the latter, we follow the opinions and example of eminent individuals. Authority is most detrimental to all inquiries after truth, and has perhaps obstructed more the progress of knowledge than all other causes conjoined. It has infested and corrupted the investigations of philosophy in all ages. Even the enlightened spirit of the present age is not altogether delivered from its dominion.. Whenever men pretend to teach knowledge, by adopting systems without consulting nature, the influ- ence of authority must be unlimited and indisputable, because the inquirer has sought for no test of truth but the opinion of the author of the system. It is fortunate for knowledge that this mode of philosophizing is now exploded, and will never perhaps regain establishment. After reigning uncontrollably from the days of Aristotle to those of Descartes, it was consigned to oblivion, with all the speculations of this eminent projector, by the sound philosophy of Kewton. The general prevalence 94 THE AUTHORITY OF FOREFATHERS. of the experimental method, recommended by Bacon, has gained entire ascendency in every enlightened na- tion of Europe. Had the Cartesian mode of philosophizing continued to prevail, the true system of nature had remained un- known. It was the banishment of authority, and the investigation of nature, that revealed her secrets. If the influence of authority shall revive, the knowledge of these secrets may be withdrawn. Let, then, the opinions of every theorist be examined with perfect patience and impartiality, but never let his authority supply the place of argument. [As sources of prejudice, the authority of our fore- fathers, and of ancient authors, is most remarkable. It is granted that the ancients had many wise and great men among them, and some of their writings, which time has delivered down to us, are truly valuable; but those writers lived rather in the infant-state of the world, and the philosophers as well as the polite au- thors of our age are properly the elders, who have seen the mistakes of the younger ages of mankind, and cor- rected them by observation and experience. Some persons believe every thing that their kindred, their parents, and their tutors believe. I freely grant that parents are appointed by God and nature to teach us all the sentiments and practices of our younger years — and happy are those whose parents lead them into the paths of wisdom and truth. I grant, further, that when persons come to years of discretion, and judge for themselves, they ought to examine the opinions of their parents with the greatest modesty, and with an humble deference to their superior character; they ought>, in matters perfectly dubious, to give the preference to their parents' advice, and always to pay them the first respect, nor ever depart from their opinions and prac- AUTHORITY OF PARENTS, ETC. 95 tice, till reason and conscience make it necessary. But, after all, it is possible that parents may be mistaken, and therefore reason and Scripture ought to be our final rules of determination in matters that relate to this world and that which is to come. To believe in all things as our predecessors did, is the ready way to keep mankind in an everlasting state of infancy, and to lay an eternal bar against the improve- ment of our reason and of our happiness. Besides, let us consider that the great God, our com- mon Maker, has never given one man's understanding a legal and rightful sovereignty to determine truths for others, at least after they are past the state of childhood or minority. No single person, how learned, and wise, and great soever, or whatsoever natural, or civil, or ecclesiastical relation he may have to us, can claim this dominion over our faith. It is proper to take notice, however, that as education, custom, and authority are no sure evidence of truth, so neither are they certain marks of falsehood; for reason and Scripture may join to dictate the same things which our parents, our tutors, our friends, and our coun- try believe and profess. Yet there appears sometimes in our age a pride and petulancy in youth, zealous to cast off the sentiments of their fathers and teachers, on purpose to show that they carry none of the prejudices of education and authority about them. They indulge all manner of licentious opinions and practices, from a vain pretence of asserting their liberty. But, alas ! this is but changing one prejudice for another, and some- times it happens, by this means, that they make a sac- rifice both of truth and virtue to the vile prejudices of their pride and sensuality. There is another tribe of prejudices which are more akin to those of authority, and that is, when we receive 96 MANNER OF PRESENTING A DOCTRINE. a doctrine because of the manner in which it is pro- posed to us by others. Neither the positive, the awful or solemn, the terrible or the gentle methods of address, carry any certain evidence with them that truth lies on that side. In such a degenerate world as we live in, w r e must learn to distinguish well between the substance of any doctrine and the manner of address, either in proposing, attacking, or defending it — and thereby set- ting a just and secure guard of reason and conscience over all the exercises of our judgments, resolving to yield to nothing but the convincing evidence of truth, religiously obeying the light of reason in matters of pure reason, and the dictates of revelation in things that re- late to our faith. — Watts' Logic, part ii. chap, iii.] LECTURE VII. RULES TO PREVENT PREJUDICES PRINCIPLES AND RULES OF JUDGMENT. I have now treated pretty fully of prejudices, to pre- pare us to detect them, and to put us on our guard against them, because they are most detrimental in the investigation of knowledge. I intimated formerly, that I intended to point out, not only the rocks and shelves, which we must avoid, but to present the compass by which we must steer, in order to perform a successful voyage on the hazardous sea of inquiry. I proceed to perform this promise, and to conclude the branch of logic under discussion, by subjoining a few rules which must direct our practice, if we expect to form just and useful judgments. RULES TO PREVENT PREJUDICES. 97 1. Beware of precipitation, and never decide concern- ing the truth or falsehood of any proposition, till you have attended to all the preliminaries formerly m,en- tioned : whether the words accurately express the ideas, whether you have distinct conceptions of the ideas, whether your minds are divested of prejudices, and whether you have fully canvassed the evidence. I do not maintain that all this precaution is necessary to prevent mistake in every judgment we form. In all sciences, arts, and affairs, we pass many judgments without much attention or premeditation, because the agreement or disagreement of the ideas compared is obvious on the slightest inspection. But when the pur- suit of truth solicits us into new, and perhaps obscure, paths of inquiry; when we reach judgments, which lead to inferences extraordinary and alarming; or, when our decisions differ from those of men eminent for ca- pacity and discernment, or are likely to involve us in controversy, we should reiterate, with patient attention, every precaution. Such a practice is suitable to, and is demanded by, the character of a candid inquirer. It may perhaps retard our progress, but it will cause us to march on surer ground. It will habituate our minds to accuracy, and will give us confidence in their operations. It will save the irksome sensation which results from the detection of precipitation and mistake ; and it may pre- vent much trouble by excluding errors from theories, which, if carelessly or rashly overlooked in their prin- ciples, may lay in ruins the la^or of many painful hours. The most patient investigators have always been the most successful inquirers, and the most prudent and fortunate men have generally been most remarkable for the candor and the coolness of their understandings. 98 BACON AND NEWTON. The two greatest philosophers the world ever saw, Lord Bacon and Sir Isaac Newton, are in nothing so much superior to all other philosophers, as in the deliberation and patience with which they proceeded in their researches. No confidence, no presumption, no vain censure of the precipitancy of former inquirers, no zeal for party, no partiality to system or authority, ever mislead their minds or disgrace their investigations. They seek truth alone, and they search for her with the caution of men conscious of her im- portance, and of the difficulty of finding her. They embrace her with cordiality wherever they meet her, but they will not adopt speculation for fact, nor be satisfied with the semblance in place of the reality. Prudent judgment in business chiefly distinguishes the wise man from the fool. The fool frequently pos- sesses sensibility, vivacity, recollection, and informa- tion. He is often in these articles superipr to the man of wisdom and discretion, but he cannot, or will not, make a proper use of the materials he has provided. He finds ideas to agree which do not agree. He judges precipitately and erroneously. His conduct is directed by his judgments. His opinions, accordingly, expose him to ridicule and contempt, and his actions to re- proach and misfortune. The essence of wisdom, on the other hand, consists in the passing of just judgments on the men and the things about which, in the affairs of life, we are called to decide. It is the offspring or companion of discern- ment, and discernment is nothing more4han that pru- dent examination, previous to judgment, which leads to decide according to truth. The wise man, it is said, sees farther into futurity than other men, or excels in the faculty of anticipation ; but this superiority is an evidence only of the accuracy of his judgment relative to things past. He supposes that future events, in similar circumstances, will resemble the past. His conceptions of the past -are accurate, and he can scarce ly err in his opinions of the future SUSPENSE IN JUDGING. 99 2. If, after employing every precaution, you still find information incomplete, or ideas not sufficiently clear, suspend judgment till further investigation or greater experience shall qualify you to decide. I am aware that this rule may be supposed to be comprehended under the preceding ; because, if we never judge with precipitation, we must, eventually, suspend that operation whenever the evidence is not satisfactory. But the prudent and rational conduct this rule inculcates is so momentous, both in science and in business, that it appeared to merit a separate enuncia- tion and illustration. A degree of skepticism, which presupposes a doubt of the truth of every proposition we have not examined, is requisite to every candid inquirer. But to many minds hesitation and suspense are uneasy feelings, and they are impatient to reach a determination. In many instances, if we proceed with propriety, we must ob- serve the necessity of suspense of judgment, because our inquiries terminate in subjects beyond our compre- hension. The cases, however, to which I would espe cially apply this rule, are those in which judgment comes within our comprehension; but we hesitate, either because ideas are not sufficiently distinct, or be- cause we have not discovered the intermediate steps which show their relation. In such cases a candid in- quirer must suspend judgment, because he can do noth ing else. Should he go on, it is perfect accident if he reach a just determination. When the mind is embarrassed and perplexed, it is often proper to relinquish the subject of inquiry for some time ; and to resume it, after an interval of other employment. Its faculties return to the charge with new vigor, more experience, quicker discernment, and frequently with success. But the more common inethori 100 SUSPENSE IN JUDGING. is, to pore upon the topic which engages attention, and instead of seeking for intermediate ideas, if it be a sub- ject of argument, or further information, if it be a mat- ter of fact, the inquirer retires to his closet, and forms theories which have no foundation either in reason or in truth. This spirit is fortunately banished, in a great measure, from the regions of philosophy, but it still re- mains in politics and in business. A theoretical politician is exceedingly wise in conversation, but his speculations are rarely verified by experience. He proceeds on fallacious principles. He reasons on the supposition, that the mo- tives and conduct of men are what they should be; or that men will act from steady principles of justice or interest. But the far greater part of their actions is the result of unaccountable at- tachment or passion, of fancy, feeling, whim, caprice. These can make no part of any theory, because they transcend all rules of calculation, and falsify every conclusion founded on reason and common sense. A man, therefore, who wishes to gain real influ- ence in the world, will never rest resolutions on speculation. He will mix with mankind, and accommodate his opinions to charac- ters and circumstances; and if these lead not to decision, he will patiently suspend judgment, and remain inactive ; or he will act so ambiguously, that he may avail himself of better information when it shall occur. Suspense of judgment, at least suspense in uttering judgments, if they contain any thing harsh, disagree- able, unpleasant, or even unpolite, is particularly neces- sary in all good company, and among all men of knowl- edge. Without this exercise of civility we cannot ex- pect to be favored with the communications of superior information. We cannot render ourselves acceptable to those from whom we may derive the most essential benefits. We shall discompose and embarrass delicate society, we shall be exposed to critical reprehension, or involved in controversy, the bane of all good inter- course, and insuperable impediments in the acquisition of truth SATISFACTION WI'^H PROPER EVIDENCE. 101 Modesty in judgment is peculiarly graceful and promising in young inquirers. It is always interpreted in the most favorable sense ; as a mark of ingenuousness, and a consciousness of the difficulty of attaining useful knowledge ; dispositions which powerfully solicit liberal and enlightened minds to impart important aid. On the other hand, petulance, forwardness, and presump- tion, subject young inquirers to every disadvantage, and to many mortifications. They alarm men of superior parts and improvement, and render them averse to in- timacy with persons from whom nothing is to be ex- pected but irritation and disgust. They bring into sus- picion the soundness of their understandings ; so that these can hardly obtain the reputation of just judgment even when it is deserved. 3. Be satisfied with the evidence which the nature of a proposition admits. To decide without evidence, is weakness and absur- dity. To be satisfied with no evidence, is skepticism. To demand the same kind or degree of evidence for every proposition, is unnatural and unreasonable. The propositions of science, of arts, and of business, are sup- ported by different kinds of evidence. No candid rea- son er will demand the same species of evidence for them all. He is entitled to no other than the nature of each affords. Few subjects admit that complete convic- tion which excludes the possibility of doubt. The far greater part presents only higher or lower degrees of probability. Though in the sciences of quantity the mind proceeds on the firm ground of demonstration, it would be absurd to expect equal satisfaction in morals, politics, or natural history, because these sciences are incapable of such evidence. Moral and political propositions are supported by evidence de- duced from the human constitution, the order of nature, the hap- 102 COMPARATIVE VALUE OF TESTIMONY. piness of individuals, and of communities, which is far from being so conclusive and direct as to exclude hesitation, or even difference of opinion : yet these propositions involve truths very important to mankind. The rewards or punishments, assigned by their own minds, by the opinions of their fellow-creatures, and by the laws of society, depend upon them. hi natural history, which furnishes an account of animals, vege- tables, and minerals : in geography, which supplies instruction con- cerning the surface of the earth, what parts are covered with land or water, where hills, valleys, capes, cities are situated, tides run, and winds blow: in civil history which recounts the transactions, opinions, and manners of nation.* in former times : in the adminis- tration of justice and civil government, which applies the laws of the community to the actions of individuals, in order to protect the lives and property of the innocer t, and to punish the guilty : in the relations we daily receive from foreign countries, concerning the public events of nations, or the .ndustry, customs, and sentiments of individuals : — in all these cases we must depend upon the evi- dence of testimony ; and if the information be not in its nature in- credible, and we have no reason to question the veracity of the relater, we ought to be satisfied with that evidence. Testimony is perhaps among the least satisfactory channels by which truth is conveyed to the mind. It is less satisfactory than those of intuition and reasoning, at least in the sciences of quantity. It is also inferior to those of consciousness and sensation ; but it is, not- withstanding, of high importance to the comfort, peace, and happiness of society. No inconvenience results from following it with discretion. Were it rejected, every disorder and danger would ensue. Man is made to be satisfied with it. His situation often admits noth- ing more convincing. It was chiefly to vindicate the credibility of this species of evidence, to which inquirers Bometimes will not allow the influence it deserves, that I advanced the rule under consideration ; and it may not be improper to sketch the limits within which this evidence appears to be unexceptionable. EVIDENCE IF TESTIMONY. 10S The first thing to be considered, then, is the nature of the narration which solicits our belief; because, if it be incredible, we need not go farther ; we may reject the testimony without examination, because we are more certain that what is incredible cannot be true, than we can be certain of the truth of any testimony. A narration is incredible in two ways, either by containing an action in itself impracticable, or by containing cir- cumstances contradictory to one another. If, for instance, we were told, that an ordinary man bore a mountain on his back from Italy to France ; or that there are men in the world who believe two and three make six ; we would reject such relations as unworthy of the least credit, because they con- tain actions and opinions which contradict all our conceptions and experience of human powers and faculties. If, again, a relation represent the performer of an action in different places at the same time, we refuse credit, because it involves a contradiction, and sup- poses the coexistence of things which we know to be impossible. But if the action be practicable, if the agent be adequate to the per- formance, and if the account be intelligible and consistent, the next step is to examine the nature of the testimony ; and if that also be unexceptionable, the mind is prepared to believe, and it will be im- patient if not permitted to bestow assent. The circumstances of inquiry relative to the credit bility of the testimony, are, whether the relater was fully informed of the nature and particulars of the ac- tion ; and whether he could be seduced by any temp- tation to misrepresent them. The article of full information may be subdivided into several other inquiries ; whether the action was an object of the senses of the relater ; whether he had full time to examine it, and possessed the perfect use of his faculties at the time of examination ; whether he exam- ined the same action, or similar actions, at different times, and always formed similar judgments; and, 104 EVIDENCE OF TESTIMONY. finally, whether this account is supported, at least not contradicted, by other accounts of credit.* With regard to the character of the relater, we have reason to rely on his veracity, if we have no cause to doubt it ; and if, at the same time, marks of sincerity, attention, or discernment appear, we cannot demand better foundation for assent. If an historian be exposed to no temptation to falsify or misrepresent, we suppose that he relates the truth ; because it is much more easy to relate truth than to relate falsehood. Truth requires no anxious caution to preserve consistency, no struggle to repress the remonstrances of conscience, which even the most abandoned men cannot altogether silence. It follows the natural and consistent train of causes and effects. It presents a credibility and authority which command conviction. But if, besides a general attachment to truth, we dis- cover in an historian other symptoms of integrity, such as relating truth when it was his interest to conceal or misrepresent it, when it might hurt friends, gratify ene- mies, or expose himself to danger from the resentment of those whom it might offend ; we have the best reason to credit his testimony ; because he discovers not only great attachment to truth, but the strongest aversion to falsehood, and evinces, that the temptations which in- duce men of little virtue to disguise truth, and those of no virtue to suppress it, do not affect him. He is at [* Says Dr. Whately : " When the question is as to a fact, it is plain we have to look chiefly to the honesty of a witness, his accuracy, and his means of getting information. When the question is ahout a matter of opinion, it is e» v ally plain that his ability to form a judgment is no less to be taken into account. But though this is admitted by all, it is very common with in- considerate persons to overlook, in practice, the distinction, and to mistake as to what it is that, in each case, is attested." For further excellent remarks on Testimony, consult Whately's Rhetoric, part i. chap. ii. § 4.] EVIDENCE OF TESTIMONY. 105 least sincere, and his testimony must be believed, unless it can be proved that he was misinformed or mistaken. If a narration be consistent, the only ground for charging its author with mistake or misinformation, is its contradiction of other accounts of credit, or its con- taining transactions of which we can explain neither the motives nor the manner. If two historians contradict one another, which seldom happens unless in cases of the most violent prevalence of party spirit, the evidence of both will be destroyed, or the small portion of credit that remains will operate in favor of the more respecta- ble author. If one author omit what is related by another, the omission may excite suspicion, but forms no direct argument against the credibility ; because many circumstances unknown to us might occasion the oversight of which we complain. Neither is the containing of transactions, of which we cannot explain the motives or the manner, a good argument against the authenticity of a narrative ; be- cause the deficiency may be chargeable on the hearer or the reader, not on the relater. Men of all ages measure the motives, opinions, and actions of others, however different from themselves in constitution, or dissimilar in situation, by their own ; and we need not be told that nothing can be more fallacious than such a standard. A remarkable passage of history may be produced to illustrate this observation. Herodotus, in travelling to collect materials for his history of Greece, received intelligence that some Phoenician seamen had em- barked on the Red Sea, sailed round the south coast of Africa, and returned home by the Columns of Hercules, or the Straits of Gib- raltar. In which voyage they must have circumnavigated the Cape of Good Hope, commonly accounted one of the most brilliant discoveries of modern enterprise. The historian subjoins his own opinion ; that the incident was incredible, because the voyagers re- ported that in sonn part of their navigations they bad beheld the 5« 106 PRACTICE OF RULES OF LOGIC. ecliptic, or the line of motion of the sun, situated to the north of the zenith of their course. The historian, however, judged by a false standard ; he condemned as incredible what he did not under- stand ; because it was unknown, perhaps, in his time, that the ap- pearance specified actually takes place, in the navigation he had related. He reprobates the account for a circumstance which is the most plausible characteristic of its authenticity ; for it could haidly be supposed to have been conjectured unless it had been seen. I have now offered every rule and observation which appeared of importance to be attended to in forming our judgments in science, arts, and business. I have unfolded the sources of those prejudices which obstruct the rectitude of our judgments ; I have inculcated pa- tience and attention in forming them when we have full information; I have enjoined suspense of judgment when information is wanting or deficient ; I have rec- ommended, finally, satisfaction with the best evidence that can be procured, and the propriety of judging and acting on that evidence. I know nothing more that can be done to render our judgments sound and logic- al, but that we carefully habituate ourselves to the practice of these rules. Without practice in this art, as in all others, performance will be awkward and im- perfect; the rules will soon be forgotten, or will cease to have effect. They may become the subject of a little speculation, or conversation, perhaps ; but will be of no service in the search of truth or in the conduct of life. A man ignorant of all rule, but habituated to candid and diligent exercise of his faculties, will decide more expeditiously and accurately than one skilled in all the theory of reasoning without the practice. No theory of any art can make an expert practitioner; Logic pretends not to make mechanical reasoners. All it does.-all it cau do, is to show the way to find out truth, PRINCIPLES AND RULES OF JUDGMENT. 107 and to guide the exertions of our faculties in the pur- suit of it. But if inquirers will neither travel in the road that leads to the temple of truth, nor employ their faculties to discriminate her when they have reached her sacred residence ; if they will not attempt to ob tain an acquaintance and intimacy with her, her hand- maid, logic, can furnish them no further service. She must leave them to that ignorance and insignificance to which they seem consigned by nature ; and must solace herself by lending aid to candidates who will be more grateful for her favors, and improve them to better advantage. PRINCIPLES AND RULES OF JUDGMENT IN MATTERS OF REASON AND SPECULATION. [Condensed from Watts' Logic, Part II., Chapter V.] 1. Whatsoever is sufficiently clear and evident ought not to be denied, though there are other things belong- ing to the same subject which cannot be comprehended 2. If any opinion proposed has equal arguments for and against it, we must remain in perfect suspense about it till convincing evidence appear on one side. 3. Of two opinions, if one has unanswerable difficul- ties attending it, we must not reject it immediately, but ascertain whether the contrary opinion has not difficul- ties as unanswerable. 4. If each opinion has objections against it which we cannot answer or reconcile, we should rather em- brace that which has the least difficulties in it, and which has the best arguments to support it ; and let our assent bear proportion to the superior evidence. 5. If any doctrine has very strong and sufficient evi- dence to command owr assent, we should not reject it 108 PRINCIPLES AND RULES OF JUDGMENT. because there are some objections urged against it which we may not be able to answer / for otherwise a common Christian would be baffled out of every article of his faith, and must renounce even the dictates of his reason and his senses. 6. Where two extremes are proposed, either in mat- ter of speculation or practice, and neither of them has convincing evidence, it is generally safest to take the middle way, which is more likely to come near the truth than doubtful extremes. 7. When two different propositions have each very strong evidence, and do not plainly appear inconsistent, we may believe both of them, though we cannot at pres- ent see the way to reconcile them. Reason, as well as our own consciousness, assures us that the will of man is free, and that multitudes of human actions are in that respect contingent ; and yet reason and scripture assure us that God foreknows them all, and this implies a cer- tain fatality. Now, though learned men have not to this day hit on any so clear and happy method as is desired to reconcile these propositions, yet since we do not see a plain inconsistency in them we justly believe them both, because their evidence is great. 8. Let us not, therefore, too suddenly determine in Uffioult matters, that two things are utterly inconsistr ent • for there are many propositions which may ap- pear inconsistent at first, and yet afterwards we find their consistency, and the way of reconciling them may be made plain and easy ; as also there are other propo- sitions which may appear consistent at first, but after due examination we find their inconsistency. 9. For the same reason we should not call those diffi- culties utterly insoluble, or those objections unanswera- ble, which we are not presently able to answer. Time and diligence may give more light. PRINCIPLES AND RULES OF JUDGMENT. 109 10. If we happen to have our chief arguments for any opinion refuted, toe should not immediately give up the opinion itself j for, perhaps, it may be a truth still, and we may find it to be supported by other argu- ments, which we might once think weaker, or perhaps by new arguments which we knew not before. 11. We ought to esteem that to he sufficient evidence of a proposition where both the hind and the force of the arguments or proofs are as great as the nature of the thing admits, and as the necessity or exigence of the case requires. So if we have a credible and certain testimony that Christ rose from the dead, we are not to expect mathematical or ocular demonstration for it, at least in our day. 12. Though we should seek what proofs may be at- tained of any proposition, and we should receive any number of arguments which are just and evident for the confirmation of the same truth, yet we must not judge of the truth of any proposition by the number of argu- ments which are brought in support of it, but by the strength and weight of them. 13. Yet where certain evidence is not to be found or expected, a considerable number of probable arguments carry great weight with them even in matters of specu- lation. That is a probable hypothesis in philosophy or theology, which goes farthest towards the solution of i>? any difficult questions arising on any subject. IN MATTERS OF MORALITY AND RELIGION. By matters of morality and religion, are meant thos< things which relate to our duty to God, ourselves, or om fellow-men. The words vice and virtue chiefly imply the r-elation of our actions to men and this world : sin 110 PRINCIPLES AND PULES OF JUDGMENT. and holiness rather imply their relation to God and the other world. 1. The will of our Maker, whether discovered by reason or revelation, carries the highest authority with it, and is therefore the highest rule of duty to intelligent crea- tures ; a conformity or non-conformity to which, deter- mines their actions to be morally good or evil. 2. Whatsoever is really an immediate duty towards ourselves, or towards our fellow-creatures, is more re- motely a duty to God, and therefore in the practice of it we should have an eve to the will of God as our Kule, and to his glory as our End. 3. Our wise and gracious Creator has closely united our duty and our happiness together, and has connected sin or vice and punishment together, both in the nature of things and by his own positive appointment. 4. Conscience should seek all due information in order to determine what is duty and what is sin, because hap- piness and misery depend upon it. 5. On this account our inclination to present temporal good, and our aversion to present temporal evil, must be wisely overbalanced by the consideration of future and eternal good or evil ; that is, happiness or misery : and for this reason we should not omit or commit a sin, to gain any temporal good or to avoid any temporal evil. 6. As there are some duties much more important than others are, so every duty requires our application to understand and practise it, in proportion to its im- portance. 7. Where tvvo duties seem to stand in opposition to each other, and we cannot practise both, the less must give way to the greater, and the omission of the less is not sinful. S. In actions where there maybe some scruple about RULES IN MATTERS OF HUMAN PRUDENCE. Ill the duty or lawfulness of them, we should choose always the safest side, and abstain as far as we can from the practice of things whose lawfulness w T e suspect. 9. In some of the outward practices and forms of re- ligion, as well as human affairs, there is frequently a present necessity of speedy action in one way or another. In such a case, having surveyed the arguments on both sides, as far as time and circumstances admit, we must guide our practice by those reasons which seem at the time to overbalance the rest ; yet always reserving room to admit further light and evidence when such occur- rences return again. It is a preponderation of circum- stantial arguments that must determine our actions in a thousand cases. IN MATTERS OF HUMAN PRUDENCE. 1. Our regard to persons or things should be gov- erned by the degrees of concernment we have with them, the relation we have to them, or the expectation we have from them. 2. We should always consider whether the thing we pursue be attainable ; whether it be worthy of our pur- suit ; whether it be worthy of the means used in order to attain it. 3. Though a general knowledge of things be useful in science and in human life, yet we should content ourselves with a more superficial knowledge of those things which have the least relation to our chief end and design. We should not grasp at every thing, lest in the end we attain nothing. 4. Where the case and circumstances of wise and good men resemble our own case and circumstances, we may borrow a great deal of instruction towards our 112 RULES IN MATTERS OF DIVINE TESTIMONY. present conduct from their example ; as well as in all cases we may learn much from their conversation and advice. IN MATTERS OF DIVINE TESTIMONY. As human testimony acquaints us with matters of fact, both past and present, which lie beyond the reach of our own personal notice; so Divine testimony is suited to inform us both of the nature of things, as well as of matters of fact ; and of things future, as well as of present or past. Whatsoever is dictated to us by God himself, or by men who are divinely inspired, must be believed with full assurance. Reason demands of us to believe what- soever Divine revelation dictates ; for God is perfectly wise, and cannot be deceived; he is faithful and good, and will not deceive his creatures ; and when reason has found out certain marks or credentials of Divine testimony to belong to any proposition, there remains then no further inquiry to be made, but only to find out the true sense and meaning of that which God hae re- vealed ; for reason itself demands the belief of it. DIFFERENT KINDS OF SEASONING. 113 LECTURE VIII. REASONING MATHEMATICAL MORAL POLITICAL PRUDEN- TIAL PROBABLE REASONING. I have discussed every topic introductory to the art of reasoning. I have explained the sources from which ideas are received, and the methods we must employ to render them clear, adequate, and conclusive. I have explained the nature of the propositions into which they may be formed, and the judgments whicli we must pass on these propositions. I have, finally, de- lineated the prejudices which pervert our judgments; and I have attempted to establish the rules we must follow, if we expect to form them with accuracy and justice. It remains only, to complete this department of the course, that I treat of reasoning, or the method of ascertaining propositions, by means of intermediate ideas, or proof s, whether demonstrative or probable. I formerly observed, that all knowledge is either intuitive, demonstrative, or probable. The first, intui- tive knowledge, is so extremely circumscribed, that if man had no other method of comparing ideas, and ex- tending information, though he might be wiser than the beasts of the field or the fowls of the air, yet he would be ignorant of all science and arts. All individuals and communities would be nearly in the same state of improvement. The only difference among them would result from their quickness or sagacity in perceiving self-evident propositions. As it is, then, the exercise of his reasoning faculty by which man attains the most decisive eminence in the 114: THE PROCESS OF REASONING. creation, by which he ascends far above the inferior animals, and by which different men and different com- munities are conspicuously exalted one above another, ill all those acquisitions which cultivate, civilize, adorn, and enlighten the mind of man, it is a matter of the most important concern to examine what sort of opera- tion reasoning is, how we shall perform it with most expedition and success, and how we shall avoid those errors by which many reasoners in all ages have been led astray. To assist in this delicate and arduous un- dertaking, is the object of the discussion on which I am now to enter. Reasoning begins where intuition ends, and consists in finding out the truth of a proposition, or the agree- ment or disagreement of its subject and predicate, by the help of intermediate ideas. The intermediate ideas form the steps, or links, by which the mind passes from the first of the primary ideas to the last, or from the subject of any proposition to its predicate, and finally perceives their relation. Reasoning assumes differeni names, according to the nature of the steps, or of the links which display the relation between the primary ideas. If the mind attain complete satisfaction in every step of its progress, or in the successive comparison of every pair of ideas, it is said to acquire certainty of the agreement or disagreement of the two primary ideas, and the reasoning is called demonstrative. If the agreement of the intermediate ideas with one another and with the extremes is not perfectly satisfac- tory — that is, if the steps of the reasoning leave the mind under some degree of hesitation, the reasoning is denominated probable, and the reasoner attains proba- bility only of the truth of the proposition he investigates. Where certainty terminates, probability commences ; and the latter admits numerous degrees, from the high BELIEF, AND DEGREES OF BELIEF. 115 est degree, which stands next to certainty, to the lowest, which makes so little impression as to permit the mind to remain in a state of suspense. If a proposition, supported by probable evidence, re- late to speculation, the judgment formed concerning it is often called opinion; if it relate to facts, chiefly sup- ported by testimony, the judgment is generally called helief* In explaining, then, the branch of logic now [* Belief and degrees of belief . In forming any judgment, we cannot avoid attaching to it a particular degree of credence, which might be, and often is, expressed by the insertion of some adverb to qualify the copula, thus: "To-morrow will (possibly) be fine;" and, "Two straight lines (in- disputably) cannot inclose a space." Although one of these judgments admits a degree of doubt which the other excludes, the difference lies in our knowledge of the things spoken of, rather than in the things them- selves. The amount of belief which we have in our judgment has been called its modality, as being the mode in which we hold it for truth. Arranging the degrees of modality in an ascending scale, we find that a judgment may be — 1. Possible, where, upon the first view, we have no cause to think that the predicate may not be truly said of the subject, but have not examined. Does this amount to a judgment? or is it the step which must precede the formation of the weakest kind of judgment? 2. Doubtful, where we have tested it in some cases, and found that Bome fceem to confirm it, whilst some are doubtful. 3. Probable, where all the trials we have made are favorable, but the oumber of them is not sufficient to warrant certainty. 4. Morally certain for the thinker himself, where, from examination oi the matter, or prejudice, or interest, he has formed his own belief, but can- not put forward sufficient grounds for it, so as to control that of others. 5. Morally certain for a class or school, where the judgment rests on grounds which are sufficient for all men of the same habits of thought, or the same education as the thinker. o. Morally certain for all ; as, for example, the belief that there is a future state, which, though not absolutely demonstrable, rests upon such grounds that it ought to influence the conduct {mores) of every man. 7. Physically certain, with a limit, where the judgment is grounded on an induction supposed to be complete, but with the possibility that future induction may supersede it. 8. Physically certain, without limitation; as our belief in the law of gravitation, the law of chemical affinity, &c. 9. Mathematically certain, where doubt cannot be admitted. Ex. gr.. the axiom — "Two straight lines cannot inclose a space;" or the theorem, "The angles at the base of an isosceles triangle are equal." 116 DEMONSTRATIVE REASONING. before us, all we have to do is to discuss, first, the na- ture of demonstrative reasoning • secondly, that of probable reasoning * and to point out the sciences and arts in which they are respectively employed. All rea- soning is either of the one kind or the other ; and in every science or art in which conviction reaches not certainty, we must be content with probability. After I have finished the explanation of legitimate reasoning, I shall investigate the nature of sophistry, and point out the chief methods by which mankind in all ages have imposed on themselves, or misled others. I shall con- clude the course with an account of the syllogism of Aristotle, and a discussion of its merit as a mode of reasoning.* Mathematics and arithmetic, I must again remark, are the only sciences susceptible of demonstrative proof , which is so satisfactory and cogent as to exclude even the supposition of falsehood. Other sciences in their principles may perhaps furnish proofs nearly, if not completely demonstrative ; but in the detail they ex- hibit nothing better than probability. The high evi- dence of the sciences of quantity, independent of the importance of the truths they teach, renders them a good exemplification of the rules of logic ; and one ot the best methods of becoming a good reasoner, is to be familiar with the processes of investigation they supply. All these degrees of belief may, upon a broader principle of division, be resolved into three. Our judgments, according to Aristotle, are either problematical, assertive, or demonstrable— the results of opinion, of belief, or of science. — Thomson's Laws of Thought, §120.] [* The word reasoning is ambiguous. In one of its acceptations, it means syllogism, or the mode of inference which may be called concluding from generals to particulars. In another of its senses, to reason, is simply to infer any assertion from assertions already admitted, and in this sense induction is as much entitled to be called reasoning as the demonstrations o*" geometry. — MUl'i Logic] DEMONSTRATIVE REASONING. 117 To illustrate the nature of demonstrative reasoning, „ sfoall analyze some propositions of the Elements of Euclid. Reasoning is a successive comparison of every pair of ideas, from the first to the last, or from the idea which forms the subject of the proposition, to the one which forms the predicate ; and in demonstration every comparison is intuitively certain. When these ideas are found to agree, the demonstration is finished, and the reasoning is concluded. I begin with the first prop- osition of the first book of the Elements, which proposes, " To describe an equilateral triangle on a given straight line." I pass over the operations by which the triangle in the figure is described, because I mean to analyze only the reasoning of the proposition. After the figure is constructed on the given line, the proposition to be proved is, that " the triangle so constructed is equilateral, or has all its sides equal." The subject of the proposition, or the first idea of it, is that of the triangle described ; the predicate of the proposition, or the second idea of it, is that of the equality of the sides of the triangle. Now, it is not intuitively certain that the three sides are all equal to one another ; therefore some interme- diate ideas must be placed between the subject and the predicate of the proposition, to show their agreement. The process consists of two steps, or one intermediate idea is necessary to prove the proposition. The first step is the com- parison of the base A B with one of the sides A C ; and of their equality we have intuitive certainty, because, by the de- scription of the figure, they are semi- diameters, or radii of the same circle. The second step is the comparison of the same side or base \ B with the other side B C ; and of their equality, also, we have intui- tive certainty, as they are both semi-diameters of another circle. This step finishes the demonstration. The base is found to agree with both the sides ; and the triangle must be equilateral, because all the sides are equal. The subject and predicate of the proposition are found exactly to agree. In the famous forty -seventh proposition of the first book of tb« 118 DEMONSTRATIVE REASONING. Elements, the truth to be established is, " That in a right-angled triangle, the square of the side opposite to the right angle is equal in quantity to the sum of the squares of the other sides." The square opposite to the right angle is the subject, the sum of the two other squares is the predicate, and the idea of the extent of the first square is to be compared with the idea of the sum of the other two squares. The process is long and beautiful, and I shall point out the different steps. The first step is to prove that G A C is one straight line, and H A B another, in order to lay a foundation for demonstrating that the triangle FB C is equal to half the square FA, and the triangle A B D equal to half the parallelogram B L. The next step is to prove the tri- angle A B D equal to the triangle F B 0. The third step is to prove the triangle A B D equal to half the parallelogram B L, and the triangle F B equal to half the square F A ; and hence to infer the equality of the square F A to the parallel- ogram B L. Three similar steps are ne- cessary to find the square A K equal to the parallelogram L ; and hence to infer the equality of the whole square B K to the two squares FA and A K, which establishes the agreement of the subject and predicate of the proposition; or that the square of the side opposite to the right angle, is equal to the squares of the two other sides. To complete this process, then, there are necessary these six capital steps, and each of these in- cludes one or more subordinate steps, so that the sum of the sub- ordinate steps amounts to no fewer than twelve ; and if these are added to the six capital ones, it appears, that to prove this propo- sition, there are requisite eighteen intermediate Ideas. The mind has a clear and distinct perception of the agreement of every pair of ideas ; and as the effect is proportional to the cause, it obtains the most complete certainty of the truth of the proposition.* All reasoning has this in common with demonstra- tion, that the agreement or disagreement of the primary ideas must be proved by intermediate ideas ; the differ- [* Dr. Abererombie furnishes some admirable remarks upon mathe- matical reasoning, pp. 202-4, InteU. Powtrs.] PROBABLE REASONING. 119 ence is, that the agreement of the intermediate ideas with one another, and with their primary ideas, amounts not to certainty ; it is no more than probable.* From this view it will appear, that the far greater part of knowledge, and even the most interesting and important part, that which concerns morality, politics, the useful arts, and business, is not supported by better evidence than probability. The probability, however, in many cases is highly convincing, approaches very near to certainty, and affords good ground for acting upon it with perfect confidence and satisfaction. It has often been wished, and sometimes asserted, that mo- rality particularly might be fortified with the evidence of certainty ; but there is much reason to apprehend that the undertaking would be unsuccessful. The duties mankind owe to the Author of nature, to their fellow- creatures, and to themselves, thougli palpable and ob- vious in their principles, yet when pursued through the ramifications in which they unfold themselves, they deviate into relations where the agreement of ideas is neither clear nor adequate. That all men should revere their Maker, and should perform every duty they conceive will be acceptable to him ; that they should do good to their fellow-creatures, and should not wantonly hurt or injure them ; that they should live in temperance and mod- eration, in order to insure the highest happiness their constitutions can enjoy ; are all conclusions, of the justness of which nobody can doubt, any more, perhaps, than they can doubt that two and three make five, or that the three angles of a triangle are equal to two right angles. The agreement of the idea we have of man, with those [which we have] of his Creator, and our fellow-creature, infers these duties with an evidence which approaches very near, if it do not reach, demonstration. But when we descend to investigate the | * At the close of the lecture wiL be added, from the pen of the late Dr. George Payne, an admirable view of the nature of Probable Keasoi ing which should be carefullv studied and mastered. I 120 EXAMPLES OF PROBABLE REASONING. nature of particular acts of regard to God, or of intercourse with our fellow-creatures; our scale applies not accurately, the agree- ment or disagreement of ideas is not perfectly clear ; and we are not certain, at least we do not agree, where regard to the Almighty terminates, and disregard begins ; where justice or charity ceases, and injustice or severity commences. Till this can be done, we have no reason to expect that the precepts of morality shall be supported by the evidence of demonstration. The same species of reasoning applies to the evidence of other sciences, of arts, and of business. In them all the mind discovers only moral certainty, that is, differ- ent degrees of probable evidence, according as the agreement of ideas is more or less clear and satisfactory. To illustrate these observations, I shall produce a few examples. Suppose some reasoning were employed to recommend the love of God, or to prove this proposi- tion, that man ought to love God. The agreement of ideas in moral reasoning, I have formerly observed, re- lates to propriety, fitness, reasonableness. The propo- sition, then, involves the question whether the idea we have of such an imperfect, dependent creature as man, agrees with the idea of his exerting love towards the great, wise, and good Being who made the universe, or whether it be fit, proper, and right that man should love God? To prove this proposition, I might employ several intermediate ideas ; I might first show that the Almighty is the most amiable Being in the universe, and that he possesses all those attributes of goodness, wisdom, and power, most calculated to excite attachment. The amiableness of God would -thus involve a large collection of particulars, or subordinate ideas, which altogether would constitute what, in the science of morals, is denominated an argument. I might prove, secondly, that the love of God is the surest means ot happiness to ourselves. It will communicate self-approbation, con fidence in the wisdom of Providence and the administration of hu- man affairs; and will extirpate those anxieties and fears which haunt and distract weak and vicious men. The illustration of thest EXAMPLES OF PROBABLE REASONING. 121 topics, also, would include a great number of subordinate ideas, and would constitute another argument for the love of God. I might further insist that love to God is reasonable and proper, in return for the numerous instances of kindness, mercy, and love, he daily exerts towards us. The illustration of these instances, likewise, would comprehend many subordinate ideas, and would furnish a third argument in support of the proposition. Suppose, again, it were to be inferred from future punishment that men must be free agents, or that the idea of future punishment agrees with that of self- determination, or the freedom of action. The following train of intermediate ideas will show that agreement. Future punishment must be inflicted by the Almighty ; the Al- mighty can inflict no punishment not just ; the punished, of course, must be guilty ; they could, then, have done otherwise, and conse- quently must be free agents. This train of ideas, more shortly ex- pressed, will stand thus : Future punishment — God the punisher — punishment just — punished guilty — could have done otherwise — self-determination. In this piece of reasoning there are four inter- mediate ideas, and five comparisons are made to discover the agreement with the extremes, and with one another. The agree- ment between the adjacent ideas in every movement, appears with a high degree of conviction ; and were each of the ideas illustrated at some length, according to the common mode of reasoning on moral topics, the whole would form an elegant deduction, and would communicate a very vivid impression. Let us suppose, further, the following political propo- sition were proposed to be proved ; and let us consider the nature of the reasoning requisite to establish it: u Industry is the capital source of national prosperity." The ideas, or terms, as the logicians express themselves, to be compared, are those pf industry and national prosperity. I must also remark, that agreement of ideas in politics refers, riot to reasonableness and fitness, as in morals, but to public utility, or national happi- ness. Tfye meaning, then, of the proposition will be, that industry makes a nation prosperous, by extending 6 122 EXAMPLES OF PKOBABLE REASONING. its opulence and exalting its reputation, in support of which I may argue in the following train : Industry increases the population of a country, by providing subsistence for additional inhabitants. An increase of inhabitants increases commerce and manufactures. Commerce and manufac- tures procure riches from foreign nations of less industry. These riches prompt a spirit of enterprise still further to extend commerce and manufactures. Hence new nerves to domestic industry. The comforts, and many of the luxuries of life, are provided for all the members of the community. Ample security is found for the con- tinuance of these advantages by the national reputation they pro- cure, and the large resources of money and men they supply to maintain it. But national prosperity consists in these things which I have enumerated ; — a wealthy, sober, industrious, and numerous people, respectable at home, and formidable abroad. Each of the steps might have been illustrated at considerable length, and might have formed a very pleasant and satisfactory discussion. They may also be condensed into more narrow bounds, and may form the following series ready for the nearest comparison. National industry — increase of people — improvements in commerce and manufactures — national riches — national enterprise — people at home, numerous and happy, respectable and formidable abroad — national prosperity. This series presents five intermediate ideas ; and six comparisons are requisite to afford conviction of the* agree- ment of the first idea with the last, or of the subject of the propo sition with its predicate. In the specimens I have advanced from morals and politics, the evidence, you will observe, though highly satisfactory, is still no more than probable; and ap- pears not with that commanding tone which compels assent. Skeptical men may find reason to suspend as- sent, and disputatious men may raise difficulties, which we are obliged to admit are not destitute of foundation. Accordingly, against every step of the preceding politi- cal series, some cause of hesitation may be started. It may be urged, that industry is not always attended with an increase of people ; it may even sometimes produce the contrary offect ; it may induce the people to emigrate to other countries, VALUE OF PROBABLE REASONING. 123 where their labor will be better rewarded than at home. It may be urged again, that the most warlike and powerful nations are often the poorest and most hardy, while arts and industry only supply riches to tempt such adventurers to seize both the country and its wealth. It may be contended, that arts and industry ener- vate mankind, multiply wants and vices, and render people miser- able in the midst of every provision for happiness ; that they re- press all the great and splendid, and consequently many of the most pleasant exertions of the mind. It is the possibility of con- structions of this sort, in all probable investigations, which dimin- ishes their evidence, and renders the conviction they produce infe- rior to that of demonstration. But, however susceptible of controversy these speci- mens of reasoning may be, they are much more satis- factory than many of the conjectural opinions on which men must every day act in some of the most important concerns of life. Many of the engagements we form, every new line of life on which we enter, involve nu- merous considerations to determine our conduct, which are scarcely supported by better evidence than specula- tion. The wisdom of the most prudent man is fre- quently not more meritorious than the sagacity which leads him to conjecture with most probability, or which teaches him to proceed with recollection and attention to surrounding objects, so as to avail himself of events as they occur. I mention these particulars to evince, that we have no good reason to be dissatisfied with our condition, though we should not receive, on many subjects of knowledge, other evidence for truth than that of proba- bility. It is sufficient to^guide us to happiness, while uncertainty about futurity in particular is, perhaps, one of the most merciful dispensations with which the providence of heaven could have favored mankind. The highest happiness we can partake in this world, is extremely circumscribed. One of the chief ingredi- 124 ANALOGICAL REASONING. ents of our enjoyments is hope ; and were onr anticipa tions and conjectures about futurity less equivocal, our hopes would be correspondently diminished. In our deepest distress, our ignorance of what is to come is so great as never to preclude hope. We sometimes expe- rience relief, contrary to every view of probability, and every expectation : and we have always the consolation of looking forward, and hoping fur better days. In our reasonings of anticipation, we proceed chiefly by analogy. We suppose that the future will resemble the past. In the negotiations of business, and in fore- casting the probable consequences of any plan of con- duct, we must conclude, that similar causes will pro- duce similar effects ; that men will act in time to come as they have done in time past ; and that the course of nature will proceed by the established rules which have directed it since the world began. We argue from the characters, the opinions, the interests, the pas- sions, the weaknesses, and the caprices of men ; and we endeavor to form systems of conduct for them, derived from the situations which they occupy. The trains of reasoning we adopt in such cases, are in a great meas- ure hypothetical ; and the probability of the evidence frequently is of., the lowest kind. . Conjectures often so counterbalance one another, as to leave the mind in a state of total suspense. OBSERVATIONS ON PROBABLE REASONING. [From Dr. George Payne's Mental Science.] [According to Dr. Thomas Brown, reasoning, as ex- pressed in words, consists of a series of propositions, each of which embodies and expresses a feeling of the relation of comprehension. "Man is an intellectual being.; he should not, therefore, pursue the gra^ifica-. ANALYSIS OF PROBABLE REASONING. 125 tions of sense only." The preceding sentence contains two distinct propositions ; and the whole is an effect of what is called reasoning. Each of these propositions expresses nothing more than a recognized relation — the relation of comprehension. The first one exhibits some- thing which forms a part of our complex notion of man, viz., intellect ; the second, something which enters into our complex notion of an intellectual being, viz., eleva- tion above the pleasure of mere appetites. u In a single proposition," says Dr. Brown, u we take one step, or feel one relation ; in an enthymeme we take two steps, or feel two relations ; in a syllogism we take three steps, or feel three relations : whatever is affirmed in any stage of our reasonings, is a relation of some sort, — of which, as felt by us, the proposition that affirms the re- lation is only a verbal statement." All reasoning, then, verbally expressed, consists of a series of propositions : but every series of propositions does not constitute reasoning. M God is infinitely wise," " Man is prone to err," " Heaven is the abode of hap- piness." Here is a series of propositions, each of them embodying a judgment, or the notion of a relation; but there is no ratiocination here. To constitute reason- ing, there must be a certain connection in the proposi- tions enunciated, by which the last is connected as ef- fectually as the second with the first. What, then, is the nature of this connection of the propositions in a process of reasoning? This will, per- haps, be best ascertained by' examining a particular instance, viz., u Man is possessed of intellect, will, free- dom, &c. ; he is, therefore, a capable subject of moral government." In this example, the term man is what is called the subject of the first proposition ; and his affirmed capability of moral government is denomina- ted its predicate. It will be observed, however, that l26 analysis of probable reasoning. this predicate becomes the subject of the second propo- sition, which, when fully expressed, stands as follows : A being possessed of intellect, will, &c, is a capable subject of moral government. We are accordingly led by this particular instance to the general doctrine that, to confer upon a series of propositions a claim to the character of reasoning, it is essential that the predicate of each of the propositions constitute the subject of the proposition which immediately follows it ; in that case the predicate of the last will be as certainly connected with the subject of the first proposition, as though they stood in juxtaposition. By lengthening the preceding series of propositions, the truth and importance of this statement will be rendered apparent. Man is possessed of intellect, will, freedom, &c. The possessor of intellect, &c, is a capable subject of moral government. A capable subject, &c, &c., may expect that his con- duct will hereafter undergo the scrutiny of the Judge of all. In the above series, it will be seen that the predicate of the first becomes the subject of the second proposi- tion, — and the predicate of the second, the subject of the third ; and further, that the subject man of the first is connected with the predicate of the last : thus, Man may expect that his conduct will hereafter undergo, &c. The reason of this connection will be apparent, when it is remembered that each of the predicates declares what is comprehended in the complex notion expressed by its subject. The possession of intellect, will, &c, is involved in our complex notion of man ; capacity of moral government is involved in our complex notion of a being possessing intellect, &c, &c. ; and the certainty of the scrutiny referred to is involved in our complex notion of a capable subject of moral government. Now, ANALYSIS OF PROBABLE REASONING. 127 if the second is involved in the first — the third in the second — and the fourth in the third — it is manifest that the fourth is as really involved in the first as in the third. And thus it is in every train of reasoning, how- ever long that train may be. An analysis takes place in our mind, of the complex notion denoted by the first, or original subject, in consequence of which we are enabled to predicate something of it. That which is thus predicated undergoes a similar process of analysis, the result of which is embodied in the subsequent prop- osition ; so that when we arrive at the conclusion, how distant soever it may be, the last predicate is as truly contained in the first as is its particular predicate, though it does not become visible to us till exhibited, as it were, in its elementary state, by the repetition of analysis after analysis.] LECTURE IX. DIFFERENT PROCESSES OF REASONING EXAMINATION OF THE VALIDITY OF A PROCESS OF REASONING DIFFERENT KINDS OF SOPHISTRY THE VARIOUS USE AND ORDER OF SEVERAL KINDS OF PROPOSITIONS AND OF ARGUMENTS THE EXERCISE OF A SOUND JUDGMENT. In the preceding lecture I explained the nature of reasoning, and the different degrees of evidence it con- veys to the mind, according as it is demonstrative or probable. I have shown that it consists in perceiving whether ideas agree or disagree ; and I have illustrated the meaning of this agreement in mathematics, morals, politics, and business. It only remains, that I explain 128 REASONING DIRKCT OR INDIRECT. the different methods, in common use, of distributing or arranging ideas in different processes of reasoning. In this view, reasoning is said to be either direct or indirect. In direct reasoning, we prove a proposition in the manner I have explained, by finding interme- diate ideas that show the agreement of the terms of which it consists. In indirect reasoning, we do not trace the agreement of the terms of a proposition ; it- takes place only when the predicate of a proposition admits an alternative, and when either the predicate or the alternative must be true, or must agree with the subject of the proposition, because they exhaust every case that can exist. We prove that the alternative annot be true, and therefore the predicate must be true. An example will make this matter perfectly clear. Euclid lays down this proposition — u That a straight line drawn at right angles from the extremity of a diameter, falls without the circle." No intermediate idea, it seems, occurred, by which he could deduce the proof directly from the nature of the circle, or of the perpendicular or the extremity of the diameter. He proceeds, therefore, by indirect demonstration, and introduces an alternative. The perpendicular must fall either without the circle, or within it. No third supposition can be made relative to the manner of its falling, for it cannot fall upon the circumference of the circle, ex- cept in one point. He proves that the alternative cannot be true, or that the perpendicular cannot fall within the circle. The predi- cate, then, must be true, that the perpendicular falls without the circle. Again — " The moon is either an opaque or a transparent body." It is not transparent, because, if it were, it would transmit the rays of the sun when it comes between the sun and the earth ; and no eclipse of the sun could happen from the intervention of it between the sun and the earth ; but this conclusion is contrary to truth, for such eclipse does happen. The alternative, therefore, that the moon is a transparent body must be false, and consequently the predicate must be true, than the moon is an opaque body. The refutation of the alternative is always pursued till it terminates in DIRECT AND INDIRECT REASONING COMPARED. 129 some contradiction, falsehood, or absurdity ; and on this account indirect reasoning is sometimes called u reductio ad absurdum" by the logicians. It has often been disputed, whether indirect reasoning is less elegant and satisfactory than direct ; but I need not spend time in remarks on this controversy. Both convey truth with perfect evidence ; and when a rea- soner has got possession of an indirect proof, he will not, I believe, trouble himself much in searching for a direct one. It is, however, generally supposed, that mathe- maticians never employ the former but in cases of necessity, when they cannot have recourse to the latter. The great number of beautiful specimens of demonstra- tion of which their science is susceptible, may rendei them nice or delicate even about the elegance and manner of their reasonings ; but on other subjects, and in other sciences, when the mind is glad to reach im* portant truth on any terms, it will be abundantly satis- fied with good indirect proof. It may, perhaps, be doubted whether the charge of inelegance is not the offspring of squeamishness and caprice, rather than of just taste. An indirect train of ideas is often long, and is conjoined with as much clearness and propriety as any direct one. The step from the falsehood of the alternative to the truth of the predicate, is perfectly satisfactory, if not elegant ; and it may be added, that indirect reasoning imparts variety to the nature of the proof.* [ * Dr. Watts thus describes some arguments of an indirect form : (1.) W T hen some contradictory proposition is proved to be false, improba- ble, or impossible ; or when, upon supposition of the falsehood, or denial of the original proposition, some absurdity is inferred. This is called a proof per impossibile, or a reductio ad absurdum. (2.) When some other proposition is proved to be true, which is less probable ; and thence it follows that the original proposition is true, because it is more probable. (3.) When any other proposition is proved, upon which it was before agreed to yield the original question.] *''.*' • - 6« 130 A PRIORI AND A POSTERIORI REASONING. Reasoning, further, is said to proceed either a priori, or a posteriori — a distinction which relates entirely to cause and effect. In reasoning a priori, we begin with the cause, and infer from it the reality or the species ot the effect. In reasoning a posteriori, we reverse this process ; we begin with the effect, and reason back- ward from it, to the establishment of the. existence and qualities of the cause. If, for example, I maintain, that the soul of man is a thinking substance, and therefore that it is immaterial, because matter can- not think ; and hence again infer that it is immortal, because what is immaterial cannot die or be destroyed — I reason a priori ; I de- duce the effect from its cause, and prove the soul to be immortal from the nature of its constitution. If, again, I argue that the people who live fifteen degrees further east than we will have their day beginning and ending an hour sooner than ours ; that naviga- tors, of course, who have sailed fifteen degrees eastward will have lost an hour of our day, and will have gained an hour from the day of the people of that longitude ; that these navigators will expe- rience a similar loss and gain in point of time, for every fifteen de- grees eastward on the face of the globe ; and that, as they must pass through four and twenty times fifteen degrees in sailing round the globe, so, on returning home, they will calculate time a day sooner than their countrymen, because they have lost twenty-four hours of the time of their countrymen in their voyage: in this process I reason a priori, because I deduce a curious fact, verified by experience, from the figure of the earth, round which the navi- gation is performed. In reasoning a posteriori, we argue from the effect to the cause, and conclude from the former the nature or existence of the latter. For example, from the wisdom, power, and goodness discernible in all the works of nature, I infer that there must be some wise, benevolent, and omnipotent cause, from which these effects proceed. I cannot doubt of the effects, because I experience them every mo- ment of my existence ; I can as little doubt that they must proceed from some cause, and that the cause must possess the qualities conspicuous in the effects. I observe, again, that the shadow ot ARGUMENTS WITH RESPECT TO SUBJECT-MATTER. 131 the earth projected on the face of the moon, in a lunar eclip?e, is of a circular form ; and from this effect I justly infer that the figure of the earth is round, because this figure only could produce such a shadow. Keasonings a priori are much circumscribed, because causes are seldom so well known as their effects. From effects, chiefly, we ascend to the knowledge of causes and on this account, reasoning a posteriori is much more frequent. It is much employed in inquiries into nature ; it is the groundwork of the famous method of induction for investigating natural knowledge, recom- mended in the " Novum Organum" of Lord Bacon ; and it is of frequent use in politics and morals. The best way to obtain an acquaintance, both with the Author of nature, and with the secondary causes which produce the effects we daily behold, is to survey with patience the effects themselves, because we have no means of information concerning the causes, except in this channel. In like manner, to understand the duties a man owes to his country, or to his neighbor, we must scrutinize his constitution, what forms the happiness of such a being, both as a member of society and a moral agent ; what are his mental facul- ties and his bodily powers, his attachments and antipathies, his gratifications and his wants. In all these inquiries we begin from the effect, and ascend to the cause, or we reason a posteriori. [We will now leave our author for a while, and draw upon Dr. Whately : He distributes arguments with respect to their sub- ject-matter, into two great classes, viz. : First, such arguments as might have been employed — not as argu- ments, but — to account for the fact or principle main- tained, supposing^ its truth granted. Secondly, such as could not be so employed. The former class (the a priori) is manifestly argument from cause to effect, since to account for any thing signifies to assign the cause of it ; this is the popular sense. As far, then, as any cause, popularly speaking, hms 132 ARGUMENTS FROM AN EFFECT TO A CONDITION. a tendency to produce a certain effect, so far its exist ence is an argument for that effect. If the cause be fully sufficient, and no impediments intervene, the effect in question follows certainly ; and the nearer we ap- proach to this, the stronger the argument. This is the kind of argument which produces (when short of abso- lute certainty) that species of the probable which is usually called the "plausible." The second class of arguments (referred to above) are designated by the terms "sign" and "example." The former is an argument from an effect to a condition ; — a species of argument of which the analysis is as fol- lows : As far as any circumstance is what may be called a condition of the existence of a certain effect or phenomenon, so far it may be inferred from the exist- ence of that effect : if it be a condition absolutely essen- tial, the argument is, of course, demonstrative ; and the probability is the stronger in proportion as we approach to that case. As an instance, a man is suspected as the perpetrator of a murder, from the circumstance of his clothes being bloody ; the murder being considered as in a certain degree a probable condition of that appearance ; i. e., it is presumed that his clothes would not otherwise have been bloody. Again, from the appearance of ice, we infer, decidedly, the existence of a temperature not above the freezing-point, that temperature being an essential condition of the crystallization of water. Among the circumstances which are conditional to any effect, must evidently come the cause or causes ; and if there be only one possible cause, this being abso- lutely essential, may be demonstratively proved from the effect : if the same effect might result from other causes, then the argument is, at best, but probable. But it is to be observed, that there are also many circum ARGUMENTS FROM AN EFFECT TO A CONDITION. 13 3 stances which have no tendency to produce a certain effect, though it cannot exist without them, and from which effect, consequently, they may be inferred as conditions, though not causes : e. g., a man's being 14 alive one day," is a circumstance necessary, as a con- dition, to his " dying the next," but has no tendency to produce it ; his having been alive, therefore, on the for- mer day, may be proved from his subsequent death, but not vice versa. It is to be observed, therefore, that though it is very common for the cause to be proved from its effect, it is never so proved, so far forth as it is a cause, but so far ♦brth as it is a condition, or necessary circumstance. A cause, again, may be employed to prove an effect (this being the^^ class of arguments), so far as it has a tendency to produce the effect, even though it be noi at all necessary to it (i. e., when other causes may pro- duce the same effect) ; and in this case, though an effect may be inferred from the cause, the cause can- not be inferred from the effect : e. g., from a mortai wound you may infer death, but not vice versa. Lastly, when a cause is also a necessary or probable condition, i. e., when it is the only possible or only likely cause, then we may argue both ways: e.g., we may infer a general's success from his known skill, or his skill from his known success (in this, as in all cases, assuming what is the tetter known as a proof of what is less known, denied, or doubted) : these two arguments belonging, respectively, to the two classes originally laid down. The phrase ^ a priori" argument, is generally under- stood to extend to any argument drawn from an antece- dent or a forerunner, whether a cause or not ; e. g., " the mercury sinks, therefore it will rain." Now this argu- ment being drawn from a circumstance whichj though i34 ambiguous words. an antecedent, is not a cause, would fall not under the for- mer but under the latter of the classes laid down ; since when rain comes, no one would account for the phenom- enon by the falling of the mercury, which they would call a " sign" of rain ; and yet most, perhaps, would class this among " a priori" arguments. In like manner, the expression, " a posteriori" arguments, would not in its ordinary use coincide precisely, though it would very nearly, with the second class of arguments. Many writers, in investigating the cause to which any fact or phenomenon is to be attributed, have as- signed that which is not a cause, but only a ^m^that the fact is so ; and have thus been led into an endless train of errors and perplexities. The word why, as an interrogative, is employed in three senses, viz., " By what proof?" (or reason). " From what cause ?" " For what purpose ?" This last is commonly called the " final cause :" e. g., " Why is this prisoner guilty of the crime ?" " Why does a stone fall to the earth?" u Why did you go to Lon- don?" Much confusion has arisen from not distin- guishing these different inquiries. Ambiguity has arisen from the same words having come to be applied, in common, to diverse kinds of sequence ; e. g., an effect is said to " follow" from a cause, and a conclusion to " follow" from the premises ; the words " cause" and u reason" are each applied indif- ferently, both to a cause properly so called, and to the premise of an argument, though " reason," in strictness of speaking, should be confined to the latter. " There- fore," " hence," " consequently," &c, and also " since," " because," and " why," have likewise a corresponding ambiguity. As before remarked, " reason" is employed to signify the premise, or premises of an argument: especially ARGUMENT FR.^M PROGRESSIVE APPROACH. 135 the minor premise ; and it is from " reason" in this sense that the word " reasoning" is derived. It is also very frequently used to signify a cause ; as when we say, in popular language, that the "reason of an eclipse of the sun is, that the moon is interposed between it and the earth." This should he strictly called the cause. On the other hand, " because" (i. e., u by cause") is used to introduce either the physical cause or the logical proof; and " therefore," "hence," " since," " follow," " consequence," and many other kindred words, have a corresponding ambiguity : e. g., " the ground is wet, because it has rained ;" or, " it has rained, and hence the ground is wet :" this is the as- signment of the cause. Again, " it has rained because the ground is wet ;" " the ground is wet, and therefore it has rained ;" this is assigning the logical proof : the wetness of the ground is the cause, not of the rain hav- ing fallen, but of our knowing that it has fallen. And this probably it is that has led to the ambiguous use in all languages of almost all the words relating to these two points. Next may be considered the argument from Pro- gressive Approach. In this species, the force of the series of arguments results from the order in which they are considered, and from their progressive tendency to establish a certain conclusion. For example : One part of the law of nature, called the vis inertias, is established by the argument alluded to ; viz., that a body set in motion will eternally con- tinue in motion, wi,th uniform velocity, in a right line, so far as it is not acted upon by any causes which retard or stop, accelerate or divert its course. Now, as in every case which can come under our observation, some such causes do intervene, the assumed supposition is practically impossible, and we have no opportunity of 136 ARGUMENT CALLED verifying the law by direct experiment ; but we may gradually approach indefinitely near to the case sup- posed, and on the result of such experiments our con- clusion is founded. We find that where a body is pro- jected along a rough surface, its motion is speedily re- tarded and soon stopped ; if along a smoother surface, it continues longer in motion ; if upon ice, longer still ; and the like with regard to wheels, &c, in proportion as we gradually lessen the friction of the machinery: and if we remove the resistance of the air, by setting a wheel or a pendulum in motion under an exhausted re- ceiver, the motion is still longer continued. Finding, then, that the effect of the original impulse is more and more protracted, in proportion as we more and more remove the impediments to motion from friction and the resistance of the air, we reasonably conclude, that if this could be completely done (which is out of our power), the motion would never cease, since what appear to be the only causes of its cessation would be absent. Dr. Whately adds a similar progressive argument for the being and attributes of God, and for religious toler- ation. — Rhetoric, part i. chap. ii. § 6. In the next place, under the head of Example,* Dr. [* The Example is an argument which proves something to be true in a particular case from another particular case. Thus, " Harvey might expect to be persecuted for his discovery of the circulation of the blood, because Galileo was for his discovery." But the connection between two distinct facts can only depend upon their coming under some common law, and therefore in the Example the proof is' not of one particular judgment by another, but of a particular by means of a universal, for which another par- ticular is the sign. Thus : Galileo was persecuted — Galileo was a discoverer in science ; Therefore all discoverers are likely to be persecuted. Harvey is a discoverer, Therefore he too will be persecuted. This argument is called " rhetorical induction ;" it diffexs from inductior INDUCTION. 137 Whately comprehends the arguments designated by the various names of induction, experience, analogy, parity of reasoning, &c, all of which are essentially the same as to fundamental principles : for, in all the arguments designated by these names, it will be found, that we consider one or more known individual objects or in- stances of a certain class as a fair sample, in respect of some point or other of that class ; and, consequently, draw an inference from them respecting either the whole class, or other less known individuals of it. We do not, strictly speaking, reason by induction, but reason from induction, i.e., from our observations on one, or on several individuals, we draw a conclusion respecting the class they come under ; or, in like man- ner, from several species, to the genus which compre- hends them : e. g., " The earth moves round the sun in an elliptical orbit ; so does Mercury, and Venus, and Mars, &c. ; therefore a planet (the common term com- prehending these singulars) moves round," &c. " Philip w r as reckless of human life ; so was Alexander ; so was Caesar, &c. ; therefore this is the general character of a conqueror?'' In such arguments it is assumed, that what belongs to the individual, or individuals we have examined, be- longs (certainly or probably, as the case may be), to the whole class under which they come. With respect to the argument from experience / proper in bringing in only one example instead of many, and in going on to prove another particular case, instead of stopping at the general law. This difference disappears, if, with Diogenes, Laertius, and Cicero, we de- scribe induction as an argument from particulars to like particulars. The plan in this kind of argument is obvious ; but the nearer the predi- cate of the second premise approaches to distribution (the introduction ol the whole of their subject), the less probable is an error. If it could be Bhown that " Galileo was a fair sample of all discoverers," the mode would be formally correct. But in its weaker form it is perpetually employed — Thomson.'] 138 ARGUMENT FROM EXPERIENCE AND ANALOGY. strictly speaking, we know by experience only the past and what has occurred under our own observation ; thus, we know by experience that the tides have daily ebbed and flowed during such a time, and from the tes- timony of others, as to their own experience, that the tides have formerly done so ; and from this experience we conclude, by induction, that the same phenomenon will continue. The word analogy, again, is generally employed in the case of arguments in which the instance adduced is somewhat more remote from that to which it is ap- plied ; e. g., a physician would be said to know by ex- perience the noxious effects of a certain drug on the human constitution, if he had frequently seen men poisoned by it ; but if he thence conjectured that it would be noxious to some other species of animal, he would be said to reason from analogy, the only differ- ence being, that the resemblance is less between a man and a brute than between one man and another ; and accordingly, it is found that many brutes are not acted upon by some drugs which are pernicious to man. But, more strictly speaking, analogy ought to be dis- tinguished from direct resemblance, with which it is often confounded. Analogy, being a " resemblance of ratios," that should strictly be called an argument from analogy in which the two things (viz., the one from which, and the one to which we argue) are not necessa- rily themselves alike, but stand in similar relations to some other things ; or, in other words, that the common genus which they both fall under, consists in a relation. Thus an egg and a seed are not in themselves alike, but bear a like relation to the parent bird and to her future nestling on the one hand, and to the old and young plant on the other, respectively ; this relation being the CAUTIONS CONCERNING ANALOGY. 139 genus which both fall under: and many arguments might be drawn from this analogy. In this kind of argument one error, which is very common, and w T hich is to be sedulously avoided, is that of concluding the things in question to he alike because they are analogous: to resemble each other in them- selves, because there is a resemblance in the relation they bear to certain other things; w T hich is manifestly a groundless inference. Many persons are guilty of this mistake who are, or ought to be, familiar with the Scripture parables ; in which the words " compare" and "liken" are often introduced, where it is evident that there could have been no thought of any direct resem- blance. A child of ten years old would hardly be guilty of such a blunder as to suppose that members of the church are literally " like" plants of corn — sheep — fish caught in a net, — and fruit-trees. Another caution is applicable to the whole class of arguments from example / viz., not to consider the re- semblance or analogy to extend further (i. e., to more particulars) than it does. In the parable of the unjust steward, an argument is drawn from analogy to recom- mend prudence and foresight to Christians in spiritual concerns, but it would be absurd to conclude that fraud was recommended to our imitation ; and yet mistakes very similar to such a perversion of that argument are by no means rare. Against both these mistakes our Lord's parables are guarded. in two ways. 1st. He selects, in several of them, images the most remote possible from the thing to be illustrated in almost every point except the one that is essential, as in the parable referred to just above. 2dly. He employs a great variety of images in illustra- ting each single point ; e. g., a field of corn — a net cast into the sea — a grain of mustard-seed — a lump of 14U PAKABLKS OF CHRIST. leaven, &c. For, as the thing to be illustrated cannot have a direct resemblance, or a complete analogy, in all these different things, we are thus guarded against tak- ing for granted that this is the case with any one of them. It may be added that the variety, and also the ex- treme commonness of the images introduced, serve as a help to the memory by creating a multitude of associa- tions. Our Lord has inscribed his lessons on almost every object around us. And, moreover, men are thus guarded against the mistake they are so prone to, and which, even as it is, they are continually falling into, of laying aside their common sense altogether in judging of any matter con- nected with religion ; as if the rules of reasoning which they employ in temporal matters, were quite unfit to be employed in spiritual. It may be added, that illustrations drawn from things considerably remote from what is to be illustrated will often have the effect of an " a fortiori" argument, as in some of the parables just alluded to, and in that where Jesus says, " If ye then, being evil, know how to give good gifts to your children, how much more" &-c. So, also, in the Apostle Paul's illustration from the Isthmian Games, u Now, they do it to obtain a corrup- tible crown ; but we, an incorruptible," &c. Sound judgment and vigilant caution are nowhere more called for than in observing what differences (per- haps seemingly small) do, and what do not, nullify the analogy between two cases. And the same may be said in regard to the applicability of precedents or ac- knowledged decisions of any kind, such as Scripture precepts, &c, all of which, indeed, are in their essence of the nature of example : since every recorded decla- ration or injunction may be regarded — in connection SMALL DIFFERENCES NULLIFY ANALOGY. 141 with the persons to whom, and the occasion on which it was delivered — as a known case; from w 7 hich, conse- quently, we may reason to any other parallel case, and the question which we must be careful in deciding will be to whom, and to what it is applicable. For, a seem- ingly small circumstance w T ill often destroy the analo- gy, so as to make a precedent, precept, &c, inapplica- ble : and often, on the other hand, some difference, in itself important, may be pointed out between two cases, which shall not at all weaken the analogy in respect of the argument in hand. And thus there is danger both of being misled by specious arguments of this descrip- tion, which have no real force, and also of being stag- gered by plausible objections against such examples or appeals to authority, &c, as are perfectly valid. Hence Aristotle observes, that an opponent, if he cannot show that the majority of instances is on his side, or that those adduced by his adversary are inapplicable, con- tends that they, at any rate, differ in something from the case in question. Many are misled, in each way, by not estimating aright the degree and the hind of difference between the two cases. For example, the Apostle Paul recom- mends to the Corinthians celibacy as preferable to mar- riage : hence some religionists have inferred that this holds good in respect of all Christians. Now in many most important points Christians of the present day are in the same condition as the Corinthians, but they were liable to plunder, exile, and many kinds of bitter perse- cutions from their fellow-citizens ; and it appears that this was the very ground on which celibacy was recom- mended to them, as exempting them from many afflic- tions and temptations which in such troublous times a family would entail. Now it is not, be it observed, on the intrinsic importance of this difference between 142 ANALYTIC AND SYNTHETIC REASONING. them and us that the question turns ; but on its impor tance in reference to the advice given. For other il- lustrations consult Whately's Rhet, part i. chap. ii. § 7. The phrase " parity of reasoning" is commonly em- ployed to denote analogical reasoning.] [We now return to our author.] The last distinction of reasoning divides it into analytic and synthetic, and refers chiefly to mathemat- ical reasonings. Analysis forms an elegant method of investigating the legitimacy of demonstrations. Syn- thesis puts together the different steps after investiga- tion, so as to make out a proof, and is the same thing with direct reasoning. The ancients carried on analysis by means of mathematical figures; the great instrument of it in modern times is algebra. Many examples of the ancient analysis are to be found in Apollo- nius Pergaeus, De Sectione Rationis, and in the problems published by the late Dr. Steuart, of Edinburgh. Every treatise of algebra, but particularly that of Sir Isaac Newton, will furnish specimens of the modern analysis by letters or symbols. All the demonstra- tions of the Elements of Euclid exhibit examples of synthesis; and I need not produce any of them. I shall, therefore, offer only one example of analysis. The purpose of it is to try the legitimacy of an investigation, or to discover whether the intermediate ideas, by which a mathematician suspects a demonstration may be ac- complished, are sufficient for that purpose. He begins with sup- posing that the ideas are good media for demonstrating the propo- sition in question, and constructs his figure on that hypothesis. He supposes, further, the thing done that a problem requires, or the truth established which a theorem proposes to prove. He sets out from the proposition, and reasons backward to the beginning of it ; and if he encounter no contradiction, or terminate in no absurdity, he concludes the media to be pertinent and legitimate; if he land in an absurdity or contradiction, he infers that the media are improper, and that the synthetical demonstration will be inconclusive.* [* See Dugald Stewart's Works, vol. ii. chap. ix. § 3, for a full descrip- tion of the- import of the words analysis and Synthesis.] VALIDITY OF A PROCESS OF REASONING. 143 If, for example, it were required to analyze the first proposition of the first book of the Elements of Euclid, which proposes to de- scribe an equilateral triangle on a given straight line. The mathe- matician would describe a triangle on the given line, and would suppose it equilateral. He would reason thus : If the triangle be equilateral, then making one end of the base a centre, and descri- bing a circle with the length of it as a radius, the circle will pass through the other extremities of the base, and of one of the sides ; so that the base and one of the sides must become radii of the same circle. It another circle be described from the other end of the base, with the same base taken as a radius, this circle will pass through the other extremities of the base and of the other side. The two circles, therefore, are equal, because their radii are so. This step finishes the analysis, and proves the media to be legiti- mate, because the reasoning backward has reached its principle, the equality of the two circles, from which the synthesis begins, or from which the truth of the proposition, that the triangle is equi- lateral, is demonstrated. Logicians mention some other distinctions of reason- ing, which I shall shortly explain, because they some- times occur in conversation, and often in books. When we argue from principles, or opinions, admitted by the person with whom we reason, whether they be true or not in themselves, we are said to employ an argumen- tum ad hominem. When we urge in our defence some eminent authority, which an antagonist is ashamed to oppose, we are said to employ an argumentum ad vere- cundiam. When we perplex or puzzle an adversary, we offer what is called argumentum ad ignorantiam. EXAMINATION OF THE VALIDITY OF A PROCESS OF REASONING. ) [From Dr. Abercrombie's " Intellectual Powers."] [In examining the validity of a process of reasoning, the mental operation which we ought to perform may be guided by the following considerations : 144 VALIDITY OF A PROCESS OF REASONING. 1. What statements does the author propose as mat- ters of fact / are these authentic ; are they really bear- ing upon, or connected with, the subject ; do they com- prise a full and fair view of all the facts which ought to be brought forward in reference to the inquiry; have we reason to suspect that any of them have been dis- guised or modified, — that important facts have been omitted or kept out of view, — that the author has not had sufficient opportunities of acquiring the facts which he ought to have been possessed of, — or that he has been collecting facts on one side of a question, or in support of a particular opinion ? 2. What propositions are assumed, either as first or intuitive truths, or as deductions arising out of former processes of investigation ; and are we satisfied that these are all legitimate and correct? In particular, does he make any statement in regard to two or more events being connected as cause and effect / and is this connection assumed on sufficient grounds ; does he as- sume any general principle as applicable to a certain class of facts / is this principle in itself a fact, and does it really apply to all the cases which he means to in- clude under it ; have w T e any reason to believe that it has been deduced from an insufficient number of facts, — or is it a mere fictitious hypothesis, founded upon a prin- ciple which cannot be proved to have a real existence ? 3. Do these assumed principles and facts really be- long to the same subject — or, in other words, do the facts belong to that class to which the principles apply? 4. Are the leading terms' which he employs fully and distinctly defined as to their meaning ; does he employ them in their common and recognized acceptation ; and Joes -he uniformly use than in the same sense; or does he seem to attach different meanings to the same term in different parts of the argument? VALIDITY OF A PROCESS OF REASONING. 145 5. What are the new conclusions which he deduces from the whole mew of the subject; are these correct and valid ; and do they really follow from the premises laid down in the previous parts of his argument? For, on this head, it is always to be kept in mind, that a con- clusion may be true, while it does not follow from the argument that has been brought to prove it : in such a case the argument is false. Much of the confusion, fallacy, and sophistry of rea- soning arises from these points not being sufficiently attended to, and distinctly and rigidly investigated. An argument may appear fair and consecutive, but when we rigidly examine it we may find that the rea- soner has, in his premises, contrived to introduce some statement which is not true in point of fact, or some bold general position which is not correct, or not proved ; or that he has left out some fact, or some prin- ciple, which ought to have been brought forward in a prominent manner, as closely connected with the in- quiry. Hence the necessity for keeping constantly in view the various sources of fallacy to which every process of reasoning is liable, and for examining the elements rigidly and separately before we admit the conclusion. A process of reasoning is to be distinguished from a process of investigation j and both ma} 7 be illustrated in the following manner : All reasoning must be founded on facts, and the as- certained relations of these facts to each other / viz., those of resemblance, cause, effect, &c. The statement of an ascertained relation of two facts to each other is called a proposition) such as, — that A is equal to B; that C has a close resemblance to D ; that E is the cause of F, &c. These statements, propositions, or as- certained relations, are discovered by intuition or by processes of investigation. J 46 VALIDITY OF A PROCESS OF REASONING. In a process of reasoning , again, we take a certain n umber of such propositions or ascertained relations, and deduce from them certain other truths or relations, arising out of the mutual connection of some of these propositions to each other. Thus, if I state as proposi- tions, ascertained by processes of investigation, that A is equal to B, and that B is equal to C, I immediately decide by a single step of reasoning that A is equal to C in consequence of the mutual relation which both A and C have to B. Such a process may be rendered more complicated in two ways : — 1. By the number of such ascertained re- lations, which we require to bear in mind and compare with each other before we arrive at the conclusion. Thus the relation that A is equal to E might rest on such a series of relations as the following : A is equal to B ; B is the double of C ; C is the half of D ; T> is equal to E ; therefore A is equal to E. 2. By the propositions which are the conclusions of one or more steps in a process becoming the premises in a subsequent step. Thus, — I may take as one process, A is equal to B, and B is equal to C ; therefore A is equal to C ; — and, as a distinct process, C is equal to D and D is equal to E ; therefore C is equal to E. The conclusions from these two processes I then take as the premises in a third process, thus : It has been proved that A is equal to C, and that C is equal to E ; there- fore A is equal to E. In examining the validity of such processes, there are two circumstances or objects of inquiry which we ought to keep constantly in view : 1. Have we confidence in the accuracy of the alleged facts and ascertained relations which form the premi- ses? Can we rely on the process of investigation by which it is said to have been ascertained that A is equal to B, and that B is equal to C, &e 3 VALIDITY OF A PROCESS OF REASONING. 147 2. Are the various propositions in the series so rela- ted as to bring out a new truth or a new relation f For it is to be kept in mind, that a series of proposi- tions may all be true and yet lead to nothing : such propositions, for example, as that A is equal to B, C is equal to D, E is equal to F. There is here no mutual relation, and. no new truth arises out of the series. But when I say A is equal to B, and B is equal to C, a new truth is immediately disclosed in consequence of the relation which both A and C have to B ; namely, that A is equal to C. Inventive genius, in regard to processes of reasoning % consists in finding out relations or propositions which are thus capable of disclosing new truths or new rela- tions ; and in placing them in that order which is cal- culated to show how those new relations arise out ot them. This is the exorcise of a reflecting mind ; and there may be much acquired, knowledge, that is, many facts accumulated by memory alone, without any de- gree of this exercise or habit of reflection. But both are required for forming a well-cultivated mind : the memory must be stored with information, that is, ascer- tained facts and ascertained relations ; and the power of reflection must be habituated to discover new truths or new relations by a comparison of these facts and as- certained relations with each other. For the disco veiy of new truths may consist either of new facts or of new relations among facts previously known. Thus, it might happen that we had long been familiar with two facts, without being aware that they had any particular con- nection. If we were then to ascertain that the one was the.cause of the other, it would be a real and important discovery of a new truth, though it wxmld consist only of a- new relation between facts which had long been known to us.] [We return now to Professor Barron's Lectnre.1 148 IGNORATIO ELENCHI. Logicians have divided sophistry also into different kinds ; the most remarkable of which it will be proper to specify, because they are very common. The first is called Ignoratio Elenchi, and consists in mistaking or misrepresenting the state of the question under discus- sion. This species occurs in most controversies, but particularly in political ones, which now chiefly engage men of learning and ability. Religious and philosophi- cal controversies have, fortunately for the peace of so- ciety, almost totally disappeared. The moment a writer engages in controversy, in spite of all the attention he can maintain, partialities lay hold of his mind ; his pas- sions warp and mislead his understanding. He reads the performances of his antagonist under the influence of dispositions which induce him to mistake their mean- ing. He discovers malevolent or insidious designs, which are perceptible by nobody but himself; and he imputes principles and views to his opponent which the latter never entertained or disavows. He introduces principles and views of his own, and he reasons and speculates about them as if they were admitted by the opposite party.* [* Dr. Watts thus states and illustrates the Ignoratio EUnchi : — It occurs •when something else is proved which has neither any necessary connection or consistency with the thing inquired, and consequently gives no determination to the inquiry, though it may seem at first sight to determine the question ; as if any should conclude that St. Paul was not a native Jew, by proving that he was born a Roman : or if they should pretend to determine that he was neither Roman nor Jew, by proving that he was born in Tarsus in Cihcia. These sophisms are refuted by showing that all these three may be true, for he was born of Jewish parents in the city of Tarsus, and by some pecu- liar privilege granted to his parents or his native city, he was born a deni- zen of Rome. Thus not one of these three characters of the apostle is in- consistent with the others, and therefore the proving of one of thew to be true does not refute the others. Dispute™, when they grow warm, are apt to run into this fallacy. Thev Of THE UNIVERSr or PETITIO PRINCIPII. 149 2. Another species of sophistry is called Petitio Prin- eipii, and consists in assuming as true the proposition under debate. This species is not very frequent in busi- ness, because few men are so void of discernment, or so destitute of delicacy and regard to truth, as confidently to maintain what they have not attempted to prove. It is not, however, unfrequent in philosophical and politi- cal investigations, in which, either on account of the in- tricacy or uncertainty of the subjects, disputants arro- gate more liberty of obtruding their opinions upon their antagonists, or presume more readily that a bold asser- tion may be admitted for a proof. The Peripatetics pretended to prove that the centre of the earth is the centre of the universe, by the following manifest petitio prin- cipii. M All bodies must move towards the centre of the universe, but we find from experience that all bodies move towards the cen- tre of the earth ; therefore the centre of the earth is the centre of the universe." This argument proves nothing ; for although we allow that all bodies with which we are acquainted, move towards the centre of the earth, yet it does not follow that all bodies in the universe move towards the centre of the earth. The truth is, that a body near the surface of the earth, moves towards it only by the difference of attraction it exerts above the other great bodies in na- ture; that all the bodies in the solar system are attracted towards a pomt near the surface of the sun ; and that all the bodies of our so- lar system, and perhaps of all the systems of the universe, are at- dress up the opinion of their adversary as they please, and ascribe senti- ments to him which he does not acknowledge ; and when they have, with a great deal of pomp, attacked and confounded these images of straw of their own making, they triumph over their adversary as though they had utterly confuted his opinion. . It is a fallacy of the same hind which a disputant is guilty of, when he finds that he cannot fairly prove the question first proposed : he then with subtlety turns the discourse aside to some other kindred point which he can prove , and exults in that nn one side of a question ; or arguments and authorities adduced in support of particular opinions, leaving out of view those which tend to different conclusions. Misstatement, in one form or another, may indeed be considered as a most fruitful source of controversy ; and, amid the contests of rival disputants, the chief dif- ficulty which meets the candid inquirer after truth is tc have the subject presented to his mind without distortion SOUND EXERCISE OF JUDGMENT. 163 Hence the importance, in every inquiry, of suspend- ing our judgment, and of patiently devoting ourselves to clear the subject from all imperfect views and par- tial statements. Without the most anxious attention to this rule, a statement may appear satisfactory, and a deduction legitimate, which are in fact leading us wide- ly astray from the truth. THE SOUND EXERCISE OF JUDGMENT DISTINGUISHED FROM THE ART OF DISPUTATION. [From Abercrombie.] The sound exercise of judgment is widely distinct from the art of ingenious disputation. The object of +he former is to weigh fully and candidly all the rela- tions of things, and to give to each fact its proper weight in the inquiry : the aim of the latter is to seize with rapidity particular relations, and to find facts bearing upon a particular view of a subject. This habit, when much exercised, tends rather to withdraw the attention from the cultivation of the former. Thus it has not unfrequently happened that an ingenious pleader has made a bad judge ; and that acute and powerful disputants have perplexed themselves by their own subtleties, fill they have ended by doubting of every thing. The same observation applies to contro- versial writing; and hence the hesitation with which we receive the arguments and statements of a keen con- trovertist, and the necessity of hearing both sides. We have every reason to believe that though there may be original differences in the power of judgment, the chief source of the actual varieties in this impor- tant function is rather to be found in its culture an I regulation. 164 HOW THE JUDGMENT IS IMPAIRED. 1. The judgment is impaired by deficient culture. This is exemplified in that listless and indifferent habit of mind in which there is no exercise of correct thinking, or of a close and continued application of the attention to subjects of real importance. Opinions are received from others without the exertion of thinking or examining for one's self. There is another condition of mind in which opinions are formed on slight and partial examination, perhaps from viewing one side of a question, or, at least, with- out a full and candid direction of the attention to all the facts which ought to be taken into the inquiry. 2. The judgment is vitiated, by want of due regula- tion ; and this may be ascribed chiefly to two sources — prejudice and passion. Prejudice consists in the for- mation of opinion before the subject has been examined. The highest degree of it is exemplified in that condi- tion of the mind in which a man first forms. an opinion which interest or inclination may have suggested ; then proceeds to collect arguments in support of it ; and con- cludes by reasoning himself into the belief of what he wishes to be true. The same observations apply to passion, or the influ- ence exerted by the moral feelings. There is one class of truths to which these facts ap- ply with peculiar force, namely, those" which relate to the moral government of God, and the condition of man as a responsible being* These great truths, and the evidence on which they are founded, are addressed to our judgment as rational beings ; they are pressed upon our attention as creatures destined to another state of existence ; and the sacred duty from which no individ ual can be absolved, is a voluntary exercise of his thinking and reasoning powers, — it is seriously and de- liberately to consider. On these subjects a man may PRESUMPTIONS AND BURDEN OF PROOF. 165 frame any system for himself, and may rest in that sys- tem as truth ; but the solemn inquiry is, not what opin- ions he has formed, but in what manner he has formed them. Has he approached the great inquiry with a sincere desire to discover the truth ; and has he brought to it a mind, neither misled by prejudice nor distorted by the condition of its moral feelings ; — has he directed his attention to all the facts and evidences with an in- tensity suited to their momentous importance ; and has he conducted the whole investigation with a deep and serious feeling that it carries with it an interest which reaches into eternity ? THE VARIOUS USE AND ORDER OF SEVERAL KINDS OF PRO POSITIONS AND OF ARGUMENTS IN DIFFERENT CASES [Compiled from Whately's Rhetoric, Part I. Chapter III.] Sec. 1. — Presumptions and Burden of Proof. It is a point of great importance to decide in each case, at the outset, in your own mind, and clearly to point out to the hearer, as occasion may serve, on which side the presumption lies, and to which belongs the [onus probandi] burden of proof. For though it may often be expedient to bring forward more proofs than can be fairly demanded of you, it is always desira- ble, when this is the case, that it should be known, and that the strength of the cause should be estimated ac- cordingly. A u presumption" in favor of any supposition means, not a preponderance of probability in its favor, but such sl preoccupation of the ground as implies that it must stand goo'd till some sufficient reason is adduced against it ; in short, that the burden of proof lies on the side of him who would dispute it. . 166 PRESUMPTIONS AND BURDEN OF PROOF. Thus, it is a well-known principle of the law, that every man (including a prisoner brought up for trial) is to be presumed innocent till his guilt is established. This does not, of course, mean that we are to take for granted he is innocent ; for if that were the case he would be entitled to immediate liberation; nor does it mean that it is antecedently more likely than not that he is innocent ; or, that the majority of those brought to trial are so. It evidently means only that the u bur- den of proof" lies with the accusers; that he is not to be called on to prove his innocence, or to be dealt with as a criminal, till he has done so ; but that they are to bring their charges against him, which if he can repel, he stands acquitted. Thus, again, there is a u presumption" in favor of any individuals, or bodies corporate, to the property of which they are in actual possession. This does not mean that they are, or are not, likely to be the rightful owners ; but merely, that no man is to be disturbed in his possessions till some claim against him shall be es- tablished. He is not to be called on to prove his right, but the claimant to disprove it, upon whom conse- quently the u burden of proof" lies. A moderate portion of common sense will enable any one to perceive and to show on which side the pre- sumption lies, when once his attention is called to this question ; though, for want of attention^it is often over- looked, and on the determination of this question the whole character of a discussion will often very much depend. A body of troops may be perfectly adequate to the defence of a fortress against any attack that may be made against it, and yet if, ignorant of the advan- tage they possess, they sally forth into the open field to encounter the enemy, they may suffer a repulse. At any rate, even if strong enough to act on the offensive, PRESUMPTIONS AND BURDEN OF PROOF. 167 they ought still to keep possession of the fortress. In like manner, if you have the a presumption" on your side, and can but refute all the arguments brought against you, you have, for the present at least, gained a victory ; but if you abandon this position, by suffer- ing this "presumption" to be forgotten, which is in fact leaving out one of perhaps, your strongest argu- ments, you may appear to be making a feeble attack, instead of a triumphant defence. The following are a few of the cases in which it is important, though very easy, to point out where the presumption lies. (1.) There is a presumption in favor of every exist- ing institution. Though susceptible of alteration for the better, the " burden of proof" to that effect lies with him who proposes an alteration, simply on the ground that as a change is not a good in itself, he who demands a change should show cause for it. (2.) There is a presumption against any thing para- doxical, i. e., contrary to the prevailing opinion. It may be true, but the burden of proof lies with him who maintains it, since men are not to be expected to aban- don the prevailing belief till some reason is shown. Hence it is, probably, that many are accustomed to apply " paradox" as if it were a term of reproach, and implied absurdity or falsity. But correct use is in favor of the etymological sense. If a paradox is un- supported it can claim no attention ; but, if false, it should be censured on that ground, — but not for being new. To those who, too dull or too prejudiced to admit any notion at variance with those they have been used to entertain (^apd <5dfav), that may appear nonsense which to others is sound sense. Thus, " Christ cruci- fied" was " to the Jews a stumbling-block" (paradox), u and to the Greeks, foolishness ;" because the one " re- 168 PRESUMPTIONS AND BURDEN OF PROOF. quired a sign" of a different kind from any that ap- peared ; and the others " sought after wisdom" in their schools of philosophy. (3.) Accordingly there was a presumption against the Gospel on its first announcement. A Jewish peas- ant claimed to be the promised Deliverer, in whom all the nations of the earth were to be blessed. The bur- den of proof lay with him. No one could be fairly called on to admit his pretensions till he showed cause for believing in him. If he " had not done among them the works which none other man did, they had not had sin." Now, the case is reversed. Christianity exists / and those who deny the divine origin attributed to it, are bound to show some reasons for assigning to it a hu- man origin : not, indeed, to prove that it did originate *n this or that way, without supernatural aid, but to point out some conceivable way in which it might have so arisen. It is, indeed, highly expedient to bring forward evi- dence to establish the divine origin of Christianity ; but it ought to be more carefully kept in mind than is done by most writers, that all this is an argument u ex abundant!," as the phrase is, over and above what can fairly be called for, till some hypothesis should be framed to account for the origin of Christianity by hu- man means. The burden of proof now lies plainly on him who rejects the Gospel ; which, if it were not es- tablished by miracles, demands an explanation of the greater miracle, — its having been established, in defi- ance of all opposition, by human contrivance. (4.) It is to be observed that a presumption may he rebutted by an opposite presumption, so as to shift the burden of proof to the other side. E. g., Suppose you had advised the removal of some existing restriction- MATTERS OF FACT AND OF OPINION. 169 you might be, in the first instance, called on to take the burden of proof, and allege your reasons for the change, on the ground that there is a presumption against every change. But you might fairly reply — "True, but there is another presumption which rebuts the former : every restriction is in itself an evil, and therefore there is a presumption in favor of its removal, unless it can be shown necessary for prevention of some greater evil. I am not bound to allege any specific inconvenience; if the restriction is unnecessary, that is reason enough for its abolition : its defenders, therefore, are fairly called on to prove its necessity." Sec. 2. — Matters of Fact and of Opinion. The class of argument called example, is not excluded from the proof of matters of opinion (i. e., where we are not said properly to know, but to judge); since a man's judgment in one case may be aided or corrected by an appeal to his judgment in another similar case. It is in this way that we are directed, by the highest au- thority, to guide our judgment in those questions in which we are most liable to deceive ourselves : viz., what, on each occasion, ought to be our conduct to- wards another, we are directed to frame for ourselves a similar supposed case, by imagining ourselves to change places with our neighbor, and then considering how, in that case, we should in fairness expect to be treated. This, however, which is the true use of the celebrated precept " to do as we would be done by," is often over- looked, and it is spoken of as if it were a rule designed to supersede all other moral maxims, and to teach us the intrinsic character of right and wrong. This ab- surd mistake may be one cause why the precept is so much more talked, than attempted to be applied. For it could npt be applied, with any good result, by one 8 170 ILLUSTRATION AND SIMILE DISTINGUISHED. who should have no notions already formed of what is just and unjust. To take one instance out of many : if he had to de- cide a dispute between two of his neighbors, he would be sure that each was wishing for a decision in his own favor, and he would be at a loss, therefore, how to com- ply with the precept in respect of either, without viola- ting it in respect of the other. The true meaning of the precept plainly is, that you should do to another, nol necessarily what you would wish, but what you would expect as fair and reasonable, if you were in his place. This evidently presupposes that you have a knowledge of what is fair and reasonable, and the precept then fur- nishes a formula for the application of this knowledge, in a case where you would be liable to be blinded by self-partiality. Illustration and simile distinguished. It is of the greatest consequence to distinguish between examples (of the invented kind), properly so called — i. e., which have the force of arguments — and comparisons intro- duced for the ornament of style, in the form either of simile or of metaphor. Not only is an injurious com- parison mistaken for a proof, though it be such as when tried by proper rules affords no proof at all, but also, on the other hand, a real and valid argument is not unfre- quently considered merely as an ornament of style, if it happen to be such as to produce that effect — though there is evidently no reason why that should not be fair analogical reasoning, in which the new idea introduced by the analogy chances tp be a sublime or a pleasing one. E. g., " The efficacy of penitence, and piety, and prayer, in rendering the Deity propitious, is not irrec- oncilable with the immutability of his nature and the steadiness of his purposes. It is not in man's power to alter the course of the sun, but it is often in his power PRECEDENCE OF ARGUMENTS FROM CAUSE TO EFFECT. 171 to cause the sun to shine or not to shine upon him ; it he withdraws from its beams, or spreads a curtain be- fore him, the sun no longer shines on him ; if he quits the shade, or removes the curtain, the light is restored to him ; and though no change is in the mean time effected in the heavenly luminary, but only in himself, the result is the same as if it were. Nor is the immu- tability of God any reason why the returning sinner, who tears away the veil of prejudice or of indifference, should not again be blessed with the sunshine of the divine favor." The image here introduced is ornamen- tal, but the argument is not the less perfect, since the case adduced fairly establishes the general principle required, that, " a change effected in one of two objects having a certain relation to each other, may have the same practical result as if it had taken place in the other." The mistake in question is still more likely to occur when such an argument is conveyed in a single term employed metaphorically, as is generally the case where the allusion is common and obvious ; e. g., u We do not receive as the genuine doctrines of the primitive church what have passed down the polluted stream of tradition." The argument here is not the less valid for being conveyed in the form of a metaphor. Sec 3. — Arguments from Cause to Effect have the Precedence. Men are apt to listen with prejudice to the arguments adduced to prove any thing which appears abstractedly improbable, and, this prejudice is to be removed by the argument from cause to effect, which thus prepares the way for the reception of the other arguments. For example, if a man who bore a good character were accused of corruption, the strongest evidence against 172 ARRANGEMENT OF ARGUMENTS IMPORTANT. him might avail little; but if he were proved to be of a covetous disposition, this, though it would not alone be allowed to substantiate the crime, would have great weight in inducing his judges to lend an ear to the evidence. And thus in what relates to the future also, the a priori argument and example support each other. A sufficient cause being established, leaves us still at liberty to suppose that there may be circumstances which will prevent the effect from taking place ; but examples subjoined show that these circumstances do not, at least always, prevent that effect. On the other hand, examples introduced at the first, may be suspected (unless they are very numerous) of being exceptions to the general rule, instead of being instances of it, which an adequate cause previously assigned will show them to be. For example, if any one had argued, from the temptations and opportunities occurring to a military commander, that Bonaparte was likely to establish a despotism on the ruins of the French Republic, this argument, by itself, would have left men at liberty to suppose that Such a result could have been prevented by a jealous attachment to liberty in the citizens, and a fellow-feeling of the soldiery with them ; then, the ex- amples of Csesar and of Cromwell would have proved that such preventives are not to be trusted. Arrangement is a point not perhaps of less conse- quence in argument, than in the military art. For example, in stating the evidences of our religion, so as to give them their just weight, much depends on the order in which they are placed. The antecedent prob- ability that a revelation should be given to man, and that it should be established by miracles, all would allow to be, considered by itself, in the absence of strong direct testimony, utterly insufficient to establish the conclusion. • '-•..'• ILLUSTRATION OF THIS. 173 On the other hand, miracles, considered abstractedly, as represented to have occurred without any occasion for them or reason being assigned, carry with them such a strong inherent improbability, as could not be wholly surmounted even by such evidence as would fully establish any other matters of fact. But the evi- dences of the former class, however inefficient alone towards the establishment of the conclusion, have very great weight in preparing the mind for receiving the other arguments, which, again, though they would be listened to with prejudice if not so supported, will then be allowed their just weight. The writers in defence of Christianity have not al- ways attended to this principle, and their opponents have often availed themselves of the knowledge of it, by combating in detail arguments, the combined force of which would have been irresistible. They argue respecting the credibility of the Christian miracles ab- stractedly, as if they were insulated occurrences, without any known or conceivable purpose; as, e. g., "What testimony is sufficient to establish the belief that a dead man was restored to life V and then they proceed to show that the probability of a revelation, abstractedly considered, is not such at least to establish the fact that one has been given. Whereas, if it were first proved (as may easily be done) merely that there is no such abstract improbability of a revelation as to ex- clude the evidence in favor of it, and that if one were given, it must be expected to be supported by miracu- lous evidence, then, just enough reason would be as- signed for the occurrence of miracles, not indeed to establish them, but to allow a fair hearing for the argu- ments by which they are supported. 174 arrangement of premises and conclusion. Sec. 4. — "When the Premises and when the Conclu- sion SHOULD COME FIRST. A proposition that is well known (whether easy to be established or not), and which contains nothing particularly offensive, should in general be stated at once, and the proof s subjoined / but one not familiar to the hearers, especially if it be likely to be unacceptable, should not be stated at the outset. It is usually better in that case to state the arguments first, or at least some of them, and then introduce the conclusion, thus assu- ming in some degree the character of an investigator. This, indeed, is the usual and natural way of speaking or writing, viz., to begin by declaring your opinion, and then to subjoin the reasons for it. It will sometimes give an offensively dogmatical air, to begin by advan- cing some new and unexpected assertion ; though some- times, again, this may be advisable, when the argu- ments are such as can be well relied on, and the prin- cipal object is to excite attention and awaken curiosity. And accordingly, with this view, it is not unusual to present some doctrine, by no means really novel, in a new and paradoxical shape. But when the conclusion to be established is one likely to hurt the feelings and offend the prejudices of the hearers, it is essential to keep out of sight, as much as possible, the point to which we are tending, till the prin- ciples from which it is to be deduced shall have been clearly established ; because men listen with prejudice, if at all, to arguments that are avowedly leading to a con elusion which they are indisposed to admit; whereas, if we thus, as it were, mask the battery, they will not be able to shelter themselves from the discharge. The observance, accordingly, or neglect of this rule, will often make the difference of success or failure. • ADVANCE FROM GENERAL TO PARTICULAR. 175 It will often he advisable to advance very gradually to the full statement of the proposition required, and to prove it, if one may so speak, by instalments ; estab- lishing separately, and in order, each part of the truth in question. Thus Paley (in his Evidences) first proves that the apostles, &c, suffered ; next, that they encountered their sufferings knowingly ; then, that it was for their testimony that they suffered ; then, that the events they testified were miraculous ; then, that those events were the same as are recorded in our books, &c, &c. Advance from general to particular. It will often happen that some general principle, of no very para- doxical character, may be proposed in the outset (just as besiegers break ground at a safe distance, and ad- vance gradually till near enough to batter) ; and when that is established, an unexpected and unwelcome ap- plication of it may be proved irresistibly. We shall thus have to reverse, in many cases, the order in which, during the act of composition (or pre- meditation), the thoughts will have occurred to our minds ; for in reflecting on any subject, we are usually disposed to generalise / to proceed from the particular point immediately before us, successively, to more an. stands sometimes for " All taken together" — " All these claims upon my t ne overpower me." Hence may arise an ambiguity ; instead of the all in its logical use, we may put every ; but to exercise the same liberty with the other sense of it would be absurd. The example given could not mean." Every single claim upon my time overpowers me."— Thomson.] THE FOUR SORTS OF PROPOSITION'S. 193 mals. " No animal can live without food," is a uni- versal negative proposition. A particular proposition includes only a part of a genus, or of a species, and affirms or denies something of it. Accordingly, u Some* animals are long lived," is a particular affirmative proposition. " Some animals are not endowed with reason," is a particular negative proposition. Hence it appears that four sorts of propositions only can enter a syllogism. They must be either universal affirmatives, or universal negatives; particular affirmatives, or par- ticular negatives. These four sorts of propositions, for the convenience of distinguishing them, are denomina- ted by the four following vowels, a, e, ?', o. A, signifies universal affirmative ; e, universal negative ; t, particu- lar affirmative ; and o, particular negative. To assist the memory, these vowels and their properties are formed into the two following monkish verses: " Asserit e negat a, sed universaliter ambse. Asserit i negat o, sed particulariter arnbo." Although a syllogism consists of three propositions, it contains only three ideas, which are called terms, each of which is twice used, to make up the proposi- tions. One of these ideas, which is always the predi- cate of the conclusion, is called the major term ; an- other the minor term, which is always the subject of the conclusion ; and the third, the middle term. The reasoning of the syllogism lies in pointing out the agreement or disagreement of the major and minor [* The word some is the cause of confusion in its logical use. In what sense is the " some" of a particular proposition to be understood? Does it mean, "Some, we know not how many," or, " A certain number which we may have in our thoughts ?" The word appears to be employed in the two senses, of " some or other" and " some certain," in common language ; and it becomes a question in which sense it is to be regarded in logic. — Thomson.] •'* '• 9 « 194 MAJOR, MINOR, AMD MIDDLE TERMS. terms, by comparing them with the middle term. The middle term never appears in the conclusion, or third proposition ; it is compared successively with the major and minor terms in the first two propositions, or premi- ses, as they are sometimes called. It is twice used in the premises ; it may be either the predicate of the ma- jor premise, and the subject of the minor ; or, it may be the subject of the major premise, and predicate of the minor. In like manner the major and minor terms stand once in each premise, and they are both used in the conclusion. For example, in the syllogism formerly quoted, the minor term is " man," the major term is " mortal," and the middle term is " ani- mal." In the first premise, " All animals are mortal," the middle term, "animal," is compared with the major term, "mortal." " Animal" is the subject ; " mortal" is the predicate ; and it is affirm- ed or predicated of all animals, that they are mortal. In the sec- ond premise, "Man is an animal," "man," the minor term, is com- pared with " animal," the middle term ; and it is affirmed, or predicated of man, that he is an animal. The middle term, "ani- mal," is the subject of the former premise, and the predicate of the latter. In the conclusion, " Man is mortal," the minor term, " man," is inferred to agree with the major term, " mortal," be- cause, in the premises, they were both found to agree with the same middle term, " animal." We have now advanced a considerable way in the explanation of the nature of a syllogism. In order to complete the illustration of all those which are denomi- nated regular, or categorical syllogisms, it will be ne- cessary only to unfold the meaning of mode and figure. Figure relates to the position of the middle term j mode, to the quantity and quality of the propositions of which the syllogism consists. The middle term may be the subject of the major premise, and the predicate of the minor, when the syllogism is of the first figure ; or, it may be the predicate of both premises, which makes a syllo MODE AND FIGURE. 19. r ) gism of the second figure; or, it may be the subject of both premi- ses, when the syllogism will be of the third figure ; or, it may be the predicate of the major premise, and the subject of the minor, when the syllogism will be of the fourth figure. As the middle term never appears in the conclusion, and must appear twice in the premises, it will appear that these four are all the positions of which it is susceptible ; and consequently that the number of fig- ures must also be four. I should add examples of each figure, but ' I rather choose to defer them till I have explained the meaning of mode, when the same examples will serve to illustrate both figures and modes. I have already remarked, that all syllogisms are com- posed of four sorts of propositions : universal affirma- tives, or universal negatives ; particular affirmatives, or particular negatives; and that these propositions are discriminated by the vowels a, e, i, o. The mode of a syllogism is determined by the species of the propositions of which it is composed. They may be three universal affirmatives marked by three a\ or three universal negatives marked by three e% or three particular affirmatives marked by three i's, or three particular negatives marked by three o's ; or, they may be two universal affirmatives, and one universal negative, marked by two a's and one e ; or two universal affirmatives, and one particular affirmative, marked by two a's and one i ; or two universal affirmatives, and one particu- lar negative, marked by two a's and one o. Each of these combina- tions makes a mode ; and there may be as many modes in each figure as there are possible combinations of the four vowels. It is found, by computation, that the number of possible combinations is no fewer than sixty-four for each figure, so that all the four fig- ures will furnish two hundred and fifty -six modes. But of these possible modes, a few only form legiti mate syllogisms.' The first figure has no more than four conclusive modes * one consisting of three univer- sal propositions, denoted by three a's, to which has been given, by the schoolmen, the name of Barbara, because it contains the vowel a three times. A second, consist- 196 FIRST AND SECOND FIGURKS. ing of a universal negative major proposition, a him versa] affirmative minor proposition, and a universal negative conclusion, denoted by the vowels e, a, e } to which has been given the name of Celarent, because the vowels of this mode form the vowels of that word. A thirds containing a universal affirmative major propo- sition, a particular affirmative minor proposition, and a particular affirmative conclusion, denoted by the letters a, f, % out of which is formed the word Darii, for the name of this mode. A fourth, consisting of a universal negative major premise, and a particular affirmative minor premise, and a particular negative conclusion, marked by the vowels e, e, 0, of which has been formed the word Ferio, for the name of the last mode. In the second figure are found also four conclusive modes ; and the quantity and quality of their propor- tions will be readily comprehended from their names, in which, as in the preceding figure, the vowels only are significant. Cesare is the name of the first mode ; Camestres, of the second ; Festino, of the third ; Baroco, of the fourth. The third figure has six modes, denoted by the hard words, Darapti, Felapton, Disamis, Da- tisi, Bocardo, Ferison. Hence it appears that all the legitimate modes of the first three figures are no more than fourteen. The names of these modes and figures were, to aid the memory, formed by the schoolmen into the following barbarous hexameters : "Barbara, Celarent, Darii, Ferio, dato primse; Cesare, Camestres, Festino, Baroco, secundse ; Tertia grande sonans recitat Darapti, Felapton ; Adjungens Disamis, Datisi, Bocardo, Ferison." Aristotle has not treated separately of the modes of the fourth figure, because he found they could be re- duced to those of the former figures. I shall now offer some examples to illustrate, the .theories which I have EXAMPLKS OF SYLLOGISM. 197 endeavored to explain. The following is a syllogism of the first figure, and of the mode Barbara: All bad men are miserable ; All tyrants are bad men ; Therefore, all tyrants are miserable. The major term is " miserable," the minor term is M tyrants," and the middle term is " bad men." The middle term is the subject of the major premise, "all bad men are miserable," and the predicate of the minor premise, " all tyrants are bad men." The syllogism is therefore of the first figure, which requires these positions of the middle term. The propositions are all universal affirmatives ; con- sequently, the mode is Barbara. The next shall be an example of the second figure, and of the mode Cesar e. No deceitful man merits confidence ; All honest men merit confidence ; Therefore, no honest man is deceitful. M Deceitful," is the major term ; " honest man," is the minor term; and "merits confidence," is the middle term. The middle term is the predicate of both the premises, "no deceitful man merits confi- dence," "all honest men merit confidence," which are the situa- tions of the middle term required by the second figure. The first premise is universal negative, marked by the letter /th not wnd Pope.] SORITES. 203 ence of the other premise. The premise in this case is called the antecedent ; and the conclusion, the sequela, 01 the inference.* Sorites is another species of irregular syllogism, and consists in conjoining a series of propositions in such a manner, that the predicate of the preceding proposition forms the subject of the succeeding. The following is an example : The mind is a thinking substance. A thinking substance is a spirit. A spirit has no extension. "What has no extension has no parts. What has no parts is indissoluble. What is indissoluble is immortal. Therefore, the mind is immortal. This species, like the former, is only a train of syllo- gisms abridged, into which it may easily be resolved in the following manner : All thinking substances are spirits ; The mind is a thinking substance ; Therefore, the mind is a spirit. Spirits have no extension ; The mind is a spirit ; Therefore, it has no extension. Things having no extension have no parts ; The mind has no extension ; Therefore, it has no parts. [* The arguments used in thinking, speaking, or writing, are never drawn out in strict technical form, except by practised logicians, desirous of exhibiting their art to those who, like themselves, are conversant with it. A sentence which contains the materials of a syllogism, not technically expressed, has been called an enthymeme. Aristotle understands by this a syllogism such as would be used in rhetoric, where the full and orderly expression of premises and conclusion would seem labored and artificial. And as the omission of one of the premises is a common, perhaps the com- monest, feature of enthymemes, logicians have defined them as syllogisms with one premise suppressed. But we may also omit the conclusion, or invert the order of premises and conclusion ; and unless we extend the name enthymeme to these cases, we put a considerable restriction upon its original meaning. Let the enthymeme then be defined — an argument in the form in whicti it would naturally occur in thought or speech. — W Thomson.] 204 CONDITIONAL SYLLOGISM. Things having no parts are indissoluble ; The mind has no parts ; Therefore, the mind is indissoluble. Things indissoluble are immortal ; The mind is indissoluble ; Therefore, the mind is immortal. Hence it appears, that all the intermediate proposi- tions between the first and the last of a Sorites may be formed into separate syllogisms ; and that it is equiva- lent to an argument formed of as many syllogisms as the argument contains intermediate propositions. It may also be observed, that every idea of the Sorites is twice repeated, and that it might be further abridged without any detriment to the evidence it communicates. Had it stood as follows, the agreement of its ideas would have been as clear, and its evidence as satisfac- tory, as in any other form. Mind — thinking substance — spirit — without extension — without parts — indissolu- ble — immortal.* Irregular syllogisms, further, are either conditional or disjunctive. The subsequent is a conditional syllogism. " If the air press down bodies below it, it must be a heavy body." The legitimacy of this species of reason- ing consists in the inference following necessarily from the premise. It has scarcely any logical form. It is an [* Three or more premises in which the predicate of each is the subject of the next, with a conclusion formed from the first subject and last predi- cate of the premises, have been called a sorites, or accumulating' argument, from the Greek word autpdg^ a heap. The name is not very appropriate ; the German title of chain-argument (kettenschluss) expresses better the na- ture of the process in which the mine) goes on from link to link in its rea- soning, without thinking it necessary to draw out the conclusions as it passes. Where the premises are all universal affirmative judgments, not the least confusion can arise from thus postponing till the end the realiza- tion of the results. But where the premises are judgments of different kinds, the reasoning is more difficult to follow, and it may be necessary to draw out each syllogism separately, in order to see whether it is in a valid mood, and, if otherwise, what is the fault in it.— Thotnson,.] DISJUNCTIVE SYLLOGISM-— DILEMMA. 205 inference from a principle, which inference must be admitted if the principle be granted. A disjunctive syllogism is proper and legitimate, when the predicate of the premise admits an alternative, and when the predicate and alternative involve every possible case. If the predicate be obviously false, the alternative of course must be true. Example : The mind of man is either corporeal or spiritual : It is not corporeal ; therefore, it is spiritual. If the predicate and the alternative do not exhaust every case that can exist, the conclusion will be illegiti- mate. For example : " All neighbors are either friends or enemies ; they are not friends ; therefore, they are enemies." In this instance, the predicate and the al- ternative do not include every case. The greatest part of neighbors may be neither friends nor enemies : they may be altogether indifferent, and accordingly the con- clusion is ridiculous. [The Dilemma is a complex argument, partaking both of the conditional and disjunctive. It is a syllogism with a conditional premise, in which either the antece- dent or consequent is disjunctive. It may prove a neg- ative or an affirmative conclusion. The word Dilemma means " double proposition," so that the whole argument takes its name from the one mixed judgment in it. When this is more than double, as in, " If a prisoner is legally discharged, either the magistrate must refuse to commit, or the grand jury ignore the bill, or the common jury acquit, or the crown exercise the prerogative of pardon," the argument has been called a Trilemma, Tetralemma, or Polylemma, according to the number of members the judgment may have. — Thomson."] . I observed, Lu the last leeture, that- l of the hunchied 206 RTJLES FOR SYLLOGISM. and ninety-two modes which the three figures contain, no more than fourteen are conclusive. I shall now ex- plain the means by which these inconclusive modes are set aside. Aristotle has been at great pains to examine them separately, and to demonstrate the fallacy of the conclusions they infer; but later logicians have con- tracted this process by the aid of a few rules, which are either self-evident, or result naturally from the construc- tion of a syllogism. The first rule is — " A syllogism must consist only of three terms." This rule excludes all ambiguities in the expression which would introduce supernumerary terms. All the terms are twice repeated ; and in every repetition the same sense should be retained. If the sense be changed the syllogism is viliated ; because the ambiguous word will supply as many terms as it has meanings. The subsequent syllogism is, therefore, fallacious and ridic- ulous. Whatever thinks is immaterial ; All spirits think ; Therefore, spirit of wine is immaterial. The double meaning of the word spirit renders the conclusion absurd. The syllogism really consists of four terms, while apparently it consists only of three. The second rule is — " No syllogism can consist entirely of particular or negative propositions." Particular propositions cannot infer a conclusion, be- cause, as I shall afterwards show, the syllogistic art hangs on this principle, " Whatever agrees or disagrees with a genus, agrees or disagrees with every species of that genus ;" if, therefore, in any syllogism no genus is found ; if different parts only, either of a genus or a species, are compared together, no conclusion can re- RULES FOR SYLLOGISM. 207 suit, because any inference from such premises is ille- gitimate. Take the following example : 8ome animals are beautiful ; Some animals are not beautiful ; Therefore, some women are beautiful, and some women are not beautiful. Three negative propositions cannot compose a legiti- mate syllogism, because they form three detached as- sertions ; and the truth or falsehood of any one of them has no dependence on the other two. The subsequent example will be an illustration : No matter thinks ; No spirit is matter ; Therefore, no matter thinks, and no spirit is matter. Another rule is — M The conclusion must be particular, if either of the premises be particular ; and negative, if either of the premises be negative." This is what the logicians mean when they tell us, that " Conclusio sequitur partem debiliorem." The u pars debilior" is a negative, or a particular premise, compared with an affirmative or a universal premise. This rule needs little illustration. If either of the premises be negative or particular, the conclusion can- not be general or affirmative, otherwise it would be more extensive than the premises from which it is de- duced. The superstructure would project beyond the foundation ; a manifest solecism both in philosophy and in arts. In the following syllogism the conclusion is negative, because the major premise is negative : No man is immortal ; All kings are men ; Therefore, no king is immortal. 208 nmMb FOR SYLLOGISM. In the subsequent syllogism the conclusion is partic- ular, because the minor premise is particular All good men are happy ; Some men are good ; Therefore, some men are happy. The last rule is — "The middle term must be taken universally in one of the premises." When the middle term is taken universally, it refers to a genus ; when it is taken particularly, it refers to a species. Were it not taken universally in one of the premises, they would not include a genus, and, conse- quently, there would be no ratiocination from it to the species. The syllogism would consist of particular propositions, and I have already shown, that from such premises no legitimate inference can result. Take the following example : Whatever thinks is immaterial ; The mind of man thinks ; Therefore, the mind of man is immaterial. The middle term, " whatever thinks," is taken univer- sally, or includes a genus in the major premise. It is aken particularly, or refers to the species, " mind of man," in the minor premise. The application of these rules evinces the illegitimacy of the inconclusive modes, and establishes the authority of the fourteen conclusive ones. I have now advanced every view and explication which appeared requisite to unfold the nature of that wonderful method of reasoning, on which Aristotle, the first and best logician, has spent so much of his time and labor; about which all the learned men of Europe were employed for many ages ; and from eminence in which the highest literary honors were, derived ; some MERITS OF THE SYLLOGISM. 209 times the administration of the most important civil offices were conferred. I proceed to discuss its merits as an engine of knowledge. That I may do it no injustice in the course of the discussion, it may be necessary again to observe, that every syllogism must not be considered as containing a complete argument, or a train of reasoning, if the argu- ment requires more than one intermediate idea. One syllogism, on the contrary, contains only one step of a train of reasoning; and in arranging a train of reason- ing in the syllogistic form, as many syllogisms must be made as there are steps or comparisons in that train. I must also observe, that by proceeding in this manner, any train of reasoning, in arts, in science, or in business, may be converted into syllogisms. These remarks may be illustrated by exhibiting the first demon- stration of the first book of Euclid in this form. It will be recol- lected, that the object of the proposition is to prove, that the tri- angle described on the given line A B, by means of the two circles, the semi-diameter of each of which is the line A B, is equilateral. From the properties of the circle, each of the sides of the triangle is found equal to the base, and the inference is drawn necessarily, that all the sides are equal. This train of reasoning, expressed bv syllogisms, will stand as follows : All the semi-diameters of the same cir- cle are equal ; The lines A B, A C, are semi-diame- ters of the same circle ; Therefore, these lines are equal. All the semi-diameters of the same circle are equal ; The lines B A, B 0, are semi-diameters of the same circle;- Therefore, these lines are equal. Whatever things are equal to the same thing, are equal to one another ; The lines A C and B C are equal to the line A B ; Therefore, the three lines A B, A C, B 0, are equal to ono an- other. 210 INUTILITY OF THE SYLLOGISTIC FORM. Triangles, having their sides equal, are called equilateral ; The triangle ABO has all its sides equal ; Therefore, it is equilateral. Now, the point to be investigated is, Whether the syllogistic method of exhibiting this demonstration, or any other train of reasoning, is preferable to that adopt- ed by Euclid, or to the method which places the suc- cessive ideas in the nearest juxtaposition, and expresses them in the fewest and plainest words. From the example I have given, it will appear that the syllogistic form is not nearly so concise as that of Euclid ; for all the ideas of Euclid's demonstration are expressed in one half of the words which are requisite to constitute these four syllogisms. Even Eu- clid's manner of expression is copious and full ; and the evidence of his demonstration would not perhaps have been impaired, had he communicated it as follows. The semi-diameters A B and A C, of the one circle, are equal ; the semi-diameters of A B and B 0, of the other circle, are equal also ; therefore, the triangle is equilateral, and described on the given line. But, besides being more prolix, the syllogistic meth- od adds no light to the evidence by which the ideas of the train of reasoning are perceived, which light the ideas possess not in their natural state of juxtaposition. Every syllogism consists of three terms, and the reason- er must have discovered the middle term, and observed the agreement of it with the extremes, before he can form the terms into a syllogism. After ihe syllogism is formed, the mind acquires no satisfaction from the contemplation of it, which the terms did not suggest in the state of juxtaposition. Suppose I were to prove that Socrates was content with his condition, because he was a wise man; I should have three terms of which a syllogism may be formed, and which in their natural order would stand thus : Socrates — a wise man — content with his condi- INUTILITY OF THE SYLLOGISTIC FORM. 2 1 1 tion. I affirm, that the agreement between Socrates and contentment, is as obvious and satisfactory in the simple juxtaposition of the terms, as it is after these terms are formed into the following syllogism : All wise men are content with their condition; Socrates was a wise man ; Therefore, Socrates was content with his condition. Further, as the syllogistic form communicates no ad- ditional light, so neither does it assist in discovering middle terms. The principal operations of any investi- gation, are the invention of intermediate ideas, and the comparison of them with one another, and with the ex- tremes. The invention of middle terms is the chief operation ; and excellence in it is the most important qualification any inquirer can possess. It seems to de- pend on natural sagacity and acuteness, fortified and improved by exercise. No art can be of any use. From syllogism, in particular, no aid can be derived. It does not even pretend to give any aid. Its only ob- ject is to assist in the second operation, the comparison of ideas; and we have seen that the syllogistic exhibi- tion is not more perspicuous than the natural one. But the most singular phenomenon of syllogism is, that the conclusion is often a self evident proposition, sometimes even trifling and insignificant. The discus- sion of this point will unfold the whole mystery and merit of the method. In converting a train of ideas into the syllogistic form, there must be made as many syllogisms as there are steps or comparisons in the train, and as many as there are ideas in the train, ex- cept one. Each idea of the train beginning w r ith the second, is the major term of its respective syllogism; the other two terms of the same syllogism are, one a genus, and the other a species of that g-enus. The ma 212 EXAMPLES OF SYLLOGISM. j<>r term is compared first with the one, and then with the other, and must be found either to agree or disagree with both. Take, for example, the train of reasoning formerly mentioned ; — Human mind — thinking sub- stance — immaterial — indissoluble — immortal ; — and convert it into syllogisms. Whatever perceives, judges, and reasons, is a thinking sub- stance ; The human mind perceives, judges, and reasons; Therefore, the human 1 find is a thinking substance. In this syllogism, the major term, "thinking sub stance," and the second idea of the train, is compared with the genus, u whatever perceives, judges, and rea- sons," in the first premise, and is found to agree with it. The same major term is compared again with the species, " the human mind," in the conclusion, and is found also to agree with it. Now, the genus, " what- ever perceives, judges, and reasons," the species, "the mind of man," and u thinking substance," are all the terms of this syllogism. Whatever thinks is immaterial ; The human mind thinks ; Therefore, the human mind is immaterial. "Immaterial," the third idea of the train, and the major term of this syllogism, is compared first with the genus, " whatever thinks," and next with the species, " the human mind," and is found to agree with both. Whatever is immaterial is indissoluble; The mind of man is immaterial ; Therefore, the mind of man is indissoluble. "Indissoluble," the fourth idea of the train, and the major term of this syllogism, is compared first with the genus, " whatever is immaterial," and next with the EXAMPLES OF SYLLOGISM. 213 species, ' ; the mind of man," and is found to agree with both. • Whatever is indissoluble is immortal ; The mind of man is indissoluble ; Therefore, the mind of man is immortal. "Immortal," the last idea of the train, and the major term of this syllogism, is compared first with the genus, " whatever is indissoluble," and then with the species, " the mind of man," and is found to agree with both. From these examples it appears, that the major term of every syllogism is one of the iiieas of the train, be- ginning with the second ; that the minor term of every syllogism is the first idea of the train; and that the middle term of every syllogism is a genus of the minor. The syllogisms I have formed are all of the first figure ; but this circumstance is no objection against the re- marks I have to make, because all the other figures and modes proceed on the same principle, namely, the com- parison of the major term first with a genus of the minor, and next with the minor as a species; or the syllogisms of the other figures may be reduced to those of the first in which these conditions take place. What, then, is the mystery of this mighty syllogistic art, which has so long engaged the attention of learned men, and is still accounted by many of that description to contain something meritorious, or to be an analysis of the art of reasoning? It is no more than this, " Whatever agrees 1 with any genus, will agree with every species of that genus / or whatever disagrees with any genus, will disagree with every species of that genus P If this . ]be .the . principle .of . the art, can we wonder at the self-evidence pf all the .conclusions of all its svllo. 214 THE SYLLOGISTIC ART USELESS. gisms, or that it never gratified science or business with the discovery of any useful truth ?* When we reflect how genus and species are formed, it is impossible but that what agrees or disagrees with the one, must agree or disagree with the other. What is a genus ? It is a collection of all the qualities com- mon to the species it includes. What agrees, then, with the common qualities of any species, must agree with the species itself, as far as these qualities extend ; and syllogism carries the agreement of the major term, with the minor and middle terms, no further than these qualities. What agrees with the genus must agree with the species ; it is only an agreement with the same thing in different situations; the major term agrees or disagrees with perfectly the same qualities, in the ge- nus, with which it agrees or disagrees in the species. Hence it appears, that after finding the agreement of the major term with the genus of the minor term, the conclusion, which asserts the agreement of the major term 'with the species, or the minor term itself, must be self-evident. To arrange things into species and genera, is extremely convenient for the purposes of language, and some of the purposes of philosophy ; but to pretend to reason from the one to the other, seems to be the quintessence of vanity or folly. Examine any demonstration of Euclid, any investiga- tion of morals, politics, or affairs, and itTwill be found that no man in earnest reasons from a genus to a spe- cies. A mathematical demonstration consists of the comparison of quantities' of the same species ; figures are compared with figures ; angles with angles ; and lines with lines. An inquiry concerning justice or charity, compares these virtues with the principles ol [* Mill's Logic, p. 117, may here be consulted with ad-vantage.} AN OBJECTION CONSIDERED. 215 reason, equity, the laws of the community, and the sit- uations of persons. A process in the arts refers to the theory of the art, and to the example of the most repu- table and successful practitioners. It is of little consequence to maintain that the syllo- gistic art sometimes makes its way into the most serious business, and that every indictment for a crime, for in- stance, is a syllogism ; of which the major premise con- tains the description of the crime, and its punishment appointed by the law; the minor premise, the applica- tion of the law to the case of the criminal, and the conclusion, an assertion that the criminal merits the punishment appointed by the law. That an indictment stands in the form of a syllogism, no doubt can exist. The major term is the punishment ; the crime committed is the minor term and the species ; the description of the crime in the law is the middle term and the genus. The major term, or the punishment, agrees with the genus, or the law ; and it agrees also, perhaps, with the minor term and the species, or the crime of the prisoner. But there is not here, strictly speaking, any reasoning. A trial is no more than a scrutiny, whether a particular crime is included under a general law, or whether the indictment accords with truth, when it asserts that the prisoner, in taking away the property or the life of his fellow-creature, has committed the crime of theft or murder, of which crimes the perpetrators are declared by the law to deserve punishment. There is no more reasoning in this case than in every application of the principles of science to the particular cases they include. The assertion, for example, that a particular field consists of a certain number of acres, is equally a syllogism with an indictment charging a culprit with the commission of a crime punishable by law. The number of acres, suppose ten, is the major term; the length and breadth of the field, is the minor term and the species ; the number of acres ,of which all fields of the length and breadth of the one under consideration consist, is the middle term and the ge- nus. The major term, ten acres, agrees with the dimensions of all fields of the extent of the one under consideration ; it agrees also with the dimensions of the one under consideration ; and, therefore, it agrees both with the genus and the species of the syllogism. 216 SYLLOGISM AS AN ENGINE OF CONTROVERSY. But, while I reprobate the syllogistic method, for being nugatory and insignificant as an instrument of reasoning, I admit its high merit as an engine of wrangling and controversy. It was the happiest con- trivance that could have been devised for conducting those public disputations and trials of skill which for ages prevailed in Europe, and in which the discovery of truth was no part of the ambition of the combatants. The most ready and acute framer of syllogisms was sure to retire triumphant. The grand contest was not whether the syllogism contained any useful truth. The object of one party was to maintain its legitimacy ; of the other, to controvert or deny one of its propositions. Wrangling thus became a science ; and the mind of man, apparently enthusiastic in the discovery of truth and knowledge, never wandered further from their paths. [Dr. George Campbell (in his Philosophy of Khetoric, p. 86), observes : In the ordinary application of the syllogistic art to matters with which we can be made acquainted only by experience, it can be of little or no utility. So far from leading the mind, agreeably to the design of all argument and investigation, from things known to things unknown, and by things evident to things obscure, its usual progress is, on the contrary, from things less known to things better known, and by things obscure to things evident. When, in the way of induction, the mind proceeds from individual instances to the discov- ery of such truths as regard a species, and from these, again, to such as comprehend a genus, we may say, with reason, that as we advance, there may be in every succeeding step, and commonly is, less certainty than in the preceding ; but in no instance whatever can there be more. DR. CAMPBKLl/s REMARKS. 217 Now the customary procedure in the syllogistic sci- ence, is from general to special, and consequently from less to more obvious. In scientific reasoning the case is very different, as the axioms or universal truths from which the mathematician argues, are so far from being the slow result of induction and experience, that they are self-evident. They are no sooner apprehended than they are necessarily assented to. But to illustrate the matter by an example, take the following specimen in Barbara, the first mode of the first figure : All animals feel ; All horses are animals ; Therefore, all horses feel. It is impossible that any reasonable man who really doubts whether a horse has feeling, or is a mere au- tomaton, should be convinced by this argument ; for, supposing he uses the names horse and animal as stand- ng in the same relation of species and genus w T hich they bear in the common acceptation of the words, the ar- gument you employ is, in effect, but an affirmation of the point which he denies, couched in such terms as include a multitude of other similar affirmations, which, whether true or false, are nothing to the purpose. Thus all animals feel is only a compendious expression for all horses feel, all dogs feel, all eagles feel, and so through the whole animal creation. I affirm, besides, that the procedure here is from things less known to things better known. It is possible that one may be- lieve the conclusion who denies the major : but the re- verse is not possible ; for, to express myself in the lan- guage of the art, that may be predicated of the species which is not predicable of the genus, but that can never be predicated of the genus which is not predicable of f .he species. If one, therefore, were under such an error 10 •2 1 S brown's analysis of the scholastic logic. in regard to the brutes, true logic, which is always co- incident with good sense, would lead our reflections to the indications of perception and feeling given by those animals, and the remarkable conformity which in this respect, and in respect of their bodily organs, they beai to our own species.] CONCLUDING CHAPTER. [The retardation of the progress of reasoning, is one circumstance which distinguishes the syllogism; but the absurdity, which is implied in the very theory of it, distinguishes it still more. It constantly assumes, as the first stage of that reasoning by which we are to ar- rive at a particular truth, our previous knowledge of that particular truth. The major is the very conclusion itself under another form, and its truth is not more felt than that which it professes to develop. Thus, to take one of the trifling examples which, in books of logic, are usually given, with a most appropriate selection, to illustrate this worse than trifling art — when, in order to prove that " John is a sinner," I do not adduce any par- ticular sin of which he has been guilty, but draw up my accusation more irresistibly by the major of a syllo- gism — " All men are sinners ;" " John is a man ;" "therefore, John is a sinner." If I really attached any meaning to my major proposition, " all men are sinners," I must at that very moment have felt as com- pletely that John was a sinner, as after I had per* sued him technically through the minor and conclusion The great error of the theory of the syllogism 'ion- BliOYVN's ANALYSIS OF TMK SCHOLASTIC LOGIC. 219 sisted in supposing that because all our knowledge may be technically reduced, in some measure, to general maxims, these maxims have naturally a prior and par- amount existence in our thoughts, and give rise to those very reasonings which, on the contrary, give rise to them. It is not on account of our previous assent to the maxim, " a whole is greater than a part," that we be- lieve any particular whole to be greater than any part of it ; but we feel this truth in every particular case by its own intuitive evidence, and the axiom only ex- presses briefly our various feelings of this kind without giving occasion to them. The general axiom, then, is in every case posterior to the separate feelings of which it is only the brief expression, or, at least, without which, as prior to our verbal statement of the axiom, the axiom itself never could have formed a part of our system of knowledge. The syllogism, therefore, which proceeds from the axiom to the demonstration of par- ticulars, reverses completely the order of reasoning, and begins with the conclusion, in order to teach us how we may arrive at it. The natural process of reasoning by two propositions instead of the three which the syllogism would force us to use, has been allowed indeed by logicians to have a place in their system ; because, with all their fondness for their own technical modes, they had not sufficient hardihood to deny, that it is at least possible for us to reason sometimes, as in truth we always reason. Their only resource, therefore, was to reduce this natural pro- cess under their own artificial method, and to give it a name which might imply the necessity of this reduc- tion, before the reasoning itself could be worthy of that honorable title. They supposed, accordingly, the propo- sition which was technically wanting to be understood ANALYSIS OF THE SCHOLASTIC LOGIC. in the mind of the thinker or hearer, and termed the reasoning, therefore, an enthymeme. It was, they said, a truncated or imperfect syllogism. They would have expressed themselves more accurately if they had de- scribed their own syllogism, as, in relation to the nat- ural analytic process of our thought, a cumbrous and overloaded enthymeme. A very little attention to the nature of the different propositions of the syllogism, will be sufficient to show that the same fundamental error which renders it use- less for discovering truth, renders it equally useless for the communication of it to others ; and that as our in- ternal reasoning is only a series of enthymemes, it is only by such a series of enthymemes as that by which truth unfolds itself to our own minds, that it can be suc- cessfully unfolded to the minds of others. In the at- tempt to communicate knowledge by the technical forms of reasoning, the major proposition, as already stated, must of course have been supposed to be understood and admitted when stated, since, if not admitted by the hearer or reader, as soon as stated, it would itself stand in need of proof; and if it was so understood and ad- mitted, of what use would the remaining propositions of the syllogism be, since they could communicate no truth that was not communicated and felt before ? The whole question relates to the feeling of the truth of the major proposition ; for if it be true, and felt to be true, all the rest is already allowed ; and yet this most important of all propositions, which, if the conclusion be of a kincl that demands- proof, must itself demand proof still more, is the very proposition which is most preposterously submitted to us in the Jlrst place for our" assent, without any proof whatever, — the honor of a proof being reserved only for a proposition which, if the major require no proof, must be itself too clear t<5 stand brown's analysis <>f the scholastic logic. 221 in need of it. Hence, the syllogism cannot fail to train the mind which receives instructions in this way, to twc of the most dangerous, practical errors, — the errors ot admitting without proof only what requires proof, and of doubting, that is to say, of requiring proof, only of what is evident. The triumph of the syllogistic art, it must be con- fessed, however, is. not as an art of acquiring or commu- nicating truth, but as an art of disputation, — as the great art of proving any thing by any thing, quidlibet 'per quodlibet jprobandi. And, if it be a merit to dis- pute long and equally well on subjects known and unknown ; to vanquish an opponent by being in the wrong, and sometimes too by being in the right, but without the slightest regard either to the right or wrong, and merely as these accidental circumstances may have corresponded with certain skilful uses of terms without a meaning. — this merit the logicians of the schools un- questionably might claim. One of the most hurtful consequences of this system, was the ready disguise of venerable ratiocination which it afforded for any absurdity. However futile an ex- planation might be, it was still possible to advance it in all the customary solemnities of mood and figure ; and it was very natural, therefore, for those who had heard what they had been accustomed to regard as reasoning, to believe that in hearing * reasoning they had heard a reason. As another very hurtful consequence of this technical system, I may remark that the constant necessity ot having recourse and then the dispute is at an end. But if he is obstinate, and will obtrude his words upon us without defining them, we ought to proceed no further till he has satis- lied us what he means. We must press him with little questions, as if we were dull of apprehension and wonld THE SOCRATIC METHOD OF REASONING. 243 be glad to understand him better. But if we can by no means prevail with him to speak plainly, it is time to put an end to the dispute, since it is evident he knows not what he would be at, or has a mind only to wrangle. If at last we bring him to declare his meaning clear- ly, we then proceed to ask him questions upon the sev- eral parts of the doctrine he advances and their conse- quences, not as objecting against them, but for the sake of better information. From these questions, if pro- posed with dexterity, it will easily appear whether the doctrine be absurd or not ; and to make the matter still clearer, it will be proper to use examples and simili- tudes. But if this be not sufficient to show the falsity of the opinion, we must inquire of the person on what arguments or proofs he grounds it, and then pursue the same conduct as we did in the first part of the dispute. Thus the learner will be led into the knowledge of truth as it were by his own invention, and being drawn by a series of pertinent questions to discern his own mistakes, he will more easily be induced to relinquish them, as he seems to have discovered them himself. AN EXAMPLE OF THIS METHOD OF DISPUTATION. Suppose M. would lead K. into the belief of a future state of rewards and punishments, it might be done in the following easy manner of reasoning. M. Did God make the world ? ]V. Certainly he did. M. Does God govern the world ? N~. As he made it, 'tis reasonable to suppose he gov erns it. M. Is not God a good and righteous governor ? JV". Doubtless he is. 244 THE SOCRATIC METHOD OF REASONING. M. What is the true idea of a good and righteom governor \ N. That he punishes the wicked, and rewards the good. M. But are the wicked always punished in this life ? N. No, every one's observation tells him the con- trary ; for the worst of men are often advanced to rich- es and honor, and have all the external comforts that the world affords. M. Are the good always rewarded in this life ? iT. No, certainly ; for poverty, persecution, and va- rious kinds of affliction, are often the lot of the most virtuous men. M. How then does it appear that God is good and righteous f JV. I confess there is but little appearance of it in the present state of tilings. M. Will there not be a time when the scene oi things will be changed, and God will make his good- ness and righteousness in the government of mankind appear ? JV. Undoubtedly such a time will come. M. But if this be not done before death, how can it be done at all ? v N. In no other way that I can think of, but by sup- posing man to have some existence after this life. M. Then you are convinced that there must be a state of rewards and punishments beyond the grave? N. Yes, I am thoroughly persuaded of it ; since the goodness and righteousness of God, as governor of the world, cannot be made to appear without it. This method of reasoning, though it has been long neglected, is certainly a natural and pleasing manner of instruction, and is much more agreeable to that candor and sincerity which every honest man ought to propose. ARRANGEMENT OF A SCIENCE. 245 than the art of wrangling which for several ages pre- vailed in the schools, and tended to overspread the minds of youth with darkness and uncertainty, and to retard or mislead them in their inquiries after truth. ARRANGEMENT OF A SCIENCE. [From Thomson's Laws of Thought.] Subordinate Parts of a Science. Judgments that relate to speculation only, are called theoretical; those which refer to practice are practical. Judgments that require or admit of proof, are called demonstrable ; those which are manifest from the very terms, are indemonstrable. Thus much being premised, we can define certain subordinate parts of a science. An Axiom is an indemonstrable, theoretical judgment. A Pos- tulate is an indemonstrable, theoretical judgment. A Theorem is a demonstrable, theoretical judgment. A Problem is a demonstra- ble, practical judgment. A Thesis is a judgment proposed for dis- cussion and proof (but with Aristotle it sometimes means an axiom of some special science or disputation). An Hypothesis is a judg- ment provisionally accepted as an explanation of some group of facts, and is liable to be discarded if it is found inconsistent with them. A judgment which follows immediately from aaother, is sometimes called a Corollary or Consectary. One which does not properly belong to the science in which it appears, but is taken from another, is called a Lemma. One which illustrates the science where it appears, but is not an integral part of it, is a Scholion. A Division of the Sciences. A division of the sciences tends to separate different districts of knowledge, with the conceptions that belong to them, from one another. It is desirable to attempt such a division, as the conclusion of a treatise on Logic ; if for no other reason, in order that we may know to how many subjects we may have to direct our rules. 11 246 A DIVISION OF THE SCIENCES. A science is a systematic arrangement of all the laws which belong to any one subject. The three great fields of human research are, — the Divine Nature, the nature of the human mind, and the nature of the universe ; and corresponding to them are three principal groups of sciences — the Theological, the Psychological, and the Cosmical or Natural. Theological Sciences. f Biblical Theology. «{ Systematical. i Mental Sciences. Mathemat- ical Sciences. Physical Sciences. Natural Sciences. Historical. Biblical Criticism. Exposition — Exegesis. Dogmatic Theology. Pastoral Theology. Church History. History of Doctrines. Mental Sciences. Reason. Choice and fection. Af- T Logic, or the Science of the forms of Thought. \ Metaphysic, which examines the ground of all knowledge of f Morality, founded on the concep- tion of Right. 1 ^Esthetic, founded on the concep- ts tion of Beauty. Cosmical Sciences. Pure Mathemat- ics. Physico Mathe- matics. Physics proper. Geology. PhytologicaL Zoological. ( Arithmetic. / Geometry, j Mechanics. } Astronomy. General Physics. Technology, or Physics applied to Arts and Manufactures. {, Descriptive Geology. \ Mining, or " Oryctotechny." j Botany. \ Agriculture. C Zoology proper < Zootechny, knowledge of the use ( of animals to man. A DIVISION OF THE SCIENCES. 247 Medical Sciences. Political Sciences. Patholo- gical Science. Physico Medical. I Medical Science [ proper. Legislation. Government. Of the Earth. ) Of the Human Race. J Medical Physics. I Hygiene. ( Pathology. ( Practical Medicine. ( Political Economy. < History of Laws and Constitu- ( tions. Administration of Law. Police and Defence. Historical Geology. Distribution of Plants and Ani- mals. \ Glossology, or Science of affinity J of Languages. j Ethnography, or Science of affin- [ ity of Races. 1KB K9B. OF THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. THE NATIONAL READERS. No. I. No. 2. No. 3. No. 4. No. 5. No. 6. By PAEKEB and WATSON. -- National Primer . . . - National First Reader . - National Second Reader - National Third Reader - National Fourth Reader - National Fifth Reader . National Elementary Speller National Pronouncing Speller 64 pp. 16 128 ' 16* 224 " 16* 288 " 12* 432 u 12° 600 « 12° 160 pp 16° 188 " 12° THE INDEPENDENT READERS. By J. MADISON WATSON. The Independent First (^ &ry ) Reader The Independent Second Reader The Independent Third Reader The Independent Fourth Reader The Independent Fifth Reader . 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The Appendix contains Rules in Spelling, Capital Letters, Punctu- ation Marks, and Abbreviations. 6 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. ORTHOGRAPHY. Smith's Series. Smith's Series supplies a Speller for every class in graded schools, and comprises the most complete and excellent treatise on English Orthography and its companior branches extant. 1. Smith's Little Speller. First round in the ladder of learning. 2. Smith's Juvenile Definer. Lessons composed of familiar words grouped with reference to similar signifies tion or use, and correctly spelled, accented, and defined. 3. Smith's Grammar-School Speller. Familiar words, grouped witli reference to the sameness of sound of syllables dif ferently spelled. Also definitions, complete rules for spelling and formation of deriva- tives, and exercises in false orthography. 4. Smith's Speller and Definer's Manual. A complete School Dictionary, containing 14,000 wor<*', with various other useful matter in the way of rules and exercises. 5. Smith's Etymology — Small and Complete Editions. The first and only Etymology to recognize the Anglo-Saxon our mother tongue; containing also full lists of derivatives from the Latin, Greek, Gaelic, Swedish, Norman, &c, &c. ; being, in fact, a complete etymology of the language for schools. Northend's Dictation Exercises. Embracing valuable information on a thousand topics, communicated in such a manner as at once to relieve the exercise of spelling of its usual tedium, and combine it with instruction of a general character calculated to profit and amuse. Phillip's Independent Writing Speller*- 1. Primary. 2. Intermediate. 3. Advanced. Unquestionably the best results can be attained in writing spelling exercises. This series combines with written exercise a thorough and practical instruction in penman, ship. Copies in capitals and small letters are set on every page. Spaces for twenty words and definitions and errors are given in each lesson. In the advanced book there is additional space for sentences. In practical life we spell only when we write. Brown's Pencil Tablet for Written Spelling. The cheapest prepared pad of ruled blanks, with stiff board back, sufficient foi 64 lessons of 25 words. Pooler's Test Speller. The best collection of " hard words " yet made. The more uncommon ones are fully defined, and the whole are arranged alphabetically for convenient reference. The book is designed for Teachers' Institutes and " Spelling Schools," and is prepared by an experienced and well-known conductor of Institutes. Wright's Analytical Orthography. This standard work is popular, because it teaches the elementary sounds in a plain and philosophical manner, and presents orthography and orthoepy in an easy, uniform system of analysis or parsing. 10 THE NATIONAL SERIES OF STANDARD SCH00L-B00K8. ORTHOGRAPHY — Continued. Barber's Complete Writing Speller. "The Student's Own Hand-Book of Ortnography, Definitions, and Sentences, con. sisting of Written Exercises in the Proper Spelling, Meaning, and Use of Words." (Published 1873.) This differs from Sherwood's and other writing spellers in its moi* comprehensive character. Its blanks are adapted to writing whole sentences instead of detached words, with the proper divisions for numbering, corrections, &c. Such aids as this, like Watson's Child's Speller and Phillip's Writing Speller, find their raison d'etre in the postulate that the art of correct spelling is dependent upon written, and not upon spoken language, for its utility, if not for its very existence. Hence the indirectness of purely oral instruction. ETYMOLOGY. Smith's Complete Etymology. Smith's Condensed Etymology. Containing the Anglo-Saxon, French, Dutch, German, Welsh, Danish, Gothic, Swedish, Gaelic, Italian, Latin, and Greek roots, and the English words derived therefrom accurately spelled, accented, and defined. From Hon. Jno. G. McMvnn, late State Superintendent of Wisconsin. " I wish every teacher in the country had a copy of this work." From Ppof. C. H. Verrill, Pa. State Normal School. "The Etymology (Smith's) which we procured of you we like much. It is the best work for the class-room we have seen." From Prin. Wm. F. Phelps, Minn. State Normal. "The book is superb — just what is needed in the department of etymology and spelling." From Hon. Edward Ballard, Supt. oj Common Schools, State of Maine. " The author has furnished a manual o/ singular utility for its purpose." DICTIONARY. Williams's Dictionary of Synonyms ; Or, Topical Lexicon. This work is a School Dictionary, an Etymology, a compilation of Synonyms, and a manual of General Information. It differs from the ordinary lexicon in being arranged by topics, instead of the letters of the alphabet, thus realizing the apparent paradox of a " Readable Dictionary." An unusually valuable school-book. Kwong's Dictionary of English Phrases. With Illustrative Sentences, collections of English and Chinese Proverbs, transla- tions of Latin and French Phrases, historical sketch of the Chinese Empire, a chrono- logical list or the Chinese Dynasties, brief biographical sketches of Confucius and of Jesus, ana complete index. By Kwong Ki Chiu, late Member of the Chinese Edu- cational Mission in the United States, and formerly principal teacher of English in the Government tichool at Shanghai, China 900 pages. 8vo. Cloth. From the Hartford Courant : " The volume is one of the most curious and interest- ing of linguistic works." From the rfew York Nation : " It will amaze the sand-lot gentry to be informed that this remarkable work will supplement our English dictionaries even for native American* " 11 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. ENGLISH GRAMMAR. SILL'S SYSTEM. Practical Lessons in English. A brief course in Grammar and Composition. By J. M. B. Sill. This beautiful book, by a distinguished and experienced teacher, at once adopted for exclusive use in the State of Oregon and the city of Detroit, simply releases English Grammar from bondage to Latin and Greek formulas. Our language is worthy of being taught as a distinct and independent science. It is almost destitute of inflections and yet capable of being systematized, and its study may certainly be simplified if treated by itself and for itself alone. Superintendent Sill* has cut the Gordian knot and leads the van of a new school of grammarians. CLARK'S SYSTEM. Clark's Easy Lessons in Language Contains illustrated object-lessons of the most attractive character, and is couched in language freed as much as possible from the dry technicalities of the science. Clark's Brief English Grammar. Part Lis adapted to youngest learners, and the whole forms a complete " brief course " in one volume, adequate to the wants of the common school. There is no- where published a superior text-book for learning thj English tongue than this. Clark's Normal Grammar. Designed to occupy the same grade as the author's veteran " Practical " Grammar, though the latter is still furnished upon order. The Normal is an entirely new treatise. It is a full exposition of the system as described below, with all the most recent im- provements. Some of its peculiarities are, — a happy blending of Syntheses with Analyses; thorough criticisms of common errors inthe use of our language; and important improvements in the syntax of sentences and of phrases. Clark's Key to the Diagrams. Clark's Analysis of the English Language. Clark's Grammatical Chart. The theory and practice of teaching grammar in American schools is meeting with a thorough revolution from the use of this system. While the. old methods offer profi- ciency to the pupil only after much weary plodding and dull memorizing, this affords from the inception the advantage of practical Object Teaching, addressing the eye by means of illustrative figures ; furnishes association to the memory, its most powerful aid, and diverts the pupil by taxing his ingenuity. Teachers who are using Clark's Grammar uniformly testify that they and their pupils find it the most interesting study of the school course. Like all great and radical improvements, the system naturally met at first with much unreasonable opposition. It has not only outlived the greater part of this opposition, but finds many of its warmest admirers among those who could not at first tolerate so radical an innovation. All it wants is an impartial trial to convince the most scep- tical of its merit No one who has fairly and intelligently tested it in the school-room has ever been known to go back to the old method. A great success is already established, and it is easy to prophesy that the day is not far distant when it will be the only system of teaching English Grammar.' As the System is copyrighted, no othei text-books can appropriate this obvious and great improvement. Welch's Analysis of the English Sentence. Remarkable for its new and simple classification, its method of treating connective* its explanations of the idioms and constructive laws of the language, &c. 13 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. GEOGRAPHY. MONTEITH'S SYSTEM. TWO-BOOK SERIES. INDEPENDENT COURSE. [Monteith's Elementary Geography. 'Monteith's Comprehensive Geography (103 maps>. S3P"" These volumes are not revisions of old works, not an addition to any series, but are entirely new productions, — each by itself complete, independent, comprehen- sive, yet simple, brief, cheap, and popular; or, taken together, the most admirable " scries " ever ottered /or a common-school course. They present the following features, skilfully interwoven, the studeut learning all about one country at a time. Always revised to date of printing. LOCAL GEOGRAPHY. — Or, the Use of Maps. Important features of the maps are the coloring of States as objects, and the ingenious system for laying down a much larger number of names for reference than are lound on any other maps of same size, and without crowding. PHYSICAL GEOGRAPHY. — Or, the Natural Features of the Earth; illus- trated by the original and striking relief maps, being bird's-eye views or photographic pictures of the earth's surface. DESCRIPTIVE GEOGRAPHY. — Including the Physical; with some account Of Governments and Races, Animals, &c. HISTORICAL GEOGRAPHY.— Or, a brief summary of the salient points of history, explaining the present distribution of nations, origin of geographical names, &c. MATHEMATICAL GEOGRAPHY. — Including Astronomical, which describes the Earth's position and character among planets ; also the Zones, Parallels, &c. COMPARATIVE GEOGRAPHY. —Or, a system of analogy, connecting new lessons with the previous ones. Comparative sizes and latitudes are shown on the margin of each map, and all countries are measured in the " frame of Kansas." TOPICAL GEOGRAPHY. — Consisting of questions for review, and testing the student's general and specific knowledge of the subject, with suggestions for geographical compositions. ANCIENT GEOGRAPHY. — A section devoted to this subject, with maps, will be appreciated by teachers. It is seldom taught in our common schools, because it has heretofore required the purchase of a separate book. GRAPHIC GEOGRAPHY, or Map-Drawing by Allen's "Unit of Measure- nent" system (now almost universally recognized as without a rival), is introduced throughout the lessons, and not as an appendix. CONSTRUCTIVE GEOGRAPHY. — Or, Globe-Making. With each book a set of map segments is furnished, with which each student may make his own globe by iollowing the directions given. RAILROAD GEOGRAPHY. — With a grand commercial map of the United States, illustrating steamer and railroad routes of travel in the United States, submarine telegraph lines, &c. Also a " Practical Tour in Europe.'* MONTEITH AND McNALLY'S SYSTEM. THREE AND FIVE BOOKS. NATIONAL COURSE. Monteith's First Lessons in Geography. Monteith's New ; Manual of Geography. McNally's System of Geography. The new edition of McNally's Geography is now ready, rewntten throughout by James Monteith and S. C Frost. In its new dress, printed from new type, and illus- trated with 100 new engravings, it is the latest, most attractive, as well as the most thoroughly practical book on geography extant. 15 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. BARNES'S NEW GEOGRAPHY. Barnes's Elementary Geography. Sm. 4to. Cloth. 96 pp. Barnes's Complete Geography. Quarto. Cloth. 140 pages. 320 maps and illustrations. The object in view, while making this series of books, was not so much cheapness U 'perfection, which is after all the truest economy. They give all the instruction in geography which it is necessary to teach From an artistic point of view they are marvellously beautiful books, and furnish the rising gem aration with instruments of education far in advance of anything hitherto produced The Elementary Geography is based upon the principle of teaching by observa- tion, and is adapted to primary grades. The Complete Geography is adapted to the intermediate and higher grades. It contains physical, descriptive, commercial, and industrial descriptions of the earth's surface. From the Neiu England Journal of Education. " These two books form a series of un- equalled beauty and perfection in the style and artistic execution of the numerous illustrations, maps, and also in the typo- graphical work. It is like looking through a portfolio of art sketches to examine and note the variety, beauty, and appropriate- ness of the illustrations of these two books. We fail to find one illustration that does not teach its proper lesson in its connection with the descriptive text of the books. Too high praise can hardly be given to these geographies in the depart- ment of design and execution of the maps and illustrations. Fortunate is the edu- cational author who has such artistic talent at his command, and special credit is due to the art department of the pub- lishers of these books. But we are aware that perfection in the mere mechanical preparation of books is not the highest test of their merit and practical usefulness as school text-books. " Turning to examine the methods of instruction adopted in this series of geog- raphy, we find a recognition, not only of the best pedagogical principles of teaching, but an application of the correct laws of culture in methods that give these books their true position in the front rank of practical school books. In the elementary book Mr. Monieith leads the young learner to look at things around him and learn of them, to observe, examine, discover, in- quire. Beginning at the school grounds the pupils are led to study for themselves their own town, city, county, state, coun- try, continent, and the world. The ad- mirably graded lessons are presented in a natural, easy, conversational style, calcu- lated to develop the reasoning powers, as well as to stimulate the individual efforts of pupils to help themselves. We espe- cially commend to the attention of teach- ers of primary schools the foot-notes, the writing exercises with language lessons, teaching by means of journeys and voyages, etc., which are found' in the Elementary Book. " In the Complete Book we find the ac- complished author has continued the ob- servational and deductive methods, begin- ning with facts, which are used wisely as stepping-stones to advanced knowledge. The physical features are attractively presented in their relation to the industries of the world. The illuminated pictures of the hemispheres, showing the earth as in a painting or on a relief globe ; the races of men in colors, showing features, com- plexions, costumes, etc. ; the trans-conti- nental views, — panoramas of the conti- nents from ocean to ocean, — teaching, at a glance, the physical features ; and the admirable maps, with the names of principal places engraved in boldfaced letters ; comparative area, comparative latitude and extent, comparative tempera- ture, comparative time of day throughout the world, is shown by means of c,lock dials, — also the standard time ; elevations of surface are shown by sectional views under the maps and the small physical charts, showing the products, seaports, highlands, lowlands, etc., of the earth. These are teatures of the Complete Book worthy of special mention and commen- dation. The language lessons and written exercises furnish valuable and interesting topical reviews. _ " In examining these books, it seems tc us that both author and publishers have vied with each other to make this two- book series of geography as near perfect as a study of correct principles and methods of teaching, the use of artistic skill in illus- trations and maps, the style and arrange- ment of type, and good paper and tasteful binding could secure. The books are a credit to American skill and taste. Wf commend them to school officers and teachers for examination and use." IV THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. MATHEMATICS. DAYIES'S COMPLETE SERIES- ARITHMETIC. Davies' Primary Arithmetic. Davies' Intellectual Arithmetic. Davies' Elements of Written Arithmetic. Davies' Practical Arithmetic. Davies' University Arithmetic. TWO-BOOK SERIES. First Book in Arithmetic, Primary and Mental. Complete Arithmetic. ALGEBRA. Davies' New Elementary Algebra. Davies' University Algebra. Davies' New Bourdon's Algebra. GEOMETRY. Davies' Elementary Geometry and Trigonometry. Davies' Legendre's Geometry. Davies' Analytical Geometry and Calculus. Davies' Descriptive Geometry. Davies' New Calculus. MENSURATION. Davies' Practical Mathematics and Mensuration, Davies' Elements of Surveying. $ Davies' Shades, Shadows, and Perspective. MATHEMATICAL SCIENCE. Davies' Grammar of Arithmetic. Davies' Outlines, of Mathematical Science. Davies' Nature and Utility of Mathematics. Davies' Metric System. Davies & Peck's Dictionary of Mathematics. 20 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. DAVIES' SERIES — Continued. THE NEW SURVEYING. Van Amringe's Davies' Surveying. By Charles Davies, LL.D., author of a Full Course of Mathematics. Revised by J Howard Van Ainringe, A.M., Ph.D., Professor of Mathematics iu Columbia College 5*56 pages. 8vo. Full sheep. Davies' Surveying originally appeared as a text-book for the use of the United State* Military Academy at West Foint. It proved acceptable to a much wider field, and underwent changes and improvements, until the author's iinal revision, and has remained the standard work on the subject for many years. In the present edition, 1883, while the admirable features which have hitherto com- mended the work so highly to institutions of learning and to practical surveyors havs been retained, some of the topics have been abridged in treatment, and some enlarged. Others have been added, and the whole has been arranged in the order of progressive development. A change which must prove particularly acceptable is the transformation of the article on mining-surveying into a complete treatise, in which the location of claims on the surface, the latest and best methods of underground traversing, &c, the calculation of ore-reserves, and all that pertains to the work of the mining-surveyor, are fully explained and illustrated by practical examples. Immediately on the publica- tion of this edition it was loudly welcomed in all quarters. A letter received as we write, from Prof. R. C. Carpenter, of the Michigan State Agricultural College, says : " I am delighted with it. I do not know of a more complete work on the subject, and I am pleased to state that it is filled with examples of the best methods of modern practice. We shall introduce it as a text-book in the college course. " This is a fair specimen of the general reception. Van Nostra ad's Eclectic Engineering Maga- zine says : — " We find in this new work all that can be asked for in a text-book. If there is a better work than this on Surveying, either for students or surveyors, our attention has not been called to it." Mathematical Almanac and Annual " Davies is a deservedly popular author, and his mathematical works are text- books in many of the leading schools and colleges." THE NEW LEGENDRE. Van Amringe's Davies' Legendre. Elements of Geometry and Trigonometry. By Charles Davies, LL.D. Revised (1885J by Frof. J. H. Van Aiming*, of Columbia College. New pages. 8vo. Full leather. The present edition of the Legendre is the result of a careful re-examination of the work, into which have been incorporated such emendations in the way of greater clear- ness of expression or of proof as could be made without altering it in form or substance. Practical exercises are placed at the end of the several books, and comprise additional theorems, problems, and numerical exercises upon the principles of the Book or Books preceding. They will be found of great service in accustoming students, early in and throughout their course, to make for themselves practical application of geometric principles, and constitute, in addition, a large and excellent body of review and test questions for the convenience of teachers. The Trigonometry and mensuration have been carefully revised throughout ; the deduction of principles and rules has been sim- plified ; the discussion of the several cases which arise in the solution of triangles, plane and spherical, has been made more full and clear ; and the whole has, in definition, demonstration, illustration, &c, been made tp conform to the latest and best methods. It is believed that in clearness and precision of definition, in general simplicity and rigor of demonstration, In the judicious arrangement of practical exercises, in orderly and logical development of the subject, and in compactness of form, Davies' Legendre is superior to any work of its grade for the general training of the logical powers ol pupils, and for their instruction in the great body of elementary geometric truth. The work has been printed from entirely new plates, and no care has been spared to ?r.dke it a model of typographical excellence. 21 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. ■ - t DAVIES'S NATIONAL COURSE OF MATHEMATICS- ITS RECORD. In claiming for this series the first place among American text-books, of whatever class, the publishers appeal to the magnificent record which its volumes have earned during the thirty-five years of Dr. Charles Davies's mathematical labors. The unremit- ting exertions of a life-time have placed the modern series on the same proud eminence among competitors that each of its predecessors had successively enjoyed in a course of constantly improved editions, now rounded to their perfect fruition, — for it seems almost that this science is susceptible of no further demonstration. During the period alluded to, many authors and editors in this department hpve started into public notice, and, by borrowing ideas aud processes original with Dr. Davie?, have enjoyed a brief popularity, but are now almost unknown. Many of the series of to-day, built upon a similar basis, and described as "modern books," are destined to a similar fate ; while the most far-seeing eye will find It difficult to fix the time, on the basis of any data afforded by their past history, when these books will cease to increase and prosper, and fix a still firmer hold on the affection of every educated American. One cause of this unparalleled popularity is found in the fact that the enterprise of the author did not cease with the original completion of his books. Always a practical teacher, he has incorporated in his text-books from time to time the advantages of every improvement in methods of teaching, and every advance in science. During ail the years in which he has been laboring he constantly submitted his own theories and those ©f others to the practical test of the class-room, approving, rejecting, or modifying them as the experience thus obtained might suggest. In this way he has been able to produce an almost perfect series of class-books, in which every department of mathematics has received minute and exhaustive attention. Upon the death of Dr. Davies, which took place in 1876, his work was immediately taken up by his former pupil and mathematical associate of many year?, Prof. W. G. Peck, L.L.D., of Columbia College. By him, with Prof. J. H. Van Amringe, of Columbia College, the original series is kept carefully revised and up to the times. Davies's System is the acknowledged National Standard for the Unitbd States, for the following reasons : — 1st It is the basis of instruction in the great national schools at West Point and Annapolis. 2d. It has received the quasi indorsement of the National Congress. 3d. It is exclusively used in the public schools of the National Capital. 4th. The officials of the Government use it as authority in all cases involving mathe- matical questions. 5th. Our great soldiers and sailors commanding the national armies and navies were educated in this system. So have been a majority of eminent scientists in this country All these refer to " Davies " as authority. 6th. A larger number of American citizens have received their education from this than from any other series. 7th. The series has a larger circulation throughout the whole country than any other, being extensively used in every State in the Union. 22 THE NATIONAL SERIES OF STANDARD SCHOxjL-BOOKS. DAVIES AND PECK'S ARITHMETICS. OPTIONAL OR CONSECUTIVE. The best thoughts of these two illustrious mathematicians are combined in the following beautiful works, which are the natural successors of Davies's Arithmetic* sumptuously printed, and bound in crimson, green, and gold: — Davies and Peck's Brief Arithmetic. Also called the " Elementary Arithmetic. " It is the shortest presentation of the sub- ject, and is adequate for all grades in common schools, being a thorough introduction to practical life, except for the specialist. At lirst the authors play with the little learner for a few lessons, by object-teaching and kindred allurements ; but he soon begins to realize that study is earnest, as he becomes familiar with the simpler operations, and is delighted to find himself master of important results. The second part reviews the Fundamental Operations on a scale proportioned to the enlarged intelligence of the learner. It establishes the General Principles and Properties of Numbers, and then proceeds to Fractions. Currency and the Metric System are fully treated in connection with Decimals. Compound Numbers and Re- duction follow, and finally Percentage with all its varied applications. An Index of words and principles concludes the book, lor which every scholar and most teachers will be grateful. How much time has been spent in searching for a half- forgotten definition or principle in a former lesson ! Davies and Peck's Complete Arithmetic. This work certainly deserves its name in the best sense. Though complete, it is not, like most others which bear the same title, cumbersome. These authors excel in clear, lucid demonstrations, teaching the science pure and simple, yet not ignoring convenient methods and practical applications. For turning out a thorough business man no other work is so well adapted. He will have a clear comprehension of the science as a whole, and a working acquaintance with details which must serve him well in al 1 emergencies. Distinguishing features of the book are the logical progression of the subjects and the great variety of practical problems, not puzzles, which are beneath the dignity of educational science. A clear- minded critic has said o; Dr. Peck's work that it is free from that juggling with numbers which some authors falsely call " Analysis." A series of Tables for converting ordinary weights aud measures into the Metric System appear in the later editions. PECK'S ARITHMETICS. Peck's First Lessons in Numbers. This book begins with pictorial illustrations, and unfolds gradually the science of numbers. It noticeably simplifies the subject by developing the principles of addition and subtraction simultaneously ; as it does, also, those of multiplication and division. Peck's Manual of Arithmetic. This book is designed especially lor those who seek sufficient instruction to carry them successfully through practical life, but have not time for extended study. Peck's Complete Arithmetic. This completes the series but is a much briefer book than most of the complete arithmetics, and is recommended not only for what it contains, but also for what is omitted. It may be said of Dr. Peck's books more truly than of any other series published, that they are clear and simple in definition and rule, and that superfluous matter of every kind has been faithfully eliminated, thus^nagnifying the working value of the book and saving unnecessary expense of time and labor. 23 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. BARNES'S NEW MATHEMATICS. In this series Joseph Ficklin, Ph. D., Professor of Mathematics and Astronomy in the University of Missouri, lias combined all the best and latest results of practical aud experimental teaching of arithmetic with the assistance of many distinguished] oiathematical authors. * Barnes's Elementary Arithmetic. Barnes's National Arithmetic. These two works constitute a complete arithmetical course in tvjo boohs. They meet the demand for text-books that will help students to acquire the greatest amount of useful and practical kuowledge of Arithmetic by the smallest expenditure of time, labor, and money. Nearly every topic in Written Arithmetic is introduced, and its principles illustrated, by exercises in Oral Arithmetic. The free use of Equations ; the concise method of combining and treating Properties of Numbers; the treatment of Multiplication and Division of Fractions in two cases, and then reduced to one; Can- cellation by the use of the vertical line, especially in Fractions, Interest, and Proportion ; the brief, simple, and greatly superior method of working Partial Payments by the "Time Table " and Cancellation; the substitution of formulas to l threat extent n>r rules ; the full and practical treatment of the Metric System, &c, indicate their com- pleteness. A variety of methods and processes for the sume topic, which deprive the pupil of the great benefit of doing a part of the thinking and labor for himself, have been discarded. The statement of principles, definitionsj rules, &c, is brief and simple. The illustrations and methods are explicit, direct, and practical. The great number «nd variety of Examples embody the actual business of the day. The very large amount of matter condensed in so small a compass has been accomplished by econo- mizing every line of space, by rejecting superfluous matter and obsolete terms, and by avoiding the repetition of analyses, explanations, and operations in the advanced topics which have been used in the more elementary parts of these books. AUXILIARIES. For use in district schools, and for supplying a text-book in advanced work for classes having finished the course as given in the ordinary Practical Arithmetics, the National Arithmetic has been divided and bound separately, as follows : — Barnes's Practical Arithmetic. Barnes's Advanced Arithmetic. In many schools there are classes that for various reasons never reach beyond Percentage. It is just such cases where Barnes's Practical Arithmetic will answer a good purpose, at a price to the pupil much less than to buy the complete book. On the other hand, classes having finished the ordinary Practical Arithmetic can proceed with the higher course by using Barnes's Advanced Arithmetic. For primary schools requiring simply a table book, and the earliest rudiments forcibly presented through object-teaching and copious illustrations, we have prepared Barnes's First Lessons in Arithmetic, which begins with the most elementary notions of numbers, and proceeds, by simpl* ileps, to develop all the fundamental principles of Arithmetic. Barnes's Elements of Algebra. This work, as its title indicates, is elementary in its character and suitable for us* 1) in such public schools as gWe instruction in the Elements of Algebra : (2) in institu- tions of learning whose courses of study do not include Higher Algebra ; (3) in school* whose object is to prepare students for entrance into our colleges and universities, ibis book will also meet the wants of students of Physics who require some knowledge erf 24 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. Algebra. The student's progress in Algebra depends very largely upon the proper treat- ment of the four Fundamental Operations. The terms Addition, Subtraction, Multiplication, and Division in Algebra have a wider meaning than in Arithmetic, and these operations have been so defined as to include their arithmetical meaning ; so that the beginner is sinrply called upon to enlarge his views of those fundamental operations. Much attention has been given to the explanation of the negative sign, iu order to remove the well-known difficulties in the use and interpretation of that sign. Special attention is bere called to " A Short Method of Removing Symbols of Aggregation," Art. 76. On account of their importance, the subjects of Factoring, Qrentrtt Common Dirisor, and Least Common Multifile have been treated at greater length than is usual in elementary works. In the treatment of Fractions, a method is used which is quite simple, and, it tl/e same time, more general than that usually employed. In connection with Rudienl Quantities the roots are expressed by fractional exponents, for the principles and rules applicable to integral exponents may then be used without modification. The Equation is made the chief subject of thought in this work. It is defined near the beginning, and used extensively in every chapter. In addition to this, four chapters are devoted exclusively to the subject of Equations. All Proportions are equations, and in their treatment as such all the difficulty commonly connected with the subject of Proportion disappears. The diapter on Logarithms will doubtless be acceptable to many teachers who do not require the student to master Higher Algebra before entering upon the study of Trigonometry. HIGHER MATHEMATICS. Peck's Manual of Algebra. Bringing the methods of Bourdon within the range of the Academic Course. Peck's Manual of Geometry. By a method purely practical, and unembarrassed by the details which rather confuse than simplify science. Peck's Practical Calculus. Peck's Analytical Geometry. Peck's Elementary Mechanics. Peck's Mechanics, with Calculus. The briefest treatises on these subjects now published. Adopted by the great Univer- sities : Yale, Harvard, Columbia, Princeton, Cornell, &c. Macnie's Algebraical Equations. Serving as a complement to the more advanced treatises on Algebra, giving special attention to the analysis and solution of equations with numerical coefficients. Church's Elements of Calculus. Church's Analytical Geometry. Church's Descriptive Geometry. With plates. Z vols. These volumes constitute the "West Point Course "in their several departments Prof. Church was long the eminent professor of mathematics at West Point Military Academy, and his works are standard in all the leading colleges. Courtenay's Elements of Calculus. A standard work of the very highest grade, preseating the most elaborate attainable survey of the subject Hackley's Trigonometry. With applications to Navigation and Surveying, Nautical and Practical Geometry, and Geodesy. 25 THL NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. BARNES'S ONE-TERM HISTORY SERIES. United A Brief History- States. This is probably the most original school-book pub- lished for many years, in any department, claims are the following : — i. Brevity. — The text is complete for grammar school or intermediate classes, in 290 12mo pages, large type. It may readily be completed, if desired, in one term oi study. 2. Comprehensiveness. — Though so brief, this book contains the pith of all the wearying contents of the larger manuals, and a great deal more than the memory usually retains from the latter. 3. Interest has been a prime consideration. Small books have heretofore been bare, full of dry statistics, unattractive. This one is charmingly written, replete with anecdote, and brilliant with illustration. 4. Proportion of Events. — It is remarkable for the discrimination with which the different portions of our history are presented according to their importance. Thus the older works, being already large books when the Civil War took place, give it less space than that accorded to the Revolution. 5. Arrangement. — In six epochs, entitled respectively, Discovery and Settlement, the Colonics, the Revolution, Growth of States, the Civil War, and Current Events. 6. Catch "Words. — Each paragraph is preceded by its leading thought in promi- nent type, standing in the student's mind for the whole paragraph. 7. Key Notes. — Analogous with this is the idea of grouping battles, &c, about some central event, which relieves the sameness so common in such descriptions, and renders each distinct by some striking peculiarity of its own. 8. Foot-Notes. — These are crowded with interesting matter that is not strictly a part of history proper. They may be learned or not, at pleasure. They are certain in any event to be read. 9. Biographies of all the leading characters are given in full in foot-notes. 10. Maps. — Elegant and distinct maps from engravings on copper-plate, and beauti- fully *olored, precede each epoch, and contain all the places named. 11. Questions are at the back of the book, to compel a more independent use of the text. Both text and questions are so worded that the pupil must give intelligent answers w his own words. " Yes " and " No " will not do. 27 THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. Primary History ot the United States. Beautifully illustrated. A fitting For Intermediate Classes. 12mo. 225 pages introduction to Barnes's Historical ISeries. From, Prof. C. W. Richards, High School, Oswego, N Y. " I think it an admirable book " From D. Beach, jf Gibbons & BmcIi, 20 West 59th Street, N.Y. City. "The little History is to me a very attractive book.' 1 From Prof. C. D ville, Larkins, N.Y. Fayette- " It is the only Primary History that I ever saw that I liked." From Prot. L. R. Hopkins, Weedsport, N.Y. " I think Barnes's Primary History by far the best I ever saw." From Prof. Richard H. Lewis, Kingston ( ollege, N. C. " The subject matter is very good, and shows remarkable condensing power in the author." From Prof. Edward Smith, Supt. of Sclwols, Syracuse, N. Y. "It is a very interesting and pretty book. I should like it very much for supplementary reading.'' From General Horatio C. King, Brooklyn, N. Y. "I am especially pleased with the new Primary History, which is remarkably concise and interesting and free, from partisan bias." From Prof S. G. Harris, Dryden, N. Y. " Having a few days' vacation I found time to carefully examine the Primary History you sent me and am highly de- lighted with it. It will satisfy a long- felt want." From the Neiv Enoland Jour- nal of Education. "The book is printed in the best type, ot. the finest paper, and is illustrated in the most superb, even sump- tuous manner. Any child who studies this exceptional- ly beautiful little book will unavoidably have a higher regard for his country on account of the superior and charming character of the keok." 28* From Mr. H. H. Smith, Prest. Board ef Education, Vineyard Haven, Mass. M I should think you would feel proud of the work. " FromDn. Eugene Bouton, Albany, N.Y. " I must congratulate every one on the publication of this beautiful History. 1 ' From Prof. H. C. Talmadge, Wood- bury, Ct. "It is the book that I have been look- ing for quite a long time." From Prof. L. C. Foster. Supt. of Schools, Ithaca, N. Y. " It is indeed a very beautiful book, and it seems to me well adapted for use in the lower grammar grades." From Prof. F. H. Hall, Sinclairville, N. Y. "This History is the best thing of the kind I have ever seen How it could be improved I do not see." From Prof. J. C Crttikshank, Supt. oj Education, Passaic Co. , N.J. " It is the book needed, and will fill the gap of early historical instruction in the schools." From Prof. S. R Morse, Supt. of Educa- tion, Atlantic Co. , N.J. " I have examined Barnes's Primary History of the United States and find it just what we have wanted in our schools. " FromB.. E. Perkins, School Commissioner, Livingston Co., N.Y. " I *hink it the belr^ $^8^\*TOf ~^1M^ sa( ' riHcin o on e particle of interest. The book reads like a romance, and, while drawing the student by an irresistible fascination to his task, impresses the great outlines indelibly upon the memory. Of tn. UWVfiftS ex 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. R^-tfW, nAT it IftCTI OCT 7 ftl 9Ju!'62JR KEC'D LD JUN 2 5 1962 - • LD 21-100m-6,'56 TT . Gen . eral Library ( B931 1 slO ) 476 B^kile^ ° fma «M YB 23098 215268