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 THE ARGUMENT 
 FOR A FINITIST THEOLOGY 
 
 BY 
 
 RAY HARBAUGH DOTTERER 
 
 A DISSERTATION 
 
 !: JBMITTED TO THE BOARD OF UNIVERSITY StU J'S OF THE 
 
 Johns Hopkins University in Conformity with the 
 Requirements for the Degree of Doctor 
 of Philosophy 
 
 PRESS OF 
 
 THE NEW ERA PRINTING COMPANY 
 
 LANCASTER, PA. 
 
EXCHANGE 
 
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Digitized by the Internet Archive 
 
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THE ARGUMENT 
 FOR A FINITIST THEOLOGY 
 
 BY 
 
 RAY HARBAUGH DOTTERER 
 
 A DISSERTATION 
 
 Submitted to the Board of University Studies of the 
 
 Johns Hopkins University in Conformity with the 
 
 Requirements for the Degree of Doctor 
 
 OF Philosophy 
 
 PRESS OF 
 
 THE NEW ERA PRINTING COMPANY 
 
 LANCASTER, PA. 
 
 I917 
 

 
PKEFACE. 
 
 It was my first intention to take Vaihinger's PhilosopJiie 
 des ALS OB as the subject of my doctoral dissertation; and 
 in the spring of 1916 in partial fulfilment of the requirements 
 for the Master's degree I did submit an essay on The Philos- 
 ophy of the As If in Its Application to Theology, I became 
 convinced, however, as the investigation proceeded, that an ex- 
 amination of the doctrine of a ^^ finite God " ought to precede 
 any attempt to appraise the value of the method of conscious 
 illusion. 
 
 I gladly avail myself of the opportunity afforded by a preface 
 to acknowledge my indebtedness to Professor A. O. Lovejoy 
 for his encouragement and for his patient as well as searching 
 and helpful criticism. As I owe much more to his lectures 
 and to his oral and written suggestions than to his published 
 writings, this general statement may take the place of par- 
 ticular acknowledgments and references in detail, which in the 
 nature of the case could not often be given. 
 
 R. H. .D. 
 
TABLE OF CONTENTS. 
 
 CbAPter Pase 
 
 I. Introductory Considerations 1-10 
 
 II. The Monistic Absolute as the Philosophic Equiv- 
 alent of God 11-21 
 
 III. The Doctrine of a Finite God 22-31 
 
 IV. Theological Finitism as the Outcome of a Rational 
 
 Theodicy 32-39 
 
 V. Logical Finitism and the Idea of God 40-49 
 
 VI. Theology and the " New Infinite " 50-70 
 
 VTI. Concluding Reflections on Finitist Theology . . . 71-79 
 
 Bibliography 80-82 
 
I. 
 
 Introductory Considerations. 
 
 1. The Method of Theological Inquiry, — Theology may 
 adopt any one of three methods or it may combine two or all 
 of them with varying emphasis upon each. It may appeal to 
 the immediate experience of the mystic, or it may simply 
 affirm and arrange in systematic form the doctrines authorita- 
 tively taught by the Church and the Bible, or it may depend 
 upon the "reason" and "conscience" of the individual in- 
 quirer. 
 
 The first method would of course be the best if the ex- 
 perience in question were not so rare. Assuming that the ex- 
 perience of the mystic constitutes a genuine insight into the 
 fundamental nature of reality, he nevertheless stands in the 
 same relation to his fellowmen as a man with normal vision 
 to a race of men blind from their birth. It would be vain for 
 the seeing man to discourse of the beautiful colors to be seen 
 on every side. Indeed, it would be impossible for him to ex- 
 press his experience in words, since language is a social 
 product, and the social mind of the hypothetical race would 
 know nothing of color. Thus the mystic's direct vision of God 
 can not be described in terms which can be understood by 
 ordinary men, and, even from his own point of view or from 
 that of a fellow mystic, his experience must ever remain in a 
 measure ineffable. Moreover, the difficulty of the mystical 
 method is aggravated by the fact that the non-mystic may not 
 be willing to grant the objectivity of the mystic's experience. 
 And the rarity of his experience may be made a reason for 
 regarding it as illusory. Indeed, it may be very plausibly 
 maintained that the alleged "revelations" of the traditional 
 mystic are evidences of a pathological condition produced by 
 
 1 
 
2 The Argument for a Finitist Theology. 
 
 his long-continued vigils and fastings. This hypothesis is 
 suggested, at least, by phenomena such as those which Wil- 
 liam James has described under the name of the " anaesthetic 
 revelation."^ Accordingly, the non-mystic may be justified 
 in believing that his lack of the sense of immediate fellowship 
 with absolute reality is not an indication of spiritual poverty, 
 but rather an evidence of sanity. 
 
 The second method — ^that of external authority — received 
 a mortal wound in the time of the Keformation, when it was 
 discovered that the two sources of authoritative teaching, the 
 Church and the Bible, did not always agree. To be sure, the 
 Protestant as well as the Roman Catholic still retained the 
 method of authority. But the mere knowledge that the 
 schism had occurred operated to impair the confidence of the 
 intelligent layman in authority of any kind ; and for the theo- 
 logically trained man the Protestant appeal to the Bible as 
 the only rule of faith and practice contained the seed of its 
 own destruction. For the careful study of the sacred writings 
 which was logically required by the formal principle of Prot- 
 estantism soon showed that these writings, instead of contain- 
 ing one uniform and consistent revelation, contain several dif- 
 ferent and even conflicting systems of doctrine, and bear clear 
 evidence of having been produced in much the same way as 
 the other sacred books of antiquity. Thus, although this was 
 certainly not the intention of the original Reformers, the log- 
 ical and historical result of the Reformation has been to refer 
 all questions of doctrine to the "private judgment" of the 
 individual Christian. 
 
 The third method, that of reliance upon reason and con- 
 science, is, accordingly, the one that is dominant at the present 
 time at least among enlightened men and women. Having 
 throvm off the authority of the Church, and being distrustful 
 of the genuineness of the mystic's experience, they take as 
 
 1 The Will to Believe, pp. 294 ff. (Note : For full titles, etc., see the 
 appended bibliography.) 
 
Introductory Considerations. 3 
 
 their only criterion of truth the reasonableness and ethical at- 
 tractiveness of the doctrines in question. 
 
 It is important to note, however, that these three theological 
 methods — that of the mystic, that of the authoritarian, and 
 that of the self-reliant reasoner — are almost never found pure. 
 The traditional mystic has usually been, or at least supposed 
 himself to be, a loyal son of the Church ; and his revelations 
 have usually been in superficial agreement with its teachings. 
 St. Thomas Aquinas employs the method of authority; but he 
 also reasons, so long, at least, as reasoning serves his purpose. 
 The " modern " man is no more consistent. Theologians who 
 in theory have given up the appeal to any external authority 
 nevertheless slip back now and then into the argument from 
 Scripture and tradition. And among religious people who are 
 not theologians, one result of the modem revolt against the 
 authority of the Church and the Book has been a curious sen- 
 timentalism in religious thinking, a sort of mitigated mysti- 
 cism, which exalts "intuition'' and "immediate feeling" as 
 over against "reason." 
 
 It must be admitted, I think, that there is a sense in which 
 the Scriptures possess authority, and ought to possess au- 
 thority, even for the completely emancipated thinker. Their 
 authority may be described as suggestive rather than coercive, 
 as accidental rather than constitutive. Many biblical doc- 
 trines are found to be true, but their truth neither consists in 
 nor is established by their quality of being biblical. In other 
 words, the authority of the Bible is not like that of a constitu- 
 tion or of a legal code, but rather like that of a textbook in 
 chemistry or some other laboratory science, the statements 
 contained in which are to be accepted or rejected by the stu- 
 dent according as they are, or are not, experimentally verified. 
 
 There is also a relative justification for the claims of " in- 
 tuition," " instinct," or " immediate feeling." This justifica- 
 tion consists in the obvious fact that " reason " in the sense of 
 mere intellection is barren. Before there can be any reason- 
 ing in this narrow sense of the term, there must be (a) sense- 
 
4 The Argument for a Finitist Theology. 
 
 perception, and (Z>) perception of "goods" or of relative 
 v^alues. Viewed in this way, reason does not bring forth truth ; 
 it has the humbler office of determining which of the offspring 
 of " intuition " may be worthy of preservation and ought to be 
 acknowledged as true. In other words, we may be said to 
 reason when we inquire which of our immediate perceptions 
 of fact or of value are implied by or are incompatible with other 
 immediate perceptions. Thus there is a sense in which both 
 sense-perception and the perception of values are more fun- 
 damental than reasoning. But immediate perception alone 
 is not a sufficient criterion of truth. For one of our percep- 
 tions of fact is that immediate perceptions, whether we limit 
 our view to the experience of one mind or consider the ex- 
 perience of a larger or smaller group, are not all logically com- 
 patible; and that they ought to be logically compatible is one 
 of our perceptions of value. If this perception of value is to 
 be accepted as genuine, some immediate perceptions and some 
 inferences from such perceptions must be rejected as illusory 
 or mistaken. But when immediate perceptions are found to 
 be mutually repugnant, that is to say, when it is impossible for 
 all of them to be genuine in the same logical universe, the 
 only arbiter that can decide between them is the reason. In- 
 deed this deciding between incompatible verdicts of " intui- 
 tion '' is what we mean by reason, when we say that the method 
 of theology must be the method of reason, rather than of mys- 
 tical experience or of dependence upon authority.^ 
 
 2. The Religious Value of the Idea of God. — ^We value the 
 idea of God, and seek to convince ourselves that the idea is 
 " real,'' because we feel the need of God. Our interest, how- 
 ever, is practical rather than theoretical. As far as the man 
 of science is concerned there may be a God ; but the scientist 
 long ago discovered that he, as scientist, has " no need of that 
 hypothesis." If, for example, a geologist should tell us that 
 the strata of rocks occur in a given order because God laid 
 them down in that way, or if a botanist should say that a cer- 
 
 2 Cf. Russell, Scientific Method in Philosophy, pp. 21 f . 
 
Introductory Considerations. 5 
 
 tain flower has five petals because God made it thus, even the 
 least enlightened theist would admit that the assertion is from 
 the standpoint of science irrelevant. And, in general, to " ex- 
 plain " the occurrence of any particular phenomenon or group 
 of phenomena by reference to divine agency is an evasion of 
 the problem at issue. 
 
 The value of the idea of God is, then, to be sought in the 
 domain of practice rather than of theory. It is moral and 
 religious rather than scientific. Traditional theology has 
 given the Divine Being the attributes of omnipotence, om- 
 niscience, omnipresence, and moral perfection. Modern the- 
 ology places moral perfection first, and rightly insists that the 
 other attributes have religious value only when moral per- 
 fection is presupposed. First of all, God is good ; and his in- 
 finite wisdom and might are subservient to his infinite love.^ 
 
 Beginning, then, with the thought of the infinite goodness 
 of God, one use of the notion of Deity at once suggests itself. 
 God, as the ahaolutely good being, is man's moral goal or pat- 
 tern. ^'Be ye perfect as your Father in heaven is perfect," 
 becomes the maxim of the truly devout worshipper. God is 
 the supremely perfect hero, the supreme object of imitation. 
 
 N"ext, combining the notion of perfect goodness with that of 
 omniscience, we derive the idea of God as the righteous and 
 completely informed Judge of human conduct. The more 
 naive worshipper thinks of a day of judgment at the end of 
 the world; the more sophisticated, of a judgment continually 
 going on. Whichever way the thought is taken, the believer 
 in an all-wise and perfectly good Being has always before him 
 the idea of an impartial and all-seeing Spectator who " search- 
 eth the reins and the hearts." What is concealed from one's 
 fellowmen is fully knowa to him. Wherein one has been mis- 
 judged by his fellows, he is judged rightly by God. At the 
 tribunal of the Omniscient One, absolute justice is dispensed. 
 
 Furthermore God is all-powerful. He is the Sovereign of 
 the Universe. He has created, and now upholds and governs 
 
 8 Cf . Clarke, Tlie Christian Doctrine of God, pp. 70 ff. 
 
6 The Argument for a Finitist Theology. 
 
 all. Because he is omnipotent his universal purpose will 
 eventually be completely fulfilled. The life of the believer 
 himself and that of the group to which he belongs can not 
 become a failure. Defeats are merely reverses, suffering is 
 chastisement. Faith in an omnipotent God is the ground of 
 an assured confidence in the ultimate triumph of the right and 
 the eternal survival of the good. 
 
 Lastly, the attribute of omnipresence makes possible the 
 thought of a divine Companion and Friend. Though foes 
 may scorn and friends forsake, there is a heavenly Father to 
 whom one may ^ee for sympathy. Though the believer is 
 alone in the world, he is not alone, for God is with him. 
 
 Such, crudely and inadequately expressed, is the meaning 
 of God in the experience of his worshippers. In a word, the 
 heart of the true believer is filled with peace — with the " peace 
 of God which passeth all understanding." 
 
 But the peace of God is not a peace of quiescence. The truly 
 religious man is not simply the contented man. His content- 
 ment is combined with a divine discontent with himself and 
 his world. A " spark " has disturbed his " clod." He, indeed, 
 takes " no thought for the morrow," but he labors for the mor- 
 row and for many days thereafter. He seeks ^' first the king- 
 dom of God and his righteousness," and yet is a man of affairs. 
 He believes that the sin and the suffering and the sorrow of 
 life have their place in the divine economy, yet he is a reformer 
 and seeks to make the world better and happier. 
 
 3. Some Antinomies in the Popular Notion of God. — Such 
 a paradoxical emotional attitude can hardly be supposed to 
 be grounded in a logically consistent doctrine of God. Indeed 
 the paradoxical character of the typical religious experience 
 would suggest a self-contradictory ground. And no very 
 profound study is required to show that the popular notion 
 of God is shot through with contradictions. Some of these 
 are evident to the popular mind itself; others do not appear 
 until the notion is examined with more than ordinary care. 
 
Introductory Considerations, 7 
 
 A few of the more obvious of these difficulties are the fol- 
 lowing. 
 
 {a) Goodness versus Power in Relation to the Existence of 
 Evil, — According to traditional theology the world is partly 
 evil, and is nevertheless the work of Infinite Power and Per- 
 fect Goodness. The antinomy is obvious: How can Omnip- 
 otent Goodness be supposed to have produced or to be the 
 ground of an imperfect world? Attempts at reconciliation 
 merely repeat the difficulty in a new form. Thus we hear 
 men say that if God had not permitted some particular evil a 
 greater evil would have occurred; that the pains and suf- 
 ferings of life are means of chastisement and moral purifica- 
 tion; that sin makes possible forms of goodness which out- 
 weigh both the sin itself and the evil consequences resulting 
 from it. But it is obvious that this mode of explanation itself 
 presupposes some limitation of divine power. It assumes that 
 evil is a necessary condition of the perfection of the world, 
 and that even Omnipotence is bound by this condition. The 
 existence of evil is a proof of God's inability to remove it 
 from his world, or, what amounts to the same thing, of his 
 inability to remove or prevent it without defeating his uni- 
 versal purpose. Again, if we adopt the evolutionary point of 
 view, and admit the idea of a temporal process into our rea- 
 sonings about good and evil, we may say that, while God's 
 world is not yet perfect, its perfection will come at the end of 
 the evolutionary process, ^ut the idea of evolution, the very 
 notion of a process, is irreconcilable with omnipotence. For 
 the idea of a process implies hindrance or retardation, and 
 therefore the finitude of the energizing agent. 
 
 (fe) Righteousness versus Predestination, — This is a special 
 and aggravated case of the preceding difficulty. If God is 
 omnipotent, he is the absolute Sovereign of his world, and all 
 events are in accordance with his will; but if all events, in- 
 cluding human actions, bad as well as good, are willed by 
 God, then God is the real author of human sin. 
 
 N 
 
8 The Argument for a Finitist Theology. 
 
 (c) The Hearing of Prayer versus Omniscience. — If God 
 be thought of after the analogy of an ancient oriental monarch, 
 prayer may be regarded as necessary in order to propitiate the 
 Despot when he is angry, or to overcome his carelessness, or 
 his indifference to the well-being of his subjects. But, surely, 
 in the case of a Sovereign who is perfectly good, prayer is not 
 needed for this purpose. Again if God's power be limited, it 
 may be maintained with considerable plausibility that prayer 
 is a means of supplementing the energy which is insufficient 
 for the accomplishment of some good purpose. But, according 
 to the traditional doctrine, there is no defect of power, and 
 prayer can not be justified in this way. Once more, if God's 
 Icnowledge were limited, prayer, in the sense of petition for 
 some definite boon, might be regarded as a means of inform- 
 ing God concerning human needs. The analogy of the eastern 
 monarch here recurs, and doubtless has figured largely in the 
 common theory of prayer. But if God is omniscient, we can- 
 not tell him anything, and the antinomy remains unsolved. 
 
 (d) Personality versus Immutability. — According to tra- 
 ditional religious thought, God is a person, sl Friend or Father 
 with whom men may enjoy fellowship. On the other hand, 
 he is also said to be "eternal," not merely in the sense that 
 his existence is without beginning or end, but in the sense 
 that he is supertemporal and immutable. But the attributes 
 of personality and immutability are plainly contradictory. 
 For a person is the subject of experience, and experience im- 
 plies time. At any rate, human persons are in time; succes- 
 sion is of the very essence of their life ; and therefore a divine 
 Person who is assumed in any meaningful sense to know them 
 and to fellowship with them must also be in time. 
 
 4. A Prospectus of the Ensuing Discussion. — ^We have seen 
 that the attempt to think of God as omnipotent, omniscient, 
 and immutable, and at the same time as a personal Being who 
 is perfectly good, and who enters into communion with men 
 and may be influenced by their petitions, is logically impos- 
 sible. Accordingly, the next three sections will be devoted to 
 
Introductory Considerations, S 
 
 a critical exposition of two rival attempts to rationalize or to 
 find a substitute for the traditional (Christian) conception of 
 Deity. These contrasted theories are the theory of monistic 
 idealism, which in its specifically theological aspect is a theory 
 of the divine immanence, and that of pluralism, with its doc- 
 trine of a " finite " God. As my examination of these rival 
 theories leads me to the acceptance of the latter, I have called 
 the whole discussion " an argument for a finitist theology." 
 
 God has been said to be infinite in two different senses: (1) 
 He has been said to be the Whole of reality, or at least to be 
 the Ground and Source of all that is. (2) He has been said 
 to be infinite in the literal numerical sense of the word; for 
 example, to know an infinite multiplicity of knowledge-ele- 
 ments, or to be " eternal," either in the sense of living through 
 an infinite sequence of moments, or in the sense of being super- 
 temporal and yet in some manner containing infinite time. 
 The God of monistic idealism, for example the "Absolute" 
 as described by Jpgiah B jQXce» is held to be infinite in both of 
 these senses. The Absolute is the all-inclusive Reality; and, 
 by virtue of Royce's fundamental epistemological presupposi- 
 tions, his one eternal or timeless Purpose includes or implies 
 an infinite multiplicity of elements. Over against this monis- 
 tic theory stand the theory of John Stuart Mill and William 
 James, on the one hand, and that of C harles Reno uvier. on the 
 other. These theories, which I shall call respectively ^^gihical 
 finitism" and "logical finitism," are mutually compatible, 
 but, as we shall see, do not necessarily imply one another. 
 The doctrine of a " finite " God as it is expounded by Mill 
 and James consists essentially in the denial of God's infinitude 
 in the former of our two senses. According to this view, God 
 is not omnipotent. It is a view which is founded chiefly upon 
 the difficulties of theodicy, upon the impossibility of " justify- 
 ing the ways of God to man," if God is assumed to be infinite 
 in the sense of possessing all knowledge and all power. Ac- 
 cording to Renouvier and his school, the finitude of the world 
 and of God logically results from the self-contradiction which 
 lurks in the conception of a " realized infinite." 
 
10 The Argument for a Finitist Theology, 
 
 The discussion of the theories of Eoyce and Renouvier will 
 lead us to an examination of the so-called New Infinite of re- 
 cent mathematics, as it has been defined by Richard Dede- 
 kind and Georg Cantor; for by his own account the idealism 
 of Royce is logically dependent upon the validity of this con- 
 ception, and the entire Renouvierist philosophy must go by 
 the board if, as is maintained, the formulation of this new 
 definition of infinity frees the notion of a realized infinite 
 from the difficulties which Renouvier found in it. In view, 
 therefore, of the strategic importance of this subsidiary issue, 
 I shall devote Section VI to an examination of these con- 
 trasted ways of thinking about the infinite. My conclusion 
 will be that the formulation of the " new " infinite has not re- 
 moved the logical objections to monistic idealism, nor at all 
 impaired the cogency of the reasonings of Renouvier and his 
 disciples. 
 
 The last section will contain a brief summary of all that 
 has gone before, together with a further examination of the 
 conception of a " finite " God. 
 
II. 
 
 The Monistic Absolute as the Philosophic Equivalent 
 
 OF God. 
 
 In our attempt to find a conception of God that is both 
 rationally satisfactory and religiously serviceable we turn to 
 the philosophers. Two types of theory may be distinguished : 
 the monistic and the pluralistic. According to the monistic 
 theories, God is the whole of existence; pluralistic theories, 
 on the other hand, make God the part, but the controlling part 
 of existence. 
 
 1. Monistic Idealism as a Fulfilment of Traditional The- 
 ology. — In this chapter we shall consider the monistic revision 
 of the traditional conception of God. The theory of Josiah 
 Koyce may be taken as a typical expression of this class of 
 theories.* 
 
 Koyce's conception of God is regarded by its author, "not 
 as destroying, but as fulfilling, the large collection of slowly 
 evolving notions that have appeared in the course of history in 
 connection with the name of God."^ He insists that "what 
 the faith of our fathers has genuinely meant by God is, despite 
 all the blindness and all the unessential accidents of religious 
 tradition, identical with the inevitable outcome of a reflective 
 philosophy."^ This conception "undertakes to be distinctly 
 theistic, and not pantheistic. It is not the conception of an 
 Unconscious Keality, into which finite beings are absorbed; 
 nor of a Universal Substance, in whose law our ethical inde- 
 pendence is lost; nor of an Ineffable Mystery, which we can 
 only silently adore. On the contrary, every ethical predicate 
 
 *For Royce's account of his philosophic ancestry, see The Beligious 
 Aspect of Philosophy, pp. ix ff. 
 
 5 Royce, et al., The Conception of God, p. 48. 
 
 ^Ihid., p. 50; see also The Problem of Christianity, Preface. 
 
 11 
 
12 The Argument for a Finitist Theology. 
 
 that the highest religious faith of the past has attributed to 
 God is capable of exact interpretation in terms of our present 
 view."^ 
 
 Professor Eoyce's contribution to the theistic discussion con- 
 sists, then, in the identification of God with the Absolute of 
 idealistic philosophy; and in attempting so to define the Ab- 
 solute as, on the one hand, to avoid the self-contradictions 
 which are to be found in the notion of Deity as ordinarily con- 
 ceived, and, on the other hand, to enrich the notion of the Ab- 
 solute so that it shall be a fit object for the religious emotions 
 or attitudes of awe and reverence, of faith, loyalty, and love. 
 It is important to remember, however, that many idealistic 
 philosophers have not been willing to regard the Absolute as 
 personal, or in any significant sense as a Self. Thus Mr. F. 
 H. Bradley does not apply the name God to the Absolute,^ 
 and, if Dr. McTaggart is right, Hegel himself, who is com- 
 monly regarded as the father of this general way of thinking, 
 ought not to have done so.^ His use of " God " and of other 
 religious terms, says McTaggart, was merely an accommoda- 
 tion to the "current mythology'' of the time. According to 
 Professor Royce, however, the Absolute of monistic idealism 
 is what the Church has really meant all along by God; but 
 this meaning has been only vaguely apprehended, and there- 
 fore only imperfectly expressed. 
 
 As defined by Royce, God, or the Absolute, includes in his 
 own consciousness and will the content of all finite minds. 
 The individual self is an identical part of the Divine Self.^^ 
 
 " Let us sum up, in a few words," says Royce, " our whole 
 argument. There is, for us as we are, experience. Our 
 thought undertakes the interpretation of this experience. 
 Every intelligent interpretation of an experience involves, 
 however, the appeal from this experienced fragment to some 
 
 7 Ihid., p. 49. 
 
 8 Appearance and Beality, pp. 446 ff. 
 
 Studies in Hegelian Cojsmology, pp. 59 ff., 213. 
 
 10 The Conception of God, p. xiii ; Eihhert Journal, I, 44. 
 
The Monistic Absolute, 13 
 
 more organized whole of experience in whose unity this frag- 
 ment is conceived as finding its organic place."-^ -^ " There 
 must be an experience to which is present the . . . actual 
 limitation and narrowness of all finite experience."^ ^ 
 
 Furthermore, since every reality exists "just in so far as 
 there is experience of its existence,"-^ ^ since, in other words, 
 everything that is, is the content of mind, it follows that the 
 " things " which we ordinarily think of as non-mental are in- 
 cluded in the content of the Absolute Self. 
 
 " The reality that we seek to know," says Koyce, " has al- 
 ways to be defined as that which either is or would be present 
 to a sort of experience which we ideally define as an organized 
 — that is, a united and transparently reasonable experience. 
 We have, in point of fact, no conception of reality capable of 
 definition except this one."^* "To assert that there is any 
 absolutely real fact indicated by our experience, is to regard 
 this reality as presented to an absolutely organized experience, 
 in which every fragment finds its place."^^ 
 
 Professor Royce's conception of the Absolute is attained, 
 then, by combining the traditional attribute of omniscience 
 with the idealistic presupposition that to be is to be known as 
 being. It may be remarked in passing that if this presuppo- 
 sition is denied, the whole edifice of monistic idealism falls to 
 the ground. We are not now concerned, however, with the 
 question of the existence of the Absolute, but only with its 
 definition. If the presupposition is granted, it is evident that, 
 as Royce maintains, "In order to have the attribute of Om- 
 niscience, a being would necessarily be conceived as essen- 
 tially world-possessing."^^ 
 
 The error and suffering and sin of our finite lives are all 
 due to the fragment ariness of our experiences. When taken 
 
 11 The Conception of God, p. 42. 
 
 12 Ihid., p. 41. Cf. The Religious Aspect of Philosophy, p. 441. 
 
 13 The Conception of God, p. 43. 
 ^*Il)id., p. 30. 
 
 isl&tJ., p. 42. 
 i6 76t<2., p. 13. 
 
14 The Argumeni for a Finitist Theology, 
 
 up into the infinite completeness of the Universal Self, all the 
 imperfections of existence cancel out, or better, all are re- 
 quired to constitute the perfection of the Whole. We, as frag- 
 ments of the Absolute, may be victims of misfortune, unhappy, 
 discontented, sinful. But the Absolute is perfectly good. Our 
 imperfection, and our thought of the world as imperfect, are 
 the consequence of the limitation of our knowledge. We know 
 in part; the Absolute knows the Whole, and pronounces it 
 complete, and perfectly good.^*^ 
 
 " Misfortune comes to us, and we ask : What means this hor- 
 ror of my fragmentary experience? — why did this happen to 
 me ? The question involves the idea of an experience that, if 
 present, would answer the question. 'Now such an experience, 
 if it were present to us, would be an experience of a certain 
 passing through pain to peace, ... of a certain far more ex- 
 ceeding weight of glory that would give even this fragmentary 
 horror its place in an experience of triumph and of self-pos- 
 session. In brief, every time we are weak, downcast, horror- 
 stricken, alone with our sin, the victims of evil fortune or of 
 our own baseness, we stand, as we all know, not only in pres- 
 ence of agonizing fragmentary experiences, but in presence of 
 besetting problems, which in fact constitute the very heart of 
 our calamity. . . . Well, then, if the divorce of idea and ex- 
 perience characterizes every form of human consciousness of 
 finitude, of weakness, of evil, of sin, of despair, you see that 
 Omniscience, involving, by definition, the complete and final 
 fulfilment of idea in experience, the unity of thought and act, 
 the illumination of feeling by comprehension, would be an 
 attribute implying, for the being who possessed it, much more 
 than a universally clear but absolutely passionless insight. An 
 Omniscient Being could answer your bitter Why? when you 
 mourn, with an experience that would not simply ignore your 
 passion. For your passion, too, is a fact. It is experienced. 
 The experience of the Omniscient Being would include it. 
 
 17 The Eeligious Aspect of Philosophy, pp. 444 and 449; Sources of Be- 
 ligious Insight, p. 224. 
 
The Monistic Absolute. 15 
 
 Only his insight, unlike yours, would comprehend it, and so 
 would answer whatever is rational about your present ques- 
 tion. ... In order to have the attribute of omniscience, a 
 being would necessarily ... be conceived as omnipotent, and 
 also as in possession of just such experience as ideally ought 
 to be; in other words, as good and perfect."^ ^ 
 
 2. Some Difficulties of Monistic Idealism. — As has already 
 been remarked. Professor Royce's proof that there is such an 
 Absolute Being as he has defined, rests upon the presupposition 
 that all being is being known, that all existence is mental. 
 Unless this assumption be granted, the argument goes to 
 pieces. Moreover, in Chapter V we shall meet a consideration, 
 which will make it impossible for us to conceive that the Ab- 
 solute Self is real. This is the self-contradiction involved in 
 the notion of a " realized infinite.'' For the present, however, 
 I shall limit myself to pointing out certain other difficulties, 
 which, it seems to me, are inseparable from the conception of 
 the Absolute as it is defined by Royce. 
 
 (a) The first of these may be called the religious difficulty. 
 We may approach it by considering a conception near akin 
 to that of the monistic Absolute, namely, the conception of 
 God as immanent in his world. If God is thought of as 
 transcendent, and the supernatural and the natural regarded 
 as mutually exclusive categories, then the friend of religion 
 must view the progress of science with alarm. A division of 
 the world between science and religion, between Nature and 
 God, might be reasonably satisfactory, if one could be sure 
 that the boundary would remain permanently fixed. But, if 
 we define the natural as that which is explicable in terms of 
 scientific law, then, as science extends its territory, and pro- 
 claims its belief in the possibility of a universal conquest, the 
 outlook for religion becomes dark indeed. If the supernatural 
 is defined as that which is not natural, the scientific view of 
 the world leaves no place for God. 
 
 In this perilous situation "liberal" theologians have em- 
 
 18 The Conception of God, pp. 11 ff. 
 
16 The Argument for a Finitist Theology. 
 
 phasized tlie immanence of God, and have said that all events 
 are supernatural, since all are produced by, or are particular 
 expressions of, the immanent God. The difficulty of this pro- 
 cedure is, however, that, in thus preserving the right to use 
 the word God, we are in danger of so impoverishing the idea 
 of God that it becomes of little value as a religious conception. 
 In order to meet this peril it is then necessary to insist that 
 God is transcendent as well as immanent. Thus to avoid the 
 danger of pantheism. Dr. William Newton Clarke, for ex- 
 ample, maintains that " Transcendence is first. ... It is the 
 transcendence that gives the immanence its meaning. . . . 
 The Christian thought of God is not so much that the im- 
 manent God is transcendent, as it is that the transcendent God 
 is immanent.''^ ^ The God who is immanent is the Personal 
 God. 
 
 The difficulty, however, is to see how a completely immanent 
 God can be personal. Mei:ely to say that God is immanent, 
 and that therefore all events are acts of God, and that for this 
 reason the theist need not be troubled by the claim of science 
 to include all events in its realm ; and also to swy that God is 
 transcendent and personal as well as immanent, does not solve 
 the difficulty ; any more than to say that a certain geometrical 
 figure is round and also has four right angles will remove the 
 self-contradiction from the notion of a square circle. In the 
 same way, for Royce merely to say that the Absolute is Per- 
 sonal, and that his theory is a theism and not a pantheism does 
 not suffice. Unless we assume that completeness, as opposed 
 to fragmentariness, is per se worthy of reverence, an assump- 
 tion which is by no means self-evident, there seems to be no 
 sufficient reason for worshipping the Absolute f^ and it seems 
 impossible for us to enter into fellowship with such an entity, 
 unless we consciously or unconsciously think of it as if it 
 were a Person distinct from, and standing over against us and 
 all others. 
 
 19 The Christicm Doctrine of God, p. 322. 
 
 20 See Professor Mezes 'a criticism of Koyce ^s Ultimate Being, The Con- 
 ception of God, pp. 54 ff. 
 
The Monistic Ahsolute. 17 
 
 {!)) Furthermore, there are certain 'psychological difficul- 
 ties in the conception of the Absolute. These result from the 
 circumstance that some of our experiences, which are by def- 
 inition experiences of the Absolute also, are conditioned by 
 our very finiteness, and therefore can not be experienced by 
 an Absolute being. Such experiences are hope and fear, for 
 example. A being who knows perfectly what the morrow will 
 bring forth can not hope for anything on the morrow ; neither 
 can he fear. If I am sure of obtaining a certain boon, I do 
 not hope to obtain it ; still less can I be said to fear lest I shall 
 not obtain it. Both of these emotions presuppose some degree 
 of uncertainty with reference to the future, and such uncer- 
 tainty is incompatible with omniscience. In the same way it 
 is impossible that an omniscient being should ever experience 
 curiosity or the joy of discovery. The Absolute, too, must be 
 without the experience of sin and repentance. Yet, as Abso- 
 lute, he must contain all these experiences. 
 
 If all we mean when we say that a being is omniscient is 
 that he Jcnows about all the experiences of all other beings (in 
 addition to all the other knowledge that he is assumed to pos- 
 sess), then these difficulties do not arise. The Absolute may 
 well enough be assumed to know all about my states of mind ; 
 but he cannot without contradiction be assumed to include in 
 the totality of his experience the identical hopes and fears and 
 feelings of repentance that I feel. 
 
 The same remark must be made of our experience of tem- 
 poral succession. God, or the Absolute, is said to know all in 
 an Eternal Now,^^ But if that is the nature of his knowledge, 
 it is impossible that He should know things in succession. It 
 must be admitted, however, that both kinds of knowledge are 
 attributed to him. It is common to make a distinction be- 
 tween a holy place in which a real experience of succession is 
 found, and a Holy of Holies in which all " bondage to succes- 
 sion '' is overcome. Thus the late Professor Bowne, although 
 
 21 The Eeligious Aspect of Philosophy, p. 441 ; The Conception of God, 
 pp. 59 f . ; The World and the Individual, II, 138 ff. 
 
18 The Argument for a Finitist Theology. 
 
 he criticizes the absolute idealism of the Hegelian school on 
 the ground that "such a system excludes all movement and 
 progress, and the appearance of movement can only be reck- 
 oned a delusion/' insists nevertheless that " from the theistic 
 standpoint the infinite must be viewed as possessing an eternal 
 mind so far as itself is concerned.'' On the other hand, " the 
 infinite must be in time, so far as the world process is con- 
 cerned."^^ 
 
 Dr. William E'ewton Clarke writes in a similar strain: 
 " Succession is essential to the significance of events in time, 
 and if God had no knowledge of it he could not understand 
 events or the history that is composed of them, or the life of 
 his children. He has both kinds of knowledge. He eternally 
 knows all things at once, and is also aware of them as they 
 become realized in time and space; and in the perfect mind 
 there is no inconsistency between these two modes."^^ 
 
 But does this last clause mean anything more than that con- 
 tradictions may be tolerated in the case of affirmations con- 
 cerning the perfect mind, which would be intolerable if the 
 mind were not perfect? And why this reluctance to subject 
 the perfect mind to the " bondage of succession " ? We may 
 say, if we will, that God would be limited by succession; but 
 is he not limited in just the same sense by the law of contra- 
 diction and the law of love ? The attempt to affirm the reality 
 of both kinds of knowledge in the Divine mind suggests, once 
 more, the attempt to define a plane figure that is both square 
 and circular. 
 
 This view can be logically defended in no other way than 
 by a denial of the reality of the experience of time. Says Pro- 
 fessor Mezes, interpreting the view of Koyce, " Speaking tech- 
 nically, time is no reality ; things seem past and future, and in 
 a sense, non-existent to us, but in fact they are just as gen- 
 uinely real as the present is. Is Julius Csesar dead and turned 
 to clay? 1^0 doubt he is. But in reality he is also alive, he 
 
 22 Metaphysics, pp. 486, 240 f . 
 
 23 The Christian Doctrine of God, p. 346. Cf . pp. 295 ff. 
 
The Monistic Absolute, 19 
 
 is conquering Spain, Gaul, Greece, Egypt. He is leading the 
 Roman legions into Britain, and dominating the envious Sen- 
 ate, just as truly as he is dead and turned to clay — just as truly 
 as you now hear the words I am speaking. Every reality is 
 eternally real ; pastness and futurity are merely illusions."^^ 
 
 But if the experience of succession is illusory, what then is 
 real ? The fact that of two experiences one comes after the 
 other is certainly as real as anything can be. If the two ex- 
 periences are cognitive, it may indeed happen that the events 
 to which they refer really occurred in a different order from 
 that in which I have experienced them; or these events may 
 really have been simultaneous; but the experiencings them- 
 selves are in the order in which they come, and it is meaning- 
 less to say that they are really in a different order, or that 
 they are simultaneous. If the Absolute were merely supposed 
 to know about them, he might have knowledge of them both at 
 the same moment, although I experience them one after the 
 other ; but if my experiencings are numerically the same as cer- 
 tain experiencings of His, then the order in which they occur 
 for me must also be the order in which they occur for Him. 
 
 (c) Last and most important of all are the ethical diffi- 
 culties of the conception of the Absolute. If all thoughts are 
 thoughts of God, and all events are acts of God, then our evil 
 desires and purposes are purposes and desires of God, and all 
 our sinful deeds are deeds of God. The antinomy between 
 predestination and the goodness of God, which has troubled 
 traditional and popular theology, thus appears in an aggra- 
 vated form in the theology of immanence. The logical conse- 
 quence is a denial of the genuineness of the distinction between 
 good and evil, right and wrong. If the Absolute must be con- 
 ceived to be " in possession of just such experience as ideally 
 ought to be, "2^ then, from the standpoint of the Absolute, there 
 is no reason for wishing that anything should be other than it 
 
 24 Eoyce, et al., The Conception of God, p. 60. 
 26 The Conception of God, p. 13. 
 
 26 The Beligious Aspect of Philosophy, pp. 454 f . ; Sowrces of Beligious 
 Insight, pp. 237, 224. 
 
20 The Argument for a Finitist Theology. 
 
 is ; no reason for pronouncing one thing evil and another good. 
 
 The fact that the partisans of the monistic Absolute, like 
 believers in the Calvinistic doctrine of predestination, have 
 been zealous in good works, and have been strenuous advo- 
 cates of reform and good haters of iniquity of all sorts, does 
 not alter the fact that the logical consequence of their creed is 
 a life of resignation and acquiescence. If the account which 
 monistic idealism gives of the world is true, not only is it 
 logically right for me to endure my private pains and disap- 
 pointments without grumbling, and to " spiritualize " and 
 "idealize" them, seeing that the Absolute is not unhappy, 
 and the Absolute is not disappointed, and that in spite of 
 these "partial evils" "in the universe as a whole the good 
 triumphs " f^ but there is no reason why I should bestir 
 myself to lighten the sorrows of my fellow men, since their 
 sorrows too, just as they are, have their proper place in the 
 eternal felicity of the Absolute and contribute to the perfec- 
 tion of the whole. 
 
 It may perhaps be said that, since nothing that we can do can 
 disturb or impair the eternal perfection of the Absolute, we 
 may still, without lack of logical consistency, and without de- 
 fect of loyalty to the good of the Whole, attempt to brighten 
 the little comer in which we are placed. But if the present 
 proportion of light and shadow is just the correct one to 
 produce the perfection of the Whole, then, assuming the 
 Whole to remain perfect, in brightening one corner, I should 
 automatically darken some other comer; and there is no suf- 
 ficient reason for wishing to do that. If, on the other hand, 
 it should be said that the precise proportion of light and shade 
 in the universe is a matter of indifference, and that conse- 
 quently I can seek my ovni happiness and that of others with- 
 out necessarily diminishing the felicity of the Absolute or of 
 any sentient being, then we should have to conclude that the 
 doctrine of the Absolute is without any moral significance 
 whatever; for, if my pains and sorrows are not necessary to 
 the felicity of the Absolute, the doctrine of the Absolute pro- 
 vides no reason why I should bear them patiently. 
 
The Monistic Absolute. 21 
 
 The monistic idealist is sure to object at this point that the 
 argument of the last few paragraphs is based upon an inade- 
 quate account of Royce's ethical theory. For Professor Royce 
 speaks not only of evils which are to be endured, but also, and 
 much more, of evils which are to be overcome; and, in his 
 theory, the typical evil is not physical pain, or mere pain of 
 any kind, but rather the bad will of a moral agent. 
 
 This objection of the monistic idealist, however, introduces 
 considerations which had better be postponed until we have 
 given an account of the ethical argument ifor theological 
 finitism. 
 
III. 
 
 The Doctrine of a Finite God. 
 
 The monistic theories make a grudging admission of the 
 individual and particular facts of life. The pluralistic 
 theories, on the other hand, emphasize these facts and take 
 their departure from them. For the pluralistic theories the 
 particular and the individual constitute the true reality. The 
 dirt and grime of actual experience must not be forgotten or 
 ignored in the thought of an Eternal Reality which is sup- 
 posed, in some mysterious or very imperfectly understood 
 manner, to be perfect, though including imperfection. Sin 
 and suffering are not illusions which are overcome in an 
 Eternal ^ow, or fragmentary experiences which together form 
 the perfect Whole of existence. On the contrary, the victory 
 of the Good is not yet achieved; the world is not completed; 
 the process of evolution is a reality. God is not all-powerful ; 
 but he is a Struggler, who is hindered and thwarted, at least 
 for the time being, by necessities which are beyond his con- 
 trol. The time process is required for the accomplishment of 
 his good purposes. 
 
 In other words, by those who hold the pluralistic view of 
 the world, the tradition that God is Absolute, Infinite, Om- 
 nipotent, Omniscient, Immutable, etc., is definitely and con- 
 sciously abandoned; and, if the belief in God is retained, he 
 is thought of as a finite being, one among many, yet supreme 
 above all. 
 
 This, in broad outline, is the doctrine of God expounded by 
 John Stuart Mill, William James, and other philosophical 
 radicals. ^^ They were not afraid of unorthodox phraseology, 
 
 27 For more recent expositions of the finitist doctrine, see H. G. Wells, 
 God the Invisible King, and E. H. Eeeman, Do We Need A New Idea of 
 God? 
 
 22 
 
The Doctrine of a Finite God, 23 
 
 they were not much influenced by the mere form and sound 
 of words. Most theological and religious writers, on the other 
 hand, and many philosophers, manifest a curious reverence for 
 words and phrases that have been hallowed by long use and a 
 corresponding reluctance to accept new forms of expression. 
 They are, accordingly, disposed to shy at such a word as finite 
 when it is employed as an adjective modifying the term God; 
 and yet many of them are not in principle so far as they seem 
 from the view suggested by the phrase formed of these two 
 words. Thus many monistic idealists have held that suffering 
 must be a genuine experience of the Absolute; and it has 
 become a commonplace of moral and religious exhortation to 
 say that we are co-workers with the Omnipotent. We may 
 question the logical consistency of Absolutist philosophers and 
 religious exhorters,. and yet rejoice that, even in opposition to 
 the logical implications of their systems, they have sought to 
 be loyal to the facts of human experience. 
 
 In the fifth chapter we shall consider the arguments of those 
 who have arrived at a finitist theology by a logical analysis of 
 the notion of the realized infinite. These thinkers have come 
 to the conclusion that it is impossible without logical incon- 
 sistency to say that anything that is, is infinite. Therefore 
 neither God nor the world can be said, if we speak strictly, to 
 be infinite. In this and the immediately following chapter, 
 we shall restrict our attention to what may be called the ethical 
 argument for the doctrine that God is finite. 
 
 This argument is essentially a theodicy, an attempt to jus- 
 tify the ways of God to men in view of the manifest evil and 
 imperfection of the world. In brief, the argument is this; 
 God can not be thought to be at once omnipotent and perfectly 
 good. If we say that he is omnipotent, that his sovereignty is 
 complete, that all events that occur are willed by him ; then it 
 follows that he is responsible for the actual world, which is 
 partly evil, and, accordingly, that he is not perfectly good. 
 If we begin at the other end, and say that God is perfectly 
 good, then we must deny that he is omnipotent. 
 
24 The Argument for a Finitist Theology. 
 
 John Stuart Mill may be taken as a representative of this 
 general tendency. His argument rests upon the evident 
 cruelty and recklessness of Nature, from which he infers the 
 limited power of the Author of JSTature. ^' I^ext to the great- 
 ness of these cosmic forces, the quality which most forcibly 
 strikes everyone who docs not avert his eyes from it, is their 
 perfect and absolute recklessness. They go straight to their 
 end, without regarding what or whom they crush on the road. 
 ... In sober truth, nearly all the things which men are 
 hanged or imprisoned for doing to one another, are nature's 
 everyday performances. Killing, the most criminal act recog- 
 nized by human laws, xTature does once to every being that 
 lives. . . . E'ature impales men, breaks them as if on the 
 wheel, casts them to be devoured by wild beasts, bums them 
 to death, crushes them with stones like the first Christian 
 martyr, starves them with hunger, freezes them with cold, 
 poisons them by the quick or slow venom of her exhalations, 
 and has hundreds of other hideous deaths in reserve, such as 
 the ingenious cruelty of a ISTabis or a Domitian never sur- 
 passed. All this, l^ature does with the most supercilious dis- 
 regard of mercy and of justice. . . . ISText to taking life is 
 taking the means by which we live ; and ^Nature does this, too, 
 on the largest scale and with the most callous indifference. A 
 single hurricane destroys the hopes of a season; a flight of 
 locusts, or an inundation, desolates a district ; a trifling chem- 
 ical change in an edible root, starves a million of people. . . . 
 Everything in short, which the worst men commit either 
 against life or property is perpetrated on a larger scale by 
 natural agents. . . . All which people are accustomed to 
 deprecate as ' disorder ' and its consequences, is precisely a 
 counterpart of Nature's ways. Anarchy and the Eeign of 
 Terror are overmatched in injustice, ruin, and death, by a hur- 
 ricane and a pestilence."^^ 
 
 The main thesis of the Essay on Nature is that it is " irra- 
 tional and immoral" to "make the spontaneous course of 
 
 28 Three Essays on Beligion, pp. 28 ff. 
 
The Doctrine of a Finite God. 25 
 
 things the model" of man^s voluntary actions.^^ The inci- 
 dental conclusion of the essay is the position which has been 
 stated by way of anticipation, namely, that it is absurd and 
 irrational to hold that God is perfectly good and also all- 
 powerfuL " The only admissible moral theory of Creation," 
 says Mill, " is that the Principle of Good cannot at once and 
 altogether subdue the powers of evil, either physical or moral. 
 . . . Those who have been strengthened in goodness by rely- 
 ing on the sympathizing power of a powerful and good Gov- 
 ernor of the world, have, I am satisfied, never really believed 
 that Governor to be, in the strict sense of the term, omnip- 
 otent. They have always saved his goodness at the expense 
 of his power." ^^ Recurring to the same thought in the essay 
 on the Utility of Religion, Mill contends that " one only form 
 of belief in the supernatural — one only theory respecting the 
 origin and government of the universe — stands wholly clear 
 both of intellectual contradiction and of moral obliquity. It 
 is that which, resigning irrevocably the idea of an omnipotent 
 creator, regards Nature and Life not as the expression through- 
 out of the moral character and purpose of the Deity, but as 
 the product of a struggle between contriving goodness and an 
 intractable material, as was believed by Plato, or a principle 
 of evil, as was the doctrine of the Manichseans."^^ 
 
 Mill shows that all the attempts that are made to escape 
 this conclusion are futile, and tacitly presuppose it. "That 
 much applauded class of authors, the writers on natural the- 
 ology, . . . have exhausted the resources of sophistry to make 
 it appear that all the suffering in the world exists to prevent 
 greater — that misery exists, for fear lest there should be 
 misery : a thesis which, if ever so well maintained, could only 
 avail to explain and justify the works of limited beings, com- 
 pelled to labor under conditions independent of their own will ; 
 but can have no application to a Creator assumed to be om- 
 
 2» lUd., p. 64. 
 30 lUd., pp. 39 f . 
 81 lUd., p. 116. 
 
26 The Argument for a Finitist Theology. 
 
 inpotent, who, if he bends to a supposed necessity, himself 
 makes the necessity which he bends to. If the maker of the 
 world can all that he will, he wills misery, and there is no 
 escape from the conclusion." 
 
 If we nevertheless attempt to escape by saying that "the 
 goodness of God does not consist in willing the happiness of 
 his creatures, but their virtue," Mill replies that "if the 
 Creator of mankind willed that they should all be virtuous, 
 his designs are as completely baffled as if he had willed that 
 they should all be happy."^^ 
 
 "But, it is said, all these things are for wise and good 
 ends." It may be said that "we do not know what wise 
 reasons the Omniscient may have had for leaving undone 
 things which he had the power to do. It is not perceived that 
 this plea itself implies a limit to Omnipotence. When a thing 
 is obviously good and obviously in accordance with what all 
 the evidences of creation imply to have been the Creator's de- 
 sign, and we say we do not know what good reason he may 
 have had for not doing it, we mean that we do not know to 
 what other, still better object — ^to what object still more com- 
 pletely in the line of his purposes, he may have seen fit to post- 
 pone it. But the necessity of postponing one thing to another 
 belongs only to limited power. Omnipotence could have made 
 the objects compatible. Omnipotence does not need to weigh 
 one consideration against another. . . . l^o one purpose im- 
 poses necessary limitations on another in the case of a Being 
 not restricted by conditions of possibility."^^ 
 
 Therefore " the notion of a providential government by an 
 omnipotent Being for the good of his creatures must be en- 
 tirely dismissed."^^ If we believe that God is all-powerful 
 and that iN'ature is his handiwork, our "worship must either 
 be greatly overclouded by doubt, and occasionally quite dark- 
 ened by it, or the moral sentiments must sink to the low level 
 of the ordinances of Mature: the worshipper must learn to 
 
 32 Ihid., p. 37. 
 
 33 iMd., pp. 179 f. 
 
 34 ihid., p. 243. 
 
The Doctrine of a Finite God. 27 
 
 think blind partiality, atrocious cruelty, and reckless injustice, 
 not blemishes in an object of worship, since all these abound to 
 excess in the commonest phenomena of Nature. . . . He who 
 comes out with least moral damage from this embarrassment, 
 is probably the one who . . . confesses to himself that the 
 purposes of Providence are mysterious, that its ways are not 
 our ways, that its justice and goodness are not the justice and 
 goodness which we can conceive and which it befits us to prac- 
 tise. When, however, this is the feeling of the believer, the 
 worship of the Deity ceases to be the adoration of abstract 
 moral perfection. It becomes the bowing down to a gigantic 
 image of something not fit for us to imitate. It is the worship 
 of power only."^^ 
 
 The very argument which has been chiefly relied upon to 
 prove the existence of God, namely, the argument from design, 
 far from establishing his omnipotence, is easily shown to be 
 incompatible with it. "It is not too much to say that every 
 indication of Design in the Kosmos is so much evidence 
 against the Omnipotence of the Designer. For what is meant 
 by Design ? Contrivance : the adaptation of means to an end. 
 But the necessity of contrivance — the need of employing means 
 — ^is a consequence of the limitation of power. . . . Wisdom 
 and contrivance are shown in overcoming difficulties, and there 
 is no room for them in a Being for whom no difficulties exist. 
 The evidences, therefore, of Natural Theology distinctly im- 
 ply that the author of the Kosmos worked under limitations; 
 that he was obliged to adapt himself to conditions independent 
 of his will, and to attain his ends by such arrangements as 
 those conditions admitted of."^^ 
 
 A creed like this makes human life significant. "A vir- 
 tuous human being assumes in this theory the exalted char- 
 acter of a fellow-laborer with the Highest, a fellow-combatant 
 in the great strife ; contributing his little, which by the aggre- 
 gation of many like himself becomes much, towards that pre- 
 ss ihid., pp. 112 f. 
 86 ihid., pp. 176 n. 
 
28 The Argument for a Finitist Theology. 
 
 gressive ascendancy, and ultimately complete triumph of good 
 over evil, which history points to, and which this doctrine 
 teaches us to regard as planned by the Being to whom we owe 
 all the benevolent contrivance we behold in l^ature."^^ 
 
 Mill's position is enthusiastically endorsed by William 
 James in his volume on A Pluralistic Universe, " When John 
 Mill said that the notion of God's omnipotence must be given 
 up if God is to be kept as a religious object, he was surely ac- 
 curately right ; yet so prevalent is the lazy monism that idly 
 haunts the region of God's name, that so simple and truthful 
 a saying was generally treated as a paradox. God, it was said, 
 could not be finite. I believe that the only God worthy of the 
 name must be finite."^^ With all its ambiguities and incon- 
 sistencies, the common conception of God is at bottom that of 
 a finite Being. The God of David or of Isaiah, the Heavenly 
 Father of the 'New Testament, is not the Absolute. " That 
 God," says James, " is an essentially finite being in the cosmos, 
 not with the cosmos in him." " The God of our popular 
 Christianity is but one member of a pluralistic system. He 
 and we stand outside of each other, just as the devil, the saints, 
 and the angels stand outside of both of us."^^ 
 
 Mill's polemic is directed against the doctrine of omnip- 
 otence as held by traditional orthodoxy; that of James is di- 
 rected against the conception of the Absolute, which has been 
 supposed by its adherents to solve diflSculties such as those 
 raised by Mill.^^ " The absolute," insists James, " taken 
 seriously, and not as a mere name for our right occasionally to 
 drop the strenuous mood and take a moral holiday, introduces 
 all those tremendous irrationalities into the universe which a 
 frankly pluralistic theism escapes, but which have been flung 
 as a reproach at every form of monistic theism or pantheism. 
 It introduces a speculative ^problem of evil' namely, and 
 
 37 IJ)id., p. 117. 
 
 38 James, A Pluralistic Universe, p. 124. 
 
 39 Ibid., pp. 110 f . ; see also The Will to Believe, pp. 116 and 134 f . 
 
 40 Beligious Aspect of Philosophy, p. 453 ; Sources of Beligious Insight, 
 pp. 240 ff. 
 
The Doctnne of a Finite God. 29 
 
 leaves us wondering why the perfection of the absolute should 
 require just such hideous forms of life as darken the day for 
 our human imaginations. If they were forced upon it by 
 something alien, and to 'overcome' them the absolute had 
 still to keep hold of them, we could understand its feeling of 
 triumph, though we, so far as we were ourselves among the 
 elements overcome, could acquiesce but sullenly in the resultant 
 situation, and would never just have chosen it as the most 
 rational one conceivable. But the absolute is represented as 
 a being without environment, upon which nothing alien can 
 be forced. ... Its perfection is represented as the source of 
 things, and yet the first effect of that perfection is the tre- 
 mendous imperfection of all finite experience."^ ^ 
 
 To this the partisan of the Absolute will, of course, object 
 that the imperfection of the finite is a logically indispensable 
 condition of the perfection of the Infinite. And not only the 
 monistic idealist, but the defender of traditional theology may 
 take this position. Thus St. Augustine long ago taught that 
 evil does not disturb the order and beauty of the universe ; for 
 " as a painting with dark colors rightly distributed is beau- 
 tiful, so also is the sum of things beautiful for him who has 
 power to view them all at one glance, notwithstanding the 
 presence of sin, although, when considered separately, their 
 beauty is marred by the deformity of sin. God would not have 
 created those angels and men of whom he knew beforehand 
 that they would be wicked, if he had not also known how they 
 would subserve the ends of goodness." " The whole world 
 thus consists, like a beautiful song, of oppositions. "^^ Or, to 
 employ an illustration of the Platonic-Augustinian doctrine 
 which is repeated by Royce, " as one looking over the surface 
 of a statue with a microscope, and finding nothing but a stony 
 surface, might say, how ugly! but on seeing the whole at a 
 glance would know its beauty ; even so one seeing the world by 
 bits fancies it evil, but would know it to be good if he saw it 
 
 41 A Plv/ralistic Universe, p. 117. 
 
 *2 Ueberweg, Geschichte der PMlosophie, 161 f . 
 
30 The Argument for a Finitist Theology. 
 
 as a whole. And the seeming but unreal evil of the parts may 
 be necessary in order that the real whole should be good."*^ 
 
 This, however, is not precisely the view of Royce himself. 
 He is not content to say that the evil must exist to sd; the 
 good off by way of contrast. He maintains that the " evil will 
 is a conquered element in the good will, and as such is neces- 
 sary to goodness." "Goodness . . . has as its elements the 
 evil impulse and its correction. The evil will as such may be 
 conquered in our personal experience, and then we are our- 
 selves good ; or it may be conquered, not in our thought con- 
 sidered as a separate thought, but in the total thought to which 
 ours is so related, as our single evil and good thoughts are 
 reilated to the whole of us. . . . As the evil impulse is to the 
 good man, so is the evil will of the wicked man to the life of 
 God, in which he is an element."^* 
 
 The doctrine which we have found in the earliest of Pro- 
 fessor Royce's books is found also in those which appeared 
 shortly before the end of his life. Thus in The Sources of 
 Religious Insight he writes of evils " which cannot, yes, which 
 in principle, and even by omnipotence, could not, be simply 
 removed from existence without abolishing the conditions 
 which are logically necessary to the very highest that we know. 
 Life in the spirit simply presupposes the conditions that these 
 ills exemplify. . . . Such sorrows, such idealized evils, which 
 are so interwoven with good that if the precious grief were 
 wholly removed from existence, the courage, the fidelity, the 
 spiritual self-possession, the peace through, in, and beyond 
 tribulation which such trials alone make possible, would also 
 be removed, surely show us that the abstract principle : * Evil 
 ought to be abolished,' is false."^^ 
 
 Royce holds that a world like the one we know, which con- 
 tains courage, fidelity, etc., and the evils which make these 
 noble human qualities possible, is ethically preferable to a 
 
 43 Religious Aspect of Philosophy, p. 265. 
 
 44 Ihid., pp. 455 f . 
 
 45 Sources of B,eligious Insight, pp. 250 ff. See also The Problem of 
 Christianity, I, 308 and elsewhere. 
 
The Doctrine of a Finite God. 31 
 
 world which would contain no evil and therefore none of the 
 virtues which presuppose it. For him the ideally perfect 
 whole is not composed of none but perfect parts. On the con- 
 trary the imperfection of some of the parts is a logical con- 
 dition of the complete perfection of the whole. To such rea- 
 sonings, James replies that "the ideally perfect whole is cer- 
 tainly that whole of which the parts also are perfect — if we 
 can depend on logic for anything, we can depend on it for that 
 definition.'' Is then a whole that consists of parts all of 
 which are themselves perfect ethically preferable to a whole 
 the perfection of which includes some imperfection, and, in- 
 deed, consists at least in part in the overcoming of imperfec- 
 tion ? Here we have the issue between the pluralistic and the 
 monistic ethics in a nutshell. In the next chapter we shall 
 consider this issue in so far as it is relevant to the problem of 
 theodicy. 
 
IV. 
 
 Theological Finitism as the Outcome of a Eational 
 
 Theodicy. 
 
 If the world is conceived in a pluralistic or dualistic 
 fashion, the case for theological finitism is complete. MilFs 
 argument is unanswerable. If we think of God as a Person 
 who stands in moral relations with other persons, then, even 
 if we assume these others to be his creatures, it is impossible 
 to hold that he is omnipotent and at the same time perfectly 
 good. The notion of omnipotence is, in itself, logically unob- 
 jectionable: it is logically possible to hold that the Supreme 
 Being is omnipotent. But, if he is omnipotent, he is either 
 malevolent or else non-moral. The Supreme Being might be 
 one who would take pleasure in the sufferings of his creatures, 
 only doling out to them sufficient satisfactions to induce them 
 to continue the business of living ; or he might be wholly indif- 
 ferent to their joys and sorrows. Such a being, however, 
 would not deserve to be called God ; for God, we say, is good. 
 But if God is good, then he is not omnipotent. 
 
 1. The Failure of Monistic Theodicy. — In this section I 
 propose to show that, if we think of the world monistically , a 
 rational theodicy is impossible. Let us then, for the present, 
 ignore the logical and psychological difficulties of monistic 
 idealism, except as we shall find them to be bound up with its 
 ethical difficulties. Let us assume the monistic theory of the 
 world and inquire concerning its treatment of the problem of 
 evil. 
 
 It is one of the merits of Koyce's discussion that he insists 
 upon finding a solution that shall be rational. He does not 
 demand the right to make mutually contradictory statements 
 about God, on the ground that it is about God that he is 
 
 32 
 
Theological Finitism the Outcome of Rational Theodicy. 33 
 
 speaking. He is not satisfied with saying that in some way 
 that is wholly mysterious to us partial evil may be universal 
 good. The Platonic-Augustinian analogy of the beautiful pic- 
 ture which is composed of dark as well as light colors^^ is not 
 satisfactory to him. It gives us no enlightenment as to why 
 just these particular evils are necessary to make the perfec- 
 tion of the whole. It suggests an ethics of quietism; for it 
 logically implies that the distinction between good and evil is 
 mere appearance and not genuinely valid. 
 
 For Royce, then, evil is not merely " an illusion of the par- 
 tial view; . . . but . . . seems in positive crying opposition 
 to all goodness." " We do not say that evil must exist to set 
 the good off by way of contrast. . . . We say only that the 
 evil will is a conquered element in the good will, and is as 
 such necessary to goodness." " The good act has its existence 
 and life in the transcending of experienced present evil." 
 " Goodness as a moral experience is for us the overcoming of 
 experienced evil; and in the eternal life of God the realiza- 
 tion of goodness must have the same sort of organic relation to 
 evil as it has in us."^*^ According to the theory of monistic 
 idealism, then, evil has its place in the perfect world. It is 
 the condition of the possibility of the good. Even the worst 
 conceivable evil, the deed of a traitor, may be the condition of 
 an atoning deed by which the world is so re-created and trans- 
 formed that it is " better than it would have been had all else 
 remained the same, but had that deed of treason not been done 
 at all."^8 
 
 'Now no one will question the reality and importance of the 
 experiences and social situations employed to illustrate the 
 " overcoming " of evil. Physical pain sweetens and sanc- 
 tifies the life of those who accept it resignedly, and bear it 
 patiently. One who meets his troubles bravely may thus make 
 them stepping-stones to a level of character which he could not 
 otherwise have attained. As we study the record of human 
 
 46 666 Chapter III. 
 
 *7 The Beligious Aspects of Philosophy, pp. 456 ff. 
 
 *8 The ProUem of Christianity, I, 308. 
 
34 The Argument for a Finitist Theology. 
 
 progress, we frequently meet cases in which an act of sin seems 
 to have been the indispensable condition of great good. The 
 conception of the " overcoming '^ of evil is then undoubtedly a 
 conception of great significance. JSTevertheless, the theodicy 
 offered by monistic idealism is not satisfactory. The monistic 
 theodicy fails for two reasons : (a.) It does not account for all 
 evils; and (h) its account of evil tacitly presupposes a 
 pluralistic view of the world. 
 
 (a) If the only evil were an evil will, and the only good a 
 good will, then the notion of the " overcoming '^ of evil would 
 be much less unsatisfactory. Let us grant for the sake of the 
 argument, that the will may be good or evil in itself, that is to 
 say, without reference to the consequences likely to flow from 
 its choices (a theory which is, however, very hard to under- 
 stand). But, even if we grant that will may be good or bad 
 'per se, there is no reason to hold that there are no other goods 
 and evils. The enumeration of " goods " is a sort of personal 
 confession of faith. I^o ultimate rational ground can be given 
 for calling anything good or bad. The perception of values is 
 a presupposition of all reasoning about right or wrong, good 
 or bad. Certainly, no one will claim that the goodness or 
 badness of will can be logically demonstrated. And all that I 
 am insisting upon here is, that, if we recognize good or bad 
 will, we are also justified in speaking of other "goods" and 
 "evils." 
 
 One of these other goods is pleasure, and one of these other 
 evils is pain. ITow it is true that in many cases pain sub- 
 serves a good purpose, and that the patient endurance of pain 
 (and, still more, I should say, the effort to relieve and destroy 
 it in oneself and in others) evokes some of the most admirable 
 human qualities ; but no one has proved that all pains are pro- 
 ductive of sufficient good to justify their existence, and, as we 
 shall see below, this attempted justification of pain presup- 
 poses a non-monistic view of the world. 
 
 Another " good " is life, considered apart from its pains and 
 pleasures. The corresponding " evil " is death, especially pre- 
 
Theological Finitism the Outcome of Rational Theodicy, 36 
 
 mature death. An earthquake destroys a thousand men; a 
 child, previously strong and healthy, falls a prey to a con- 
 tagious disease, in consequence of the ignorance or careless- 
 ness of its parents and the negligence of the community. If 
 the life of the person has ceased, he cannot be said to havb 
 been strengthened or ennobled by the misfortune that has 
 befallen him. If, on the other hand, we assume that the per- 
 son is immortal, and that his moral development continues in 
 spite of what we call death, there is no reason for holding that 
 his character has been improved by his unfortunate experience, 
 or that it was in any sense good for him that his entrance into 
 the next world should have been hastened through human 
 ignorance and sin. In either case, there is no reason for be- 
 lieving that the perfection of the Absolute requires the termi- 
 nation of human lives in this manner. 
 
 Another "good'' is sound intelligence, and the correspond- 
 ing " evil," insanity. This presents an especially difficult case 
 for the monistic idealist. The physical life continues, but all 
 opportunity for moral achievement is cut off. The evil is 
 surely not overcome in the individual, and there is no reason 
 for supposing it to be overcome in the Absolute, unless, indeed, 
 one is willing to hold that mere variety of content is to be 
 so highly esteemed, that the content of the perfect Mind must 
 be assumed to include the insane delusions of these unfor- 
 tunates. Very similar considerations confront us when we 
 think of those cases in which men's wills have been weakened 
 by disease ; or in which immature moral agents are compelled 
 by economic conditions to live in an environment that is con- 
 ducive to sin. 
 
 ISTow so long as there remains a single evil that cannot ra- 
 tionally be supposed to be "overcome," or even that cannot 
 be rationally shown to be overcome, we must conclude that the 
 monistic theodicy has failed. It is, of course, possible to find 
 a great many oases in the life of the race, as also in the ex- 
 perience of the individual moral agent, where evil seems to 
 have been thus overcome. But these cases may be matched 
 
36 The Argument for a Finitist Theology. 
 
 with others where just the contrary seems to be true. The 
 " treason " of the sons of Jacob led eventually to the elevation 
 of their brother to the virtual kingship of Egypt, and to the 
 preservation of the whole Israelite clan from famine ; but the 
 assassination of Abraham Lincoln led to bitter days in the 
 life of the American people, which, there is reason to believe, 
 might have been shortened or prevented, if the great President 
 had been permitted to live a few years longer. To be sure, we 
 do not know what the course of events would have been, had 
 Lincoln served out his second presidential term; but neither 
 do we know what the course of events would have been, if 
 the brethren of Joseph had never sinned, or if Judas had not 
 betrayed his Lord. 
 
 As we look back over our lives, we see temptations over- 
 come and difficulties bravely met and conquered; but what 
 shall we say of the temptations that were not overcome, of the 
 difficulties that were not conquered ? 
 
 Professor Royce himself speaks of a class of evils that, so 
 far as we can see, are not overcome. " Pestilence, famine, the 
 cruelties of oppressors, the wrecks of innocent human lives by 
 cruel fortunes — all these seem, for our ordinary estimates, 
 facts that we can in nowise assimilate, justify, or reasonably 
 comprehend. ... To such evils, from our human point of 
 view, the principle : ^ They ought to be simply driven out of 
 existence,' is naturally applicable without limitation."^^ 
 
 These evils, then, are not seen to be necessary to the per- 
 fection of the universal good. They are not yet " spiritual- 
 ized." But, then, with respect to all such evils, the theodicy 
 is not rational. Unfortunately, philosophy must be written 
 " from our human point of view." So far as these evils are 
 concerned, we are no farther on than were Plotinus or Augus- 
 tine. All we can say is that, in spite of certain ugly black 
 spots, the picture may be beautiful as a whole for a Mind that 
 can behold it thus. 
 
 (h) Our second reason for rejecting the monistic theodicy 
 
 *9 Sources of Religious Insight, p. 233. 
 
Theological Finitism the Outcome of Rational Theodicy, 37 
 
 is that it tacitly presupposes a pluralistic view of the world. 
 What can we make of the claim that evil is " f ragmentari- 
 ness"? Is fragmentariness, as such, evil? Then nothing is 
 really good except the Whole ; and the contrast of " good " and 
 "bad" is identified with the contrast between the "more in- 
 clusive " and the " less inclusive." But why the more inclusive 
 should be regarded as better, and the all-inclusive as best of 
 all, is by no means clear. 
 
 Well, then, does "overcoming" mean more than the mere 
 relation of Whole to part? If it is to have any ethical sig- 
 nificance, it certainly must mean more than this. Some parts 
 of the Absolute, to wit good men and good impulses, are 
 " good " ; others are " evil " ; and this difference is not a dif- 
 ference of size, or of complexity of organization. There is 
 here a genuine difference of character; and therefore if the 
 notion of " overcoming " is to have any moral significance at 
 all, the evil that is overcome must be not merely a 'part of the 
 Absolute, but a something other than the Absolute. For this 
 reason James is right in saying that the ideally perfect whole 
 is that whole of which the parts also are perfect.'^^ It may 
 not be true that the ideally perfect world, or the ideally per- 
 fect group of moral agents, is that world or group all the parts 
 of which are perfect; but this is true of a whole; for within a 
 whole it is logically impossible for good and evil to come into 
 conflict. Moral "overcoming" implies a conflict of persons, 
 or at least of numerically distinct forces, tendencies, or im- 
 pulses; and not merely a contrast of parts with one another 
 or with their Whole. 
 
 Furthermore, if monistic idealism is not to give us an ethics 
 of acquiescence, if the notion of " overcoming " is to be taken 
 seriously, we must assume the reality of temporal succession. 
 All the illustrations of the overcoming of evil, the case of the 
 traitor and all cases in which a person is strengthened and en- 
 nobled by misfortune, imply the notion of time. If it were 
 possible to assign any meaning at all to the notion of a time- 
 ■50 The Plv/ralistio Universe, p. 123. 
 
38 The Argument for a Finitist Theology, 
 
 less act, it might be possible to think of an eternal 'prevention 
 of evil ; but not of an eternal overcoming of evil. 
 
 2. The Outline of a Finitist Theodicy. — In so far, then, 
 as the conception of "overcoming" is valid and morally sig- 
 nificant, it presupposes a finitist theology. If we no longer 
 try to think of God as all-inclusive, and no longer think of 
 him as omnipotent, then this conception of the logical neces- 
 sity and practical value of evil is a conception of great im- 
 portance. But we need not affirm that all evils are necessary 
 for the perfection of the world. We may admit the reality of 
 stem and opaque necessities, which can not be transcended, 
 which are not completely understood, it may be, by the Su- 
 preme Person himself. 
 
 The theological finitist may say without logical inconsistency 
 that it is better that there should be sin than that no oppor- 
 tunity should be afforded for freedom and personality. 
 
 He may say that it is better that the operations of N^ature 
 should be uniform, than that E"ature, like an over-kind nurse, 
 should be continually stepping in to shield us from the results 
 of ignorance, recklessness, or indolence. 
 
 He may say that some of the evils which we endure are the 
 condition of the prevention of greater evils. He may, there- 
 fore, without inconsistency, explain much of our physical pain 
 as a warning against courses of action that would lead to 
 greater misery. 
 
 He may expatiate upon the educative function of suffering 
 of every description, and show how its patient endurance, 
 when it is irremediable, will produce a beautiful and saintly 
 character. 
 
 In short, the theological finitist may take over into his sys- 
 tem of thought all the particular instances of " compensation," 
 but need not attempt to show that the "compensation" is 
 complete or universal. Many evils exist which ought to be 
 "simply destroyed"; but God is not strong or wise enough, 
 and certainly we are not, to destroy them immediately. In 
 other words, the finitist may take seriously the thought of 
 
Theological Finitism the Outcome of Rational Theodicy, 39 
 
 evolution or progress — a conception which the absolutist is 
 logically forbidden to entertain. 
 
 "We have found a thought," says Royce in his first philo- 
 sophical book, "that makes this concept of progress not only 
 inapplicable to the world of the infinite life, but wholly super- 
 fluous." " Progress in this world as a whole is therefore sim- 
 ply not needed."^ ^ For the theological finitist, on the con- 
 trary, the concept of progress, far from being " superfluous," 
 is of immense significance. He hopes for, and believes in the 
 possibility of, a better world ; and, while lamenting the logical 
 inconsistency of his monistic brother, works by the side of the 
 latter in the effort to hasten the coming of this better world. 
 
 «i The Beligious Aspect of Philosophy, pp. 464, 466. 
 
V. 
 
 Logical Finitism and the Idea of God. 
 
 In the preceding chapters we have come to the conclusion 
 that it is impossible to think of God as infinite in the first of 
 the two senses of the word. (See Chapter I, Section 4.) The 
 hard facts of human experience forbid us to say that God is 
 the Whole of reality, or that he is omnipotent. In the present 
 chapter I wish to discuss the arguments of a school of thinkers 
 who have maintained the logical absurdity of holding that 
 God is infinite in the second of our two senses. According to 
 these thinkers we cannot say without self-contradiction that 
 God (or the world, or anything) consists of or includes an 
 infinite multiplicity of elements, or perdures through an in- 
 finite sequence of moments. While this theory and the view 
 which I have called " ethical finitism " do not imply each 
 other, inasmuch as they deny the infinity of God in two dif- 
 ferent senses, yet these two kinds of finitism are mutually com- 
 patible, and support one another, since both are opposed to 
 monistic idealism, which maintains that God, or the Absolute, 
 is infinite in both senses. 
 
 The founder of this school of thinkers was Charles Kenou- 
 vier (1815-1903), who is said by James to have been the 
 " strongest philosopher of France in the second half of the 
 nineteenth century."^ ^ As important disciples we may name 
 F. Pillon, F. Evellin, and E. Boutreux. Henri Bergson, 
 France's most eminent living philosopher, has been greatly in- 
 fluenced by Renouvier, but it would scarcely be just to call 
 him a disciple.^ ^ 
 
 " ISTeocriticism," as the Renouvierist philosophy is called in 
 
 52 Problems of Philosophy, p. 163. This, the last book of William James, 
 is dedicated * ' to the great Eenouvier 's memory. ' ' 
 
 53 Thilly, History of Philosophy, pp. 511 f. 
 
 40 
 
Logical Finitism and the Idea of God, 41 
 
 recognition of its historic relation to the system of Kant, is 
 characterized by Windelband as a synthesis of Kant and 
 Comte. Renouvier, however, while no doubt influenced by 
 Comte, always emphasized the difference between his own 
 philosophy and positivism. Positivism begins with a discus- 
 sion of the natural sciences and of the implications of scientific 
 method, and is led to a rejection of the notions of being-in- 
 itself and transitive cause. ^N^eocriticism reaches a similar 
 conclusion by a different road. It "begins with the logical 
 investigation of mental phenomena, . . . and completes the 
 Humian critique of the concepts of substance and causality 
 by means of an apriorism related to that of Kant: in mental 
 phenomena we have to seek ^ essentially ' the laws of all being. 
 Thus neocriticism is indeed phenomenalism, but not empiri- 
 cism."5* 
 
 1. The Finitist View of the World. — The best introduction 
 to the philosophy of Renouvier is a study of the Kantian " an- 
 tinomies.'' According to the first of these it can be proved 
 that the world has a beginning in time and limits in space; 
 and it can be proved with equal cogency that it has no begin- 
 ning and no limits. The second antinomy affirms that every 
 compound substance consists of simple, that is indivisible, 
 parts; and also that there is nothing simple, but that every- 
 thing is infinitely divisible. The third and fourth antinomies 
 treat in the same way the issue of causality versus freedom, 
 and the question of the existence of an absolutely necessary 
 Being.^^ 
 
 There are certain obvious weaknesses or oversights in the 
 demonstration. Yet it is possible so to revise Kant's argu- 
 ments as to make them much more cogent.^^ If, then, the 
 demonstration of both thesis and antithesis, in the case of each 
 or only of some of these examples of the conflict of reason with 
 
 «* Windelband, Lehrhuch der Geschichte der Philosophie, S. 515; Feigel, 
 Der Franzosische NeoTcritidsmus, S. 9. 
 
 55 Kant, Kritik der Beinen Vernunft, A, 426-461 (Mueller, pp. 344 flf.). 
 
 56 See Renouvier, Critique de la Doctrine de Kant, pp. 29 f. Cf. Les Di- 
 lemmes de la M4taphysique Pwre. 
 
42 The Argument for a Finitist Theology. 
 
 itself, be regarded as valid, the natural outcome might seem 
 to be a thoroughgoing scepticism, an utter despair of the pos- 
 sibility of attaining the right to be certain about anything. 
 For if the human reason thus falls into necessary self-contra- 
 diction, what ground have we for trusting it even in those cases 
 in which no contradiction is discoverable? Such a complete 
 scepticism, however, is practically impossible; and, accord- 
 ingly, it is more common for those who hold that both the 
 theses and the antitheses are valid to argue that the existence 
 of these antinomies constitutes a reason for the subordination 
 of the human reason to the authority of the Church or the 
 Bible. From these necessary conflicts they conclude that 
 human reason has its limits, that we are not always safe in 
 refusing to believe some propositions, even though they appear 
 to us to be logically absurd or self-contradictory. Difficulties 
 and even self-contradictions may be found in the historic 
 creeds, if we look for them ; but the same is true of some of 
 the most commonly received conceptions, such as the notions 
 of space and time. Therefore, these thinkers argue, we are 
 justified in believing "mysteries,'' that is to say, in holding 
 to the truth of propositions that are logically inconceivable.^^ 
 In one of his earliest philosophical works, Le Manuel de 
 Philosophie moderne (1842), Charles Renouvier himself had 
 thought it possible to believe both the theses and the an- 
 titheses of these antinomies.^ ^ But the Essais de Critique 
 generale began a polemic against this position ;^^ and, in his 
 mature philosophy, logical conceivability, that is to say, free- 
 dom from self-contradiction, became the criterion, not only of 
 all valid thinking, but also of real existence. Thus it is a car- 
 dinal principle of the neo-criticist school that one of the two 
 sides of each of the mathematical antinomies must be false. 
 There is no meaning in saying that hoth are true. As Evellin 
 puts it, " To say yes and no of the same thing at the same time 
 
 67 See Mansel, The Limits of Eeligious Thought; Newman, The Gram- 
 mar of Assent; Hamilton, Lectures on Metaphysics. 
 
 58 Arnal, Philosophie Meligieuse de Charles Eenouvier, p. 29. 
 
 59 Ibid., p. 33. 
 
Logical Finitism and the Idea of God, 43 
 
 and under the same point of view, this is contradiction; and 
 for the understanding contradiction is death."^^ 
 
 Accordingly the neo-criticists recognize the principle of 
 contradiction as the fundamental principle of thought. More- 
 over, they refuse to exempt any topic of discussion whatever 
 from the sway of this principle. You can't appeal to it in 
 order to demolish the theories of other people, and then refuse 
 to admit its universal validity when it threatens to demolish 
 some pet theory of your own. This principle, they insist, is 
 essential, not only to human intelligence, but to intelligence 
 as such. You may speak if you will of an intelligence that is 
 higher than human ; but, unless the principle of contradiction 
 is a principle of this higher intelligence also, the phrase 
 "higher intelligence" is a phrase without meaning. Or, if 
 you say that you believe in "truths above reason," which on 
 the plane of human reason take the form of self -contradictory 
 propositions, they will tell you that you are the dupe of words. 
 Each of the words of a self-contradictory proposition may in- 
 deed have a perfectly clear and definite meaning when taken 
 separately, but the combination has no meaning, and the so- 
 called proposition is, strictly speaking, no proposition at all, 
 but merely a succession of words. You may believe that you 
 believe it ; but in reality you do not believe it, for it is neither 
 true nor false but meaningless. 
 
 The principle of contradiction is thus the comer-stone of 
 the Renouvierist philosophy. ISText in importance, and, as 
 Renouvier and his disciples maintain, a necessary consequence 
 of it, is the " principle of number." This is the principle that 
 an infinite number is a self-contradictory notion, and that 
 there can therefore be no actual infinite. Again and again in 
 his voluminous writings^ ^ Renouvier recurs to this point, and 
 seeks to establish it in various ways, but especially by an ex- 
 amination of the properties of the series of cardinal numbers. 
 
 60 Evellin, Infini et Quantite, p. 19. Of. Eenouvier, Les Dilemmes de la 
 Metaphysigue Pure, pp. 2 f . 
 
 61 See Les Dilemmes de la MStaphysique Pure, pp. 122-125; Nouvelle 
 Monadologie, p. 35 ; Logique G4n4rale, I, pp. 46 f ., 57, and elsewhere. 
 
44 The Argument for a Finitist Theology. 
 
 A typical illustration of the absurdity of supposing that an 
 infinite unmber may actually be given is borrowed from the 
 writings of Galileo. It runs as follows: 
 
 " Suppose the series of natural numbers to be given. We 
 can then form another sequence composed exclusively of the 
 squares of the first, for it is always possible to find the square 
 of a number. Thus, by hypothesis, the second sequence will 
 have a number of terms equal to the number of terms of the 
 first. 'Now the first contains all the numbers, squares as well 
 as not-squares, while the second contains only the squares. 
 The first has, therefore, a number of terms greater than that 
 of the second, since, containing all the numbers, it contains all 
 the squares, and it contains besides the numbers that are not 
 squares. But by hypothesis or construction, these numbers of 
 terms are equal. Therefore there are some equal numbers of 
 which one is greater than another. But this consequence is 
 absurd. Therefore it is absurd to suppose the natural series 
 of numbers to be actually given."^^ ^ow if the natural series 
 of numbers were given, it would of course be an actually in- 
 finite multitude. But we have seen that it is absurd to sup- 
 pose that the entire series of cardinal numbers is given ; and, 
 if this is true of the series of numbers, it is obviously true of 
 every infinite series, since the terms of any series may be num- 
 bered "one," "two," "three," etc. Therefore the notion of 
 an actual infinite is absurd. In other words, every multitude 
 has a number ; but the notion of an infinite number is logically 
 impossible; and therefore it is impossible that there should 
 be any actually existing infinite multitude. 
 
 Here, however, an important distinction is to be made. We 
 
 should discriminate between the notion of an infinite which is 
 
 merely potential and that of an infinite in the absolute sense 
 
 of the term. " The first consists in this : that, however great 
 
 or small we assume a given entity to be, and however much we 
 
 imagine it to be increased by repeated multiplications, there 
 
 62Renouvier, Les Principes de la Nature, p. 37; also Ann^ Philoso- 
 phique, 1890, pp. 83 ff. 
 
Logical Finitism and the Idea of God, 45 
 
 must still be thought to be something greater or smaller. The 
 second infinite consists in this: that a thing has actually and 
 absolutely so much magnitude or smallness that one can not 
 imagine more of it."^^ The first infinite is called by Kenou- 
 vier and his disciples the indefinite. 'Now the indefinite is a 
 clear idea; but of the absolute infinite it is psychologically 
 and logically impossible to form any conception. It is evi- 
 dent from the above definition of the indefinite that it never 
 is, but always becomes. Accordingly the indefinite may also 
 be called the potential infinite. 
 
 2. The God-Conception of the Logical Finitist. — Some of 
 the theological implications of logical finitism are discussed 
 by Pillon in the Annee Philosophique for 1890, in an article 
 entitled "La Premiere Preuve Cartesienne De L'Existence 
 De Dieu et La Critique De L'Infini." In this article, from 
 which several citations have already been made, Pillon re- 
 minds us that Descartes, after removing the doubt of his own 
 existence by the help of the cogito ergo sum, seeks to escape 
 from egoistic idealism by means of the idea of infinity or per- 
 fection. The truth of our ideas about an external world is 
 inferred from the existence of God; and the existence of God 
 is inferred from our possession of the idea of God. 
 
 "Among my ideas there is one which represents a God, 
 sovereign, eternal, infinite, immutable, omniscient, and uni- 
 versal creator of the things which are outside of him." This 
 idea, says Descartes, must have a cause ; and Descartes assumes 
 that there must be at least as much " reality " in the efficient 
 cause as in its effect. No idea c^ contain more objective 
 reality than the formal reality of its cause. !N'ow, the only 
 cause adequate to the production of this idea of God, which we 
 find in our minds, is God. Therefore God exists. Therefore 
 the external world is a real world. Such is Descartes's 
 reasoning. 
 
 Pillon remarks that, in assuming the general proposition 
 that the effect can not be superior to the efficient cause, Des- 
 
 63 L 'AntiSe Philosophique, 1890, p. 56. 
 
46 The Argument for a Finitist Theology, 
 
 cartes reveals a failure to make his original doubt as uni- 
 versal as lie supposed he had made it.^'* If, with the school 
 of Kenouvier, we hold that there may be first beginnings, that 
 is to say, uncaused events, it is evident that there is no neces- 
 sity for believing that the effect can contain no more ^' reality " 
 than the cause. For, in so far as the scholastic principle is 
 regarded as demonstrable, it rests upon the assumption that 
 every event must have a cause. The scholastic philosophers 
 reasoned, and after them Descartes, that if the effect con- 
 tained more reality than the cause, then, assuming that both 
 effect and cause are divisible into parts, some parts of the 
 effect would be uncaused, since the more real being would 
 have the greater number of parts. If, however, we assume 
 that there is no necessary connection between the notion of a 
 beginning and that of an effect, the scholastic principle as- 
 sumed by Descrates sinks to the level of a pseudo-axiom. 
 Accordingly, even if we do possess the idea of an infinite and 
 perfect being, we are not justified in arguing from the fact of 
 its possession to the existence of such a being. 
 
 Moreover, says Pillon, Descartes confused the notions of 
 infinity and perfection. Descartes assumes the synonymity 
 of the words " infinite '' and " perfect." But, " the idea of the 
 perfect, which Descartes and after him Malebranche, Fenelon, 
 Leibniz, all the spiritualist philosophers of the eighteenth 
 century, as all those of our time, have always confounded 
 with that of infinity, should be rigorously distinguished from 
 it. This distinction is one of the fundamental theses of the 
 phenomenalist criticism." 
 
 "Perfection is a general idea, formed from the ideas of 
 diverse qualities of an excellence such as we contemplate with 
 unmixed satisfaction, and to which we judge nothing that we 
 <;an imagine of the same order to be preferable. These qual- 
 ities are intellectual or moral or even physical: Such are 
 knowledge, wisdom, justice, goodness, happiness, beauty, etc. 
 A perfect being is a being in which these qualities are united," 
 
 64 L 'AntiSe PhUosophique, 1890, p. 161. 
 
Logical Finitism and the Idea of God. 47 
 
 and so fittingly and harmoniously combined that there is no 
 occasion for " reproach or desire." " The ideas relative to 
 perfection and those which concern mathematical magnitude 
 form,, in reality, two separate and irreducible categories." 
 These categories rest upon two kinds of comparison; Com- 
 parison of quantity and comparison of estimation or pref- 
 erence.^^ The notion of perfection is then one which we can 
 make for ourselves. Consequently, we do not need to assume 
 the existence of a perfect being in order to explain the pres- 
 ence of the idea in our minds. 
 
 The notion of infinity, i. e., of infinity in the absolute sense, 
 we can not make. But, says the neo-criticist, we do not really 
 possess this notion, because it is logically contradictory. The 
 causal relation of our notions of infinity is just the opposite 
 of that supposed by Descartes. "It is not the idea of the real 
 and absolute infinite impressed in our soul by this infinite, 
 which explains the formation of our ideas of potential infinites. 
 It is our ideas of potential infinites drawn from ourselves, 
 which have conducted us by a process logically illegitimate, 
 but psychologically natural, to the idea of the real and absolute 
 infinite. It is the infinites, apparently actual, of the spatial 
 and temporal world that have led us to the divine attributes. "^^ 
 
 We can not, therefore, have any valid conception of infinity 
 in the absolute sense. The world is finite and God is finite. 
 
 3. The Attributes of the Finite God. — The idea of God 
 which was supposed by Descartes to have been impressed by 
 the Creator upon every human mind represented God as " sov- 
 ereign, eternal, infinite, immutable, omniscient, omnipotent." 
 The neo-criticist " principle of number," as we have seen, com- 
 pels a revision of this idea. 
 
 By Pillon, as by Koyce,^^ omnipotence is treated as the 
 typical attribute of Deity. We may justify this method of 
 procedure on the ground that, in the first place, omnipotence 
 
 65 76icZ., pp. 51, lllff. 
 
 66 Ihid., p. 110. 
 
 67 See Chapter II. 
 
48 The Argument for a Finitist Theology. 
 
 implies omniscience; knowing is only a particular kind of 
 doing. ITot to know and not to be able to find ont would be 
 not to be able to do. In the second place, and conversely, om- 
 niscience implies omnipotence. That knowledge is power is 
 attested by the etymological affinity of the German Jconnen 
 and hennen, and the English can and cunning, and by the uses 
 of the French verb savoir. To know how is the same thing as 
 to be able. An omniscient being, accordingly, will know how 
 to do all things, that is to say, will be able to do all things, will 
 be omnipotent ; and, on the other hand, if logic forbids us to 
 think of God as omniscient, then we can not logically think 
 of him as omnipotent either. 
 
 Pillon approaches the discussion of the divine omniscience 
 from the side of perfect foreknowledge. The problem is to 
 reconcile the idea of perfect foreknowledge with the neo- 
 criticist principle of number, and this reconciliation is, of 
 course, impossible. 
 
 Objection has frequently been made to the idea of a fore- 
 knowledge of "free" acts. But the objection which Pillon is 
 urging holds against the foreknowledge of determined events 
 as well. For " these necessary or determined future events do 
 not form a whole, a determined number, since they are sup- 
 posed to produce themselves in a time which has no limits. It 
 is an endless series, not simply of possibles, but of necessaries. 
 It is necessary to say that the potential infinity of these future 
 events finds itself in some manner realized in the divine under- 
 standing; or else it is necessary to reject the perfect and abso- 
 lute foreknowledge even when it is a question of necessary 
 future events."^ ^ 
 
 Yet we may distinguish two sorts of omniscience, or in the 
 special case just now in question, of perfect foreknowledge, 
 corresponding to the distinction previously made between the 
 absolute, or actual infinite and the potential infinite. There 
 is, accordingly, a sense in which it is logically unobjectionable 
 to speak of perfect foreknowledge. "Does it follow then," 
 
 68 lUd., p. 174. 
 
Logical Finitism and the Idea of God. 49 
 
 concludes Pillon, " that one ought to regard as impossihle the 
 perfection of foreknowledge? Yes, assuredly, if one makes 
 this perfection consist in the knowledge of an infinite number 
 of future realities. No, if in place of attributing to the being 
 who is supposed to be perfect a "single infinite and eternal 
 thought," one admits that his intelligence differs from ours by 
 its extent, and not in respect of its nature; that it proceeds 
 like ours by separate and successive acts of thought ; that it is 
 free to push back successively the limits of its horizon, but that 
 it is always obliged to have a horizon. Thus understood om- 
 niscience presents no contradiction. '^^^ In other words God 
 might, so far as the purely logical argument is concerned, be 
 assumed to be omniscient, in the sense of knowing all that is 
 at any given moment knowable, even if he is finite in the sense 
 of the neo-criticist. 
 
 Accordingly, the view of Mill and James and of the previous 
 chapter is not logically bound up with that of Kenouvier and 
 Pillon. Logical finitism suggests and makes room for, but 
 does not in itself require ethical finitism. As has already been 
 said, our reasons for denying the divine omnipotence and om- 
 niscience are not merely logical ; they are chiefly ethical. Yet 
 the neo-criticist argument prepares men's minds for the ac- 
 ceptance of this ethically grounded argument. Both argu- 
 ments presuppose loyalty to the principle of contradiction, 
 and both presuppose a certain freedom from the traditional 
 preference for such words as "infinite," "omniscient," "om- 
 nipotent," etc., when employed as adjectives modifying the 
 word "God." 
 «» Ilid.y p. 179. 
 
VI. 
 Theology and the "ITew Infinite." 
 
 When Renouvier wrote his principal works he could say 
 that the mathematicians were all agreed in rejecting the 
 notion of an infinite number. As Amal remarks,^^ " All the 
 mathematicians who had weighed the terms of the alternative 
 . . . were unanimous. All from Galileo to Cauchy had em- 
 phasized the impossibility of the infinite of quantity, the ab- 
 surdity of the realized infinite. . . . Why should that which 
 is impossible and absurd from the point of view of mathematics 
 be maintained from the point of view of metaphysics ? " 
 
 Since the middle of the last century, however, the math- 
 ematicians have been more favorably disposed towards the 
 quantitative infinite, and the neo-criticists' appeal to the con- 
 sensus of all mathematicians " from Galileo to Cauchy " is met 
 by the counter-appeal to a rival consensus of philosophical 
 mathematicians and mathematically-minded philosophers 
 from Bolzano to Bertrand Russell. In the judgment of sev- 
 eral contemporary thinkers one of the great achievements of 
 the latter half of the nineteenth century was the discovery of a 
 new definition of infinity, which, it is maintained, frees the 
 conception from all the difficulties and puzzles found in it as 
 formerly defined. 
 
 1. The New Definition of Infinity. — The " new " definition 
 of infinity is an incident, perhaps the culminating incident, 
 in the "generalization" of the concept of number.'''^ If we 
 had only the finite whole numbers, 1, 2, 3, etc., while the fun- 
 damental operations of addition, multiplication, and involu- 
 tion would be in every case possible, the inverse operations 
 would not be universally possible. For example, it would be 
 impossible, if we had only such numbers, to subtract 3 from 
 
 70 La Philosophie religieuse de Charles Benouvier, p. 36. 
 'iCouturat, De L'Infini Mathematiqiie, pp. 5-68, 281. 
 
 50 
 
Theology and the ''New Infinite/* 61 
 
 2, to divide 2 by 3, or to find the square root of 3. In order 
 that subtraction, division, and evolution may be universally 
 possible, mathematicians have introduced the conception of 
 negative numbers and zero, of fractional numbers, and of 
 irrational and imaginary numbers. The definition of infinite 
 or "transfinite" numbers should therefore be considered, not 
 as an isolated incident, but as a part of this larger movement 
 of mathematical thought. 
 
 One of the discoverers of transfinite number was Georg 
 Cantor. His theory of number is found in two memoirs which 
 appeared in the Mathematische Annalen for 1895 and 1897 
 under the title '' Beitrdge zur Begrilndung der Transfiniten 
 Mengenlehre.^^ These memoirs have been translated into Eng- 
 lish by Philip E. B. Jourdain under the title of " The Theory 
 of Transfinite Numbers/''^ ^ Cantor here defines the " power " 
 or " cardinal number " of an aggregate M as " the general con- 
 cept which, by means of our active faculty of thought, arises 
 from M when we make abstraction of the nature of its various 
 elements m and of the order in which they are given." If we 
 do not make abstraction of the order, but only of the nature 
 of the elements, the resulting concept is the ordinal number of 
 the aggregate M, Two aggregates are equivalent, and there- 
 fore have the same cardinal number, "if it is possible to put 
 them, by some law, in such a relation to one another that to 
 every element of each one of them there corresponds one and 
 only one element of the other."^* Employing the notions of 
 an aggregate and of equivalence, together with the notions of 
 "bindings" and "coverings," Cantor then defines the con- 
 cepts of "greater" and "less," and the operations of addi- 
 tion, multiplication, and involution.''* 
 
 72 The Open Court Publishing Company, 1915. 
 
 73 The Theory of Transfinite Numbers, p. 86. 
 
 "f^Ibid., pp. 89-95. One aggregate is said to be greater than another 
 (and therefore the cardinal number of the first greater than the cardinal 
 number of the second) when (a) there is a part of the first which is 
 equivalent to (i. e., can be put in one-to-one correspondence with) the 
 second, but (ft) no part of the second which is equivalent to the first (pp. 
 89 ff.). 
 
52 The Argument for a Finitist Theology, 
 
 This brings him to the discussion of the finite and trans- 
 finite numbers. ^^ Aggregates with finite cardinal numbers," 
 he says, " are called ' finite aggregates ' ; and all others we 
 call Hransfinite aggregates/ and their cardinal numbers 
 'transfinite cardinal numbers.' ''^^ The transfinite numbers 
 are thus those that are not finite. We must therefore seek the 
 distinguishing mark of the finite number. This is to be found 
 in the following theorem : " If ilf is an aggregate such that it 
 is of equal power with none of its parts, then the aggregate 
 (M, e), which arises from M by the addition of a single new 
 element e, has the same property of being of equal power with 
 none of its parts." This theorem is used in establishing the 
 fundamental properties of the "unlimited series of finite car- 
 dinal numbers,"^^ and becomes a virtual part of their defini- 
 tion. Finite aggregates, accordingly, are never equivalent to 
 any of their parts, while transfinite aggregates may be. " The 
 first example of a transfinite aggregate," continues Cantor, 
 " is given by the totality of finite cardinal numbers ; we call 
 its cardinal number * Aleph-zero.' " The first transfinite cai^ 
 dinal number is, then, the cardinal number of the " totality " 
 of finite cardinal numbers.''''^ 
 
 It should be noted that Cantor calmly assumes the logical 
 tenability of this notion of the "totality" of an unlimited 
 series, and as we shall presently see this is the crux of the 
 whole matter. Just now, however, it is our purpose to under- 
 stand the doctrine rather than to criticize it. 
 
 A further advance in the theory of number ought next to be 
 noted. Cantor, as we have seen, defined " cardinal number " 
 and "ordinal type" as "general concepts which arise by 
 means of our mental activity." Frege, in his Grundlagen der 
 Arithmetih of 1884, defined "the number of a class u" as "the 
 class of all these classes which are equivalent to u.^^ The same 
 definition was discovered independently by Bertrand Russell. 
 " The two chief reasons in favor of this definition," says Jour- 
 
 f^Ihid., p. 103. 
 76 Hid., pp. 97-103. 
 fTlhid., p. 103. 
 
Theology and the "New Infinite/' 53 
 
 dain, "are that it avoids, by a construction of ^numbers' out 
 of the fundamental entities of logic, the assumption that there 
 are certain new and undefined entities called ^ numbers ^ ; and 
 that it allows us to deduce at once that the class defined is not 
 empty, so that the cardinal number u exists in the sense de- 
 fined in logic; in fact, since u is equivalent to itself, the car- 
 dinal number of u has u at least as a member."^® Cantoris 
 definition of an infinite or transfinite number accordingly be- 
 comes "the class of all classes that are similar to parts of 
 themselves. ""^^ 
 
 The "New Infinite" was independently discovered by 
 Richard Dedekind.®^ His definition runs as follows :^^ "A 
 system 8 is said to be infinite when it is similar to a proper 
 part of itself; in the contrary case, 8 is said to be a finite 
 system." 
 
 The words "system," "similar," and "proper part" are 
 employed in a technical sense, and require some explanation. 
 A collection of objects is called a system (also by different 
 writers an aggregate, manifold, or set) when it fulfils the fol- 
 lowing conditions:®^ 
 
 (1) It includes all the objects to which a definite quality 
 belongs. 
 
 (2) It includes no object which does not possess this 
 quality. 
 
 (3) Each of the included objects is permanently the same, 
 and distinct from all the others. These separate objects are 
 called elements. In Dedekind's terminology, every system is 
 a part of itself; while a system which contains some, but not 
 all, of the elements of a given system is a proper part of the 
 given system. The notion of similarity is identical with Can- 
 tor's "equivalence," and exactly the same meaning is con- 
 
 T8 Ihid., pp, 202 f . 
 
 7» Russell, Principles of Mathematics, pp. 262, 3'21. 
 
 90 Essays on the Theory of Numhers, p. 41. This is a translation by 
 W. W. Beman of Dedekind's papers on ' * StetigJceit und irrationale 
 Zahlen ' ' and * * Was sind und was sollen die Zahlen. ' ' 
 
 8i76i^., p. 63. 
 
 82 Cf. Encyclopedia Britannica, 1910, Article on Number. 
 
54 The Argument for a Finitist Theology. 
 
 veyed by the phrase "one-to-one correspondence." Any two 
 groups or series are said to stand to each other in the relation 
 of one-to-one correspondence when for each element or term 
 of the one there is one and only one element or term of the 
 other, and vice versa. To borrow an illustration from Mr, 
 Kussell,^^ " The relation of father to son is called a one-many 
 relation, because a man can have only one father but may have 
 many sons; conversely, the relation of son to father is called 
 a many-one relation. But the relation of husband to wife (in 
 Christian countries) is called one-one, because a man cannot 
 have more than one wife, or a woman more than one husband." 
 
 Dedekind's point is not that two systems which are assumed 
 or already known to be infinite are similar or one-to-one corre- 
 spondent, even if the one is only a part of the other. That 
 such a similarity or equivalence is to be found between whole 
 and part was, as we have seen, the very puzzle that had per- 
 plexed the older mathematicians. The achievement of Dede- 
 kind (if it is a genuine achievement) is rather the reversal of 
 the method of attack. The " similarity " of whole and part is 
 no longer merely an observed fact, nor is it for him an inr 
 ference from their infinity; but infinity is now defined to he 
 such similarity. If a system or aggregate is similar to a proper 
 part of itself, then it is infinite; and this is the definition of 
 an infinite system. 
 
 2. The New Infinite and Logical Finitism. — It has been 
 maintained by M. Couturat and others that Kenouvier's 
 critique of infinite number, and therefore his whole system of 
 philosophy so far as it is based upon this critique, is founded 
 upon an erroneous definition of the mathematical infinite.^* 
 It accordingly becomes a matter of some importance to inquire 
 into the merits of this "new" and, as is maintained, more 
 correct definition. Our examination will lead us to the con- 
 clusion that the "new" infinite is only the old infinite in a 
 rather easily penetrable disguise; that the definition of Dede- 
 
 83 Scientific Method in Philosophy, p. 203. 
 8*Pe L'Infini Mathematique, pp. 444 ff. 
 
Theology and the ''New Infiniie/' 56 
 
 kind and Cantor is the logical equivalent of the definition sug- 
 gested by etymology; that, therefore, if the reasoning of the 
 neo-criticists is sound as long as we use the old definition, their 
 arguments lose none of their cogency when we substitute the 
 definition formulated by the new school of mathematicians. 
 
 If we had no other preceptor than etymology, we should at 
 once conclude that the infinite is that which is limitless or in- 
 capable of completion. The definition of infinity adopted by 
 Kant in his account of the " First Conflict of the Transcenden- 
 tal Ideas" appears to be no more than an elaboration of this 
 notion of Unendlichheit. " The infinity of a series," he says, 
 " consists in this, that it can never be completed by means of 
 a successive synthesis." Or again, " The true transcendental 
 concept of infinity is, that the successive synthesis of units 
 in measuring a quantity can never be completed."^^ For Kant, 
 then, the infinite is simply and literally the endless. 
 
 Another definition which is of considerable historical im- 
 portance is that of Bolzano. Professor Keyser paraphrases it 
 as follows :^^ " Suppose given a class C of elements. Out of 
 these suppose a series is formed by taking for first term one 
 of the elements, for second term two of them, and so on. Any 
 term so obtained is itself a class of elements, and is defined as 
 finite. Now either the process in question will exhaust C or 
 it will not. If it will, C is itself demonstrably finite ; if it will 
 not, C is defined to be infinite." Bolzano is recognized as the 
 initiator of the movement which led to the formulation of the 
 much-heralded " New Infinite " ; and Keyser tells us in the 
 article from which the above excerpt has been taken that Bol- 
 zano's definition, although perhaps not so convenient in the 
 actual practice of the mathematician, is in principle exactly 
 equivalent to that of Dedekind. However this may be, it is 
 clear that Bolzano's definition is exactly equivalent to that of 
 Kant. The difference between the two is formal only. Kant 
 employs the method of addition; Bolzano that of subtraction. 
 
 95 Kritilc der Beinen Vemunft, A, 426 and 432. (Mueller's translation, 
 pp. 344, 348.) 
 
 9^ Journal of PhUosophy, etc., I, 33. 
 
66 The Argument for a Finitist Theology. 
 
 The former is thinking of the completion of a somewhat that 
 exists only as a scheme or plan ; the latter is thinking of the 
 depletion of an already existing class of elements. Yet the 
 fundamental thought is the same in both: that which is in- 
 finite is endless; and because it is endless, it is impossible 
 either to construct anything so great as to equal it, or to take 
 away from it anything so great as to exhaust it. 
 
 Let us now examine the "new" definition of infinity as it 
 has been formulated by Dedekind. " A system S is said to be 
 infirdte when it is similar to a proper part of itself.'' As a 
 first step in my argument that this infinite is only the old 
 infinite in a new suit of clothes, I shall show that whenever a 
 series is found which is " similar to/' that is to say, in one-to- 
 one correspondence with, a proper part of itself, the series in 
 question may he shown to he in several other kinds of corre- 
 spondence with the same part; in fact, any sort of corre- 
 spondence that one pleases to look for may be discovered ; and, 
 furthermore, any scheme or plan of correspondence may he 
 shown to he just as rigidly determined hy law as any other — 
 and specifically, as the scheme of one-to-one correspondence, 
 which the partizans of the "New Infinite" have too hastily 
 assumed to be the relation in which the two series eternally 
 stand. 
 
 Consider as a typical case the series of even numbers, 
 which, by definition, is a proper part of the series of whole 
 numbers, and yet is required to stand in one-to-one corre-; 
 spondence with that series, by the law that each of its terms is 
 a number twice the corresponding term of the series of whole 
 numbers. This series illustrates the " similarity " of a system 
 to a proper part of itself; and, therefore, by Dedekind's defi- 
 nition, is infinite. But we find that any other correspondence 
 than the one-to-one may be seen, if we wish to see it. This 
 may be exhibited thus : 
 
 (F) 1, 2, 3, 4, 5, 6, ••• 
 "■■ (P) 2, 4, 6, 8, 10, 12, ••• 
 
11. 
 III. 
 
 IV. 
 
 Theology and the ''New Infinite/' 57 
 
 {W) 
 
 {P) 
 
 (If) 
 
 {P) 
 
 {W) 1,2, 3,4, 5,6, 7,8, 
 
 (P) 2,4,6, 8,10,12, 14,16,18, 20,22,24. 
 
 1, 
 
 2, 
 
 3, 4, 
 
 5, 
 
 2,4, 
 
 6,8, 
 
 10,12, 14,16, 
 
 18, 20, 
 
 1,2, 
 
 3,4, 
 
 5,6, 7,8, ••• 
 
 
 2, 
 
 4, 
 
 6, 8, ••• 
 
 
 Case I is the case which has been supposed to be the situ- 
 ation. In the other three cases we have respectively a one-to- 
 two, a two-to-one, and a two-to-three correspondence. Now 
 these other sorts of corresipondence are determined by clear 
 and definite rules, of exactly the same kind as, although a little 
 more complicated than, the rule which determines the one-to- 
 one correspondence. In Case II, let the rule be, that the sec- 
 ond of the two terms paired with any one term of the whole 
 series shall be four times that term ; in Case III the second of 
 the two terms of (W) is the same number as the one term of 
 (P) with which the two terms of (W) are bound up; in IV 
 every two terms of (W) are bound up with three of (P), and 
 the rule determining the correspondence is, that the last term 
 of any given group of (P) shall be three times the last term 
 of the corresponding group of (W). Now it is necessary to 
 insist that the (P) of I, of II, of III, and of IV is exactly 
 the same series. The "proper part," 2, 4, 6, 8, 10, 12, 14, 
 16, •••, is the "proper part" that is considered in each case. 
 It has been shown, then, that the whole series stands to this 
 proper part in these various relations of correspondence m 
 exactly the same sense in which it stands to it in the relation 
 of one-to-one correspondence. 
 
 The proof that this is true of any proper part of the series 
 of whole numbers that one may choose to consider, as for ex- 
 ample, the series of multiples by 3, 4, etc., or of squares, cubes, 
 etc., of the terms of the natural series of numbers, must be 
 left to the ingenuity and patience of the reader.^^ He will 
 
 87 In the typewritten copy of this dissertation, which may be found in 
 the library of the Johns Hopkins University, I have considered these and 
 other series in considerable detail, and have suggested formulae for several 
 
68 The Argument for a Finitist Theology. 
 
 find that the correspondence of a whole and a proper part o£ 
 itself, which has been taken as the essential notion in the 
 "new" definition of infinity, turns out, when more closely 
 scrutinized, to be a nose of wax ; it can be bent in any direc- 
 tion that one pleases. 
 
 How then shall we interpret Dedekind's definition, in the 
 light of our examination of these examples of the relation of 
 one-to-one correspondence of whole and part ? "A system S is 
 infinite if it is similar to a proper part of itself." Does this 
 mean (1) That the whole and the proper part in question are 
 in one-to-one correspondence, and in no other, or (2) that the 
 whole is in one-to-one correspondence with a proper part of 
 itself, but is also related to the same part in accordance with 
 other schemes of correspondence? 
 
 If the former interpretation is correct, then, so far as I am 
 aware, no genuine example of an infinite system has ever been 
 adduced. At any rate, no example of an infinite system is re- 
 vealed by an examination of the mutual relations of the various 
 series of cardinal numbers. If this is the meaning of the 
 definition, the class of all classes each of which is " similar " 
 to a proper part of itself is a class without any members; for 
 we have found that in every case where a one-to-one corre- 
 spondence is discoverable, correspondences of other sorts are 
 also discoverable. 
 
 On the other hand, if the latter is understood to be the 
 meaning of the definition, if the whole and its proper part are 
 in a relation of one-to-one correspondence, and also in rela- 
 tions of one-to-two correspondence, two-to-three correspond- 
 ence, etc., then the definition is not new, but is logically iden- 
 tical with or at all events necessarily implies the old definition 
 of the infinite as the endless; for any endless series is inex^ 
 haustihle, and, between two inexhaustible collections, it is al- 
 ways possible to exhibit a one-to-one correspondence, or any 
 sort of correspondence that one chooses to look for, inasmuch 
 
 types of proper parts, by the use of wMcli an "m-to-n. correspondence ' ' 
 (m and n being any whole numbers) may be determined between the 
 series of whole numbers and any given proper part. 
 
Theology and the "New Infinite/' 59 
 
 as, however far the pairing of terms or the correlation of 
 groups may be carried, there can never be any dearth of part- 
 ners or of groups of terms in either collection. 
 
 We should expect, then, that the logical absurdity found by 
 Renouvier in the conception of a "realized infinite" would 
 not be removed by so simple an expedient as the re-phrasing 
 of the definition of infinity. The creators of the " E"ew In- 
 finite " have indeed " taken the bull by the horns,"^^ and have 
 sought to escape the self-contradiction lurking in the notion 
 of infinity by making this very self-contradiction the heart 
 and center of their definition. But this does not remove the 
 contradiction. Although it has been sugar-coated, it is still 
 there ; and it is an obvious, though not infrequently neglected, 
 logical requirement that, to quote the words of Poincare, " in 
 defining an object we affirm that the definition does not imply 
 a contradiction.''^^ 
 
 Now when Dedekind speaks of the endless series of cardinal 
 numibers as a system, he tacitly imports the notion of finitude 
 into his definition of infinity. For we naturally think of a 
 system as a whole, a somewhat that is completely given. The 
 self-contradiction appears even more clearly when we consider 
 the phraseology of Cantor. His " infinite aggregate " is con- 
 ceived as a " totality." Thus his first example of an infinite 
 or transfinite aggregate is the " totality of finite cardinal num- 
 bers."^^ But as he himself speaks of "the unlimited series 
 of cardinal numbers,"^^ it is clear that he has fallen into a 
 self-contradiction, or else that in his usage the term " totality " 
 is not to be understood in the same sense as in the arguments 
 of the neo-criticist school. For, if the series of numbers is 
 unlimited, what right have we to speak of it as a whole or a 
 totality 9 If the word "totality" is understood in the sense 
 in which it is employed by Renouvier and Pillon, its use in a 
 definition of the number "Aleph-zero" would constitute a 
 
 88 James, Problems of Philosophy, p. 176, 
 
 89 Science et MSthode, p. 162. 
 
 90 The Theory of Transfinite Numbers, p. 103. 
 
 91 Ibid., p. 99. 
 
60 The Argument for a Finitist Theology, 
 
 begging of the whole question which is at issue between the 
 finitists and the infinitists. If, however, when Cantor speaks 
 of a "totality," he means no more than that the collection or 
 series which he denotes by the term is determinate (that is, is 
 so defined that it is in principle possible to distinguish it from 
 every other collection or series and always possible to tell 
 whether or not it includes any given term or collection of 
 terms), then such a "totality" may be infinite in the old 
 sense, that is to say, it may be endless. For example, we can 
 always tell whether or not a given number belongs to the series 
 of even numbers or to the series of odd numbers; and, inas- 
 much as these series are thus logically distinguishable, there 
 is a sense in which they are definite and thinkable unities; 
 yet each of these series is endless, because, by the very law of 
 its formation, however far it is continued, we must needs look 
 for more and still more terms. Such determinate but endless 
 series are, indeed, examples of Renouvier's " indefinite." But 
 in Renouvier's terminology an "endless totality" would be a 
 contradiction in terms. That is why a " realized infinite " is 
 logically impossible. An infinite that was realized, a some- 
 what actually existing and not merely a scheme or plan in 
 process of realization, would be a totality in the sense that no 
 part of it would be wanting; and yet as infinite it would be 
 endless or unfinished. 
 
 There may be, and no doubt are, many logically distinguish- 
 able types of endless series; and accordingly it is perfectly 
 legitimate for the mathematician to study these various types, 
 and even to call them transfinite numbers if he wishes to em- 
 ploy that terminology, and is not himself led astray by it. 
 But unless we forget this ambiguity in the meaning of the 
 term " totality," it is impossible to suppose that the definition 
 of " transfinite number " has made any contribution whatever 
 toward the solution of the logical difficulty found by the school 
 of Renouvier in the conception of a " realized infinite." 
 
 3. The New Infinite and Monistic Idealism. — ^We must 
 next inquire what bearing, if any, these recent discussions of 
 
Theology and the "New Infinite/' 61 
 
 the definition of infinity have upon the doctrine of the monistic 
 Absolute. Monistic idealism, I have said, implies the con- 
 ception of infinity in both senses. In our second chapter we 
 saw that God cannot be conceived without contradiction to be 
 infinite in the first sense — he cannot be regarded as including 
 all reality ; and now it is in order to consider the dependence 
 of monistic idealism upon the notion of infinity in the second 
 sense — upon the mathematical or numerical infinite. There 
 are two ways in which monistic idealism implies the notion of 
 a realized infinite: 
 
 {a) The Absolute is said to be in possession of all time in 
 an Eternal Now, " The real world of our Idealism has to be 
 viewed by us men as a temporal order. For it is a world where 
 purposes are fulfilled. . . ." But "this same temporal order 
 is, when regarded in its wholeness, an Eternal Order. . . . 
 The whole real content of this temporal order ,., is at once 
 
 known, i. e., is consciously experienced as a whole, by the Ab- 
 solute."92 
 
 This may perhaps mean that the temporal order is an " il- 
 lusion of the partial view," that it belongs to the realm of mere 
 appearance and not to that of genuine reality. We have 
 already pointed out the difficulty of attaching any meaning to 
 the proposition that time is illusory,^^ and need not repeat 
 what has already been said. The sentences just quoted from 
 Professor Royce are capable of another interpretation. When 
 he says that the whole content of the temporal order is known 
 at once, he himself explains the phrase at once as equivalent 
 to in the same present, Now the present, he tells us, is some- 
 times understood to be the mathematical line which separates 
 the future and the past, and as a mere boundary to be without 
 extent. Again the present " is any one temporal event, in so 
 far as it is contrasted with antecedent and subsequent events, 
 and in so far as it excludes them from coexistence with itself 
 in the same portion of any succession." In the third place, 
 
 s^Boyce, The World and the Individual, II, 134 and 138. 
 »3 Chapter II, Section 2 (6). 
 
62 The Argument for a Finitist Theology. 
 
 the present " is any portion of real time with all its included 
 events, in so far as there is any reason to view it as a whole, 
 and as known in this wholeness by a single experience."^* 
 When Koyce says, then, that the whole temporal order is 
 known ai once, his meaning ma/y he no more than that the 
 whole temporal order is a whole. All time 'is present to the 
 Absolute as a totum simuU^ 
 
 Here, however, we meet the difficulty of the realized in- 
 finite, of the totality of the unlimited. Royce seeks to justify 
 the conception of the totum simul by regarding it as analogous 
 to the "specious present" of the individual mind. We per- 
 ceive the words of a phrase or a brief clause like " The curfew 
 tolls the knell of parting day," not merely as successive, but 
 also all at once, as a whole. In the same way the Absolute, 
 thinks Royce, knows all the events of all time at once or as a 
 whole. Many questions might be asked about the analogy of 
 the " specious present " and the " totum simul." But we can 
 not ask them here. I merely wish to stress the point that the 
 idealistic doctrine of an Eternal l^ow must stand or fall with 
 the logical possibility or impossibility of the realized infinite. 
 For all time includes the unlimited past and the unlimited 
 future ; and how can that which is unlimited be a whole ?^^ 
 
 (&) The argument for monistic idealism depends upon the 
 assumption that a thing exists "just in so far as there is ex- 
 perience of its existence."^''' This principle is a special appli- 
 cation of the more general principle of the "intemality of 
 relations." If a "thing" is constituted by the relations in 
 which it stands, then the attempt to define anything must in- 
 evitably lead to an infinite regress ; and the infinite regress is 
 logically intolerable. This is the burden of Mr. F. H. Brad- 
 ley^s ^^ Appearance and Reality.'' The attempt to define any 
 of the ordinary categories of thought, as substance, quality, 
 
 9* The World and the Individual, 11, 140. 
 
 95 ihid., p. 141. 
 
 96 Compare Chapter V, Section 2. 
 
 97 The Conception of God, p. 43. 
 
Theology and the ''New Infinite/' 63 
 
 relation, the self, etc., brings us to no final or satisfactory con- 
 clusion, but merely produces an endless series. 
 
 Critics of a realistic temper may cut the knot by denying 
 the principle of the internality of relations. Royce, however, 
 is committed to this principle, and therefore seeks to avoid the 
 difficulty by maintaining that the " infinite regress " is not a 
 fatal defect. It is fatal, he holds, only when you take it term 
 by term, i. e.j successively; if you assume the infinite multi- 
 tude or series of terms to be given all at once in one single 
 purpose or plan, the infinity becomes harmless. 
 
 How then is it possible to take the " infinite regress " all at 
 once? The problem, thinks Royce, is solved for us in Dede- 
 kind's definition of infinity. Thus the 'New Infinite becomes 
 a main support of monistic philosophy. Idealism implies an 
 infinite system, and the discovery of Dedekind permits us to 
 think of the infinite not merely as endless but as an instance 
 of self-representation, "Whatever considerations make for 
 an idealistic interpretation of reality, become considerations 
 which also tend to prove that the universe is an infinitely 
 complex reality, or that a certain infinite system of facts is 
 real. For idealism, in defining the Being of things as neces- 
 sarily involving their existence for some form of knowledge, 
 is committed to the thesis that whatever is, is ipso facto known 
 (e. g., to the Absolute). . . . Since, however, the fact world 
 even for idealism contains many aspects (such as the aspects 
 called feeling, will, worth, and the like) which are not iden- 
 tical with knowledge, although for an idealist they all exist 
 as known aspects of the world, it follows that for an idealist 
 the facts which constitute the existence of knowledge are 
 themselves but a part and not the whole of the world of facts ; 
 yet, by hypothesis, this part, since it contains acts of knowl- 
 edge corresponding to every real fact, is adequate to the whole, 
 or in Dedekind's sense is equal to the whole. Hence the 
 idealist's system of facts must, by Dedekind's definition, be 
 infinite; or for the idealist the real world is a self-represen- 
 tative system, and is therefore infinite."^^ 
 
 »s Ihid., 40. 
 
64 The Argument for a Finitist Theology. 
 
 Moreover, if we try " to conceive . . . the universe in real- 
 istic terms as a realm v^^hose existence is supposed to be inde- 
 pendent of the mere accident that anyone does or does not 
 know or conceive it, . . . it is possible to show that this sup- 
 posed universe has the character of a self-representative sys- 
 tem,'' that is to say, is infinite. For, " if the supposition is 
 itself a fact, then> at that instant, when the supposition is 
 made, the world of Being contains at least two facts, namely, 
 F and your supposition about i^." Call the supposition /. 
 Then your universe is at least F -{- f. But, " this universe as 
 thus symbolized, has not merely a twofold, but a threefold con- 
 stitution. It consists of F and of f, and of their +? ^- ^'^^ ^^ 
 the relation as real as both of them, which we try to regard as 
 non-essential to the being of either of them, but which for that 
 very reason, has to be supposed wholly other than themselves, 
 just as they are supposed to be different from each other."^^ 
 
 " Hereupon, of course, Mr. Bradley's now familiar form of 
 argument enters with its full rights . . . the -j- is linked to 
 / and to F and the ^endless fission' unquestionably ^break:s 
 out/ The relation itself is seen entering into what seem new 
 relations."i<^^ 
 
 Thus Koyce agrees with Bradley that every form of real- 
 istic being " involves such endless or self-representative con- 
 stitution " ;^^^ that, in particular, realistic being breaks down 
 upon the contradictions resulting from this constitution. 
 Royce, however, does not accept the view "that to be self- 
 representative is as such to be self-contradictory." This con- 
 clusion, he thinks, is obviated by the help of the definition of 
 infinity as a self-representative system. The notion of "self- 
 representation" permits us to take an infinite multiplicity all 
 at once. 
 
 Royce illustrates his meaning in various ways. Some manu- 
 facturers have ingeniously used a picture of the package in 
 which their product is contained as a trade-mark, and have 
 
 99 The World and the Individual, p. 538 f . 
 loojfetU, p. 540. 
 101 JMd., p. 542. 
 
Theology and the ''New Infinite." 66 
 
 then placed this trade-mark as a label upon the package. But 
 the package thus labeled with its own picture, inevitably re- 
 quires the picture to contain for accuracy's sake ... a pic- 
 ture of itself. "^^^ Or suppose that somewhere upon the soil 
 of England there is a map of England. Suppose, further, 
 that this map is a perfect representation, indicating every de^ 
 tail of the surface of England. It is clear that this map must 
 contain a map of itself. 
 
 The attempt actually to construct an accurate picture or a 
 perfect map of the sort just described would indeed require 
 an endless process and therefore be impossible of fulfilment; 
 but, says Royce, the plan itself is given all at once. " Math- 
 ematically regarded the endless series of maps within maps, 
 if made according to such a projection as we have indicated, 
 would cluster about a limiting point, whose position would be 
 exactly determined. Logically speaking their variety would 
 be a mere expression of the single plan, * Let us make within 
 England and upon the surface thereof, a precise map, with all 
 the details of the contour of its surface.' . . . The one plan 
 of mapping in question necessarily implies just this infinite 
 variety of internal constitution. . . . We are not obliged to 
 deal solely with processes of construction as successive in order 
 to define endless series."^^^ " To conceive the true nature of 
 the infinite, we have not to think of its vastness, or even nega- 
 tively of its endlessness; we have merely to think of its self- 
 representative character."^^^ 
 
 Does this idea of "self-representation" escape the dif- 
 ficulty of the " endless regress " ? The issue thus raised is in 
 principle the same as that involved in the conception of the 
 "totality" of an unlimited series; yet inasmuch as we have 
 taken Professor Royce as the typical exponent of monistic 
 idealism it seems proper to devote a few paragraphs to a dis- 
 cussion of the illustration which he himself employs. "A 
 map of England, contained within England, is to represent 
 
 102 The World and the IndividuaL, pp. 506 f . 
 108 Eibhert Journal, I, 35. 
 
66 The Argument for a Finitist Theology. 
 
 down to the smallest detail every contour and marking, natural 
 or artificial, that occurs upon the surface of England."^^* The 
 perfection of the map requires that there be a "one-to-one 
 correspondence, point for point, of the surface mapped and 
 the representation." In other words, if A is the surface 
 mapped and A' the representation, "for every elementary de- 
 tail of A, namely, a, h, c, d (be these details conceived as points 
 or merely as physically smallest parts; as relations amongst 
 the parts of a continuum, or as relations amongst the units of 
 a mere aggregate of particles), some corresponding detail, a', 
 &', c', d% could be identified in A\ in accordance with the 
 system of projection used." 
 
 Let us consider first the notion of perfect representation 
 where the copy is assumed to be smaller than the original, and 
 then that of perfect seZ/-representation. 
 
 In the opinion of Royce, " that a smaller picture should be 
 a perfect representation of a larger object is a perfectly de- 
 finable ideal."^^^ But that, even as an ideal, it is not a self- 
 contradictory conception is by no means clear. If only de- 
 tails that are visible to the naked eye are pictured, there is no 
 difficulty ; for a microscope may be used to read the map. But 
 if the object to be pictured is itself viewed under the micro- 
 scope, and all the details thus visible are to be represented, it 
 is clear that if the map or picture were much smaller than the 
 original, exact legible representation would be impossible. If 
 now it be replied, as Royce would perhaps reply, that the 
 quality of being legible is irrelevant to the notion of perfect 
 mapping, that all that is meant by it is, that for every detail 
 of the original there shall be a corresponding detail in the 
 copy, then it is clear that, if both original and copy are as- 
 sumed to be made up of a finite number of indivisible units, 
 such perfect mapping is impossible, unless the copy be as- 
 sumed to possess a finer texture than the original (i, e., to 
 contain a greater number of indivisible units to the square 
 
 104 World and Individual, I, 503 ff. 
 
 105 Hihhert Journal, 1, 27. 
 
Theology and the ''New Infinite/' 67 
 
 inch). If, however, there is assumed to be no difference in 
 texture, the points or ultimate units of which the material of 
 the map or picture is composed must be infinitely numerous. 
 
 In other words, the perfect representation of any object on 
 a smaller scale implies, either that the copy, although smaller, 
 contains exactly as many ultimate units as the original, or 
 else that the copy is a continuum^ or at least a compact collec- 
 tion of points. If we assume the notion of the continuum, 
 there is, then, no diflSculty in the idea of a perfect represen- 
 tation of a larger by a smaller surface. Indeed, if we assume 
 that space is continuous or compact, such representation is an 
 everywhere-present fact ; because, for every point in a solid or 
 a surface, there must then be assumed to be a point in any 
 other solid or surface, however small the latter may be. 
 
 It is clear, then, that the idea of an absolutely perfect repre- 
 sentation, even without the added notion of 5eZ/-representa- 
 tion, requires the conception of an infinite multiplicity of ele- 
 ments, unless we make the above-mentioned assumption con- 
 cerning the finer texture of the material of the copy. It is 
 indeed essential to Royce's argument that the map be drawn 
 upon the soil of England, and therefore be an example of self- 
 representation ; but this is not essential to the idea of the map 
 as an illustration of infinity. All that is required is the as- 
 sumption that for every point in the surface of England there 
 shall be a point on the map, however small the map is drawn. 
 But as I have already remarked, this follows from the notion 
 of the continuum. If two surfaces are both assumed to be 
 continuous, then, however large the one may be and however 
 small the other, for every point in the one there is a point (or, 
 for that matter, and this destroys the notion of a definite 
 representation, there are two, three, or as many as you please) 
 in the other. Instead, then, of supposing a map within a map, 
 and so on forever, we can just as well suppose the original 
 map without the loss of any detail to become smaller and 
 smaller without limit. On either assumption the perfect map- 
 ping, even of only the visible markings of England's surface, 
 
68 The Argument for a Finitist Theology. 
 
 would imply the notion of an infinite multitude of points in 
 any designated portion of the surface upon which the map is 
 drawn. 
 
 In the case of s62/-rep resent ation, or rather of representa- 
 tion by a part of that which is represented, it is obvious that 
 the notion of infinite multitude must be assumed ; for here we 
 have representation on a smaller scale, and there is no dif- 
 ference in the texture of the original and the copy, or at least 
 of part of the original and the copy. We find then that we 
 have been traveling in a circle. In an effort to avoid the end- 
 less regress we have defined a conception of self-representation, 
 only to find, when we examine our conception a little more 
 closely, that it contains the very notion which it was designed 
 to escape. If, then, the notion of an endless regress is self- 
 contradictory, that of self-representation, or of a purpose that 
 is infinitely rich in implications, is likewise self-contradictory. 
 
 We conclude, therefore, that the " discovery " of the so- 
 called ^ew Infinite leaves the problems of theology exactly as 
 it found them ; and that the apparent bearing of the new con- 
 ception of infinity upon these problems is the result of ai 
 double use of such terms as " totality " and " equality."^^^ 
 
 106 The reader may be interested in Boyce 's use of the New Infinite to 
 explain the relation of the Absolute to the Particular Self {Bibhert Jour- 
 nal, 1, 44) and in Keyser's attempt by its aid to defend the doctrine of 
 the Trinity and that of the divine omniscience {The New In-finite and the 
 Old Theology, pp. 85 ff.). It seems clear that both writers are merely 
 playing on the word equality. 
 
 Professor Eoyce suggests that *'a wholly new light" is thrown *'upon 
 the possible relations of equality which, in a perfected state, might exist 
 between what we now call an Individual or a Created Self and God as the 
 Absolute Self. Perhaps a being, who, in one sense, appeared infinitely 
 less than God, or who at all events was but one of an infinite number of 
 parts within the divine whole, might, nevertheless, justly count it not rob- 
 bery to be equal to God, if only this partial being by virtue of an im- 
 mortal life or of a perfected process of self-attainment, received in the 
 universe somewhere an infinite expression." When we recall, however, 
 that to be 'equal' here means no more than to be of the same **Mdchtig- 
 Jceit,*' i. e., to be in the relation of one-to-one correspondence, it is far 
 from clear that the "infinite expression" of the partial being is of any 
 spiritual or ethical significance. 
 
Theology and the *' New Infinite/' 69 
 
 Professor Keyser, who is by profession a mathematician, tells us that 
 it is a great error to suppose that the whole-part axiom is universally 
 valid. It ought rather to be considered as a ''logical blade" which 
 divides the finite from the infinite. Some of the difficulties of theology, 
 Professor Keyser assures us, have been caused by assuming that this 
 axiom applies to infinites. 
 
 Thus the doctrine of the Trinity has been pronounced absurd, because 
 it implies that one infinite is composed of three infinites, and that each of 
 the three is equal not only to each of the others but to the whole which 
 they jointly constitute. But this objection, says Keyser, erroneously as- 
 sumes that the whole-part axiom holds for infinites. He illustrates the 
 logical possibility of the conception of a One which is also Three by 
 means of the relation of the number-system to certain of its parts. Let 
 M be the manifold of all rational numbers, E of the even numbers, 
 of the odd numbers, and F of the rational fractions; then it is evident 
 that E, 0, and F are proper parts of M; and also that a one-to-one corre- 
 spondence is discoverable between M and each of these parts taken sep- 
 arately. Therefore by Dedekind's definition, M, E, 0, and F are all in- 
 finite manifolds. "What is important is now obvious," says Keyser. 
 "It is that we have here three infinite manifolds, E, 0, F, no two of 
 which have so much as a single element in common, and yet the three 
 together constitute one manifold M exactly equal in wealth of elements 
 to each of its infinite components." The application to the theological 
 Trinity is of course evident. 
 
 An obvious objection here presents itself. One might naturally inquire 
 why there are just three rather than two or four persons. Indeed the 
 mathematical analogy suggests an infinity, or at least a very large number, 
 of constituent persons; and, as we have seen, Royce holds that the Abso- 
 lute may be conceived without contradiction to include a multitude, and, 
 in fact, an infinite multitude, of selves. This objection, however, misses 
 Keyser 's point, which is, not that the doctrine of the Trinity can be 
 mathematically demonstrated, but merely that, if on some other ground 
 we believe that the One is Three and the Three are One, the conception is 
 not logically absurd. 
 
 It may be questioned, however, whether the aid thus so kindly prof- 
 fered by Mathesis to Theology will be very enthusiastically received. On 
 the one hand, Trinitarians like Cardinal Newman, who seems to have liked 
 the doctrine all the more on account of its incomprehensibility (see New- 
 man, The Grammar of Assent, pp. 124 £f.), may even be disposed to 
 resent this attempt to make their cherished formula as plain and clear as 
 the multiplication table or the rule of three; for, if the Trinity is not in- 
 comprehensible, half the merit of assenting to the ancient creeds will be 
 lost. On the other hand, adherents of the "new theology" who still con- 
 sider themselves Trinitarians have learned to interpret the ancient for- 
 mulae in such a way as to remove the contradiction; and therefore do not 
 recognize the need of a demonstration of the eoneeivability of a numer- 
 ical Trinity in Unity. 
 
70 The Argument for a Finitist Theology. 
 
 The "new'' conception of infinity is also employed by Professor Keyser 
 in defense of the doctrine of the divine omniscience. Objection has fre- 
 quently been made to this doctrine on the ground that it seems to abolish 
 human freedom and to make God responsible for human sin. Keyser sug- 
 gests that we may preserve the dignity of omniscience while giving up 
 omniscience in the strict sense of the term. Suppose the knowledge of all 
 events to include an infinite number of knowledge-elements. Now suppose 
 this infinite manifold to be divided by a plane which in our imaginative 
 construction represents the present instant. Then it is evident that there 
 is a one-to-one correspondence between the manifold of elements either be- 
 fore or behind this boundary and the undivided manifold. In other words, 
 the knowledge of the past alone is just as infinite as the knowledge of 
 the events of all time. Accordingly, even if God is assumed to have no 
 knowledge of undetermined future events, His knowledge is nevertheless 
 infinite; and, in the phraseology of the partizans of the New Infinite, 
 God may still be said to possess the dignity or MdchtigJceit of omnis- 
 cience. The same argument is easily made to fit the case of omnipotence 
 or of omnipresence. In an infinite world the Deity might then be infinite 
 in knowledge, power, etc., without being omniscient, omnipotent, or omni- 
 present. One may, however, be sufficiently "tough-minded" to inquire 
 just what is the value of the word * ' infinite ' ' and the phrases ' * dignity of 
 omniscience," etc.? Certainly no one would hold that merely to be in- 
 finitely rich in numerical elements is a quality which is of any ethical 
 value; for, if it were, then any portion of a continuum would possess this 
 transcendent dignity. 
 
VII. 
 
 Concluding Reflections on Finitist Theology. 
 
 1. A Recapitulation of the Argument for the Divine Fin- 
 itude. — ^We have been led to conclude that God is finite in both 
 senses of the word — ^that he is not infinite either in the sense 
 of including or possessing an infinite number of elements, or 
 in the sense of including or controlling the whole of reality. 
 Our position is therefore completely opposed to that of monis- 
 tic idealism, according to which God or the Absolute is infinite 
 in both these senses. It may be well to give a summary re- 
 statement of the reasonings which have led us to this con- 
 clusion. 
 
 {a) As Royce himself has shown, his conception of the 
 Absolute presupposes the notion of the realized infinite. But 
 the conception of a realized infinite is a contradiction in terms ; 
 for that which is infinite or endless is not realized or complete. 
 And the " new " conception of infinity does not escape the log- 
 ical defect of the " old " ; for, as we have seen, the attempt to 
 get rid of the self-contradiction by including it in the defini- 
 tion is not satisfactory: the contradiction, though concealed 
 from view, still remains.^ ^"^ 
 
 (6) The Absolute is said to experience all in an "Eternal 
 Now " ; but the notion of an experience which is itself " time- 
 less" while yet including experiences of temporal relation is 
 self-contradictory.^^® Moreover the "Eternal Now" would be 
 a realized infinite, and on that account, too, logically impos- 
 sible.io^ 
 
 (c) The Absolute is an all-containing mind and possesses 
 
 lOT Chapter VI. 
 
 108 Chapter II, Section 2 (6). 
 
 io» Chapter VI, Section 2. 
 
 71 
 
72 The Argument for a Finitist Theology, 
 
 an all-inclusive experience. Now there can be no all-inclusive 
 experience; for it is psychologically impossible for certain of 
 the experiences of the individual mind, especially such as are 
 conditioned by limitation and isolation, to be identical parts 
 of an all-inclusive mind. For such a mind, by virtue of the 
 fact that it is all-inclusive, is unable to have these experiences. 
 And yet if it does not have them, it is not all-inclusive. ^^^ 
 
 (d) The identification of God with the Absolute is vetoed 
 by the ethical difficulty which besets every doctrine of the 
 divine omnipotence. God is good; and, in a world such as 
 ours, no good being can be omnipotent. llTot only does this 
 objection hold against the conception of the Absolute, but 
 against that of a Mind that possesses a hnowledge about all 
 things without including everything as an identical part of 
 its own experience; for, if a Being were omniscient even in 
 this restricted sense, such a Being would be, if not in Royce's 
 phrase "world possessing,'' yet certainly world-controlling, 
 that is to say, omnipotent.^^^ 
 
 (e) The theory of monistic idealism is unsatisfactory as a 
 practical philosophy, inasmuch as it logically implies a life of 
 acquiescence rather than of action.^ ^^ 
 
 (/) Considered as the equivalent of or as a substitute for 
 the traditional idea of God, the Absolute is religiously inade- 
 quate. It lacks worth, and does not satisfy man's craving 
 for fellowship with a Person}^^ 
 
 On the other hand, the theory of a Supreme Being who is 
 limited in knowledge and power is logically unobjectionable, 
 is not inconsistent with the presence of evil in the world as it 
 now is, implies the genuineness of human cooperation with 
 God in the contest with evil, and offers man an Object worthy 
 of his worship, a Person who desires his love. 
 
 3. The Difficulties of Finitist Theology. — Let us not, how- 
 ever, assume too hastily that finitist theology is completely 
 
 110 Chapter H, Section 2 (6). 
 
 111 Chapters III and IV. 
 
 112 Chapter II, Section 2 (c). 
 113 Chapter II, Section 2 (a). 
 
Concluding Reflections on Finiiist Theology, 73 
 
 satisfactory as a religious doctrine. Several questions present 
 themselves : 
 
 (a) Is Finitist Theology a Monotheism or a Polytheism? — 
 If God is the whole of existence, or even if he is assumed to 
 be distinct from, or only a part of, the universe but yet om- 
 nipotent, there can be no doubt that there is but one God ; for 
 there can not be more than one whole of existence or more 
 than one onmipotent. If, however, we maintain that God is 
 only a part of being, and that his power is so limited that some 
 parts or aspects of being are not subject to his control, the 
 proposition that there is but one God is far from self-evident. 
 
 For most of us, indeed, the issue of polytheism versus 
 monotheism does not present a " live option." It does not ap- 
 pear to have been a live issue even for William James. 
 Charles Renouvier, however, declines to decide one way or 
 the other, and, indeed, is very favorably disposed toward poly- 
 theism. " The doctrine of unity," he says, " submits all the 
 beings of the world to a royal authority which varies from the 
 most absolute autocracy to a government tempered by a meas- 
 ure of liberty conceded to the subjects."^ ^* On the other hand, 
 the doctrine of a plurality of divine beings appears to Renou- 
 vier more accordant with republicanism. " Polytheism is the 
 plurality of powers in the unity of direction." The same con- 
 siderations which make for a belief in immortality lead Renou- 
 vier to look with favor upon the conception of a plurality of 
 Gods. He thinks it improbable that all personal beings but 
 one should be such as to be included in the class of men ; and, 
 like the ancients, supposes that men may be raised to the rank 
 of Gods."^ 
 
 One of his interpreters remarks that, though one may at 
 first be surprised and possibly shocked by Renouvier's evident 
 liking for polytheism, the saint-worship of the Roman Cath- 
 olic Church would readily suggest such a doctrine. Further- 
 more, "the theology of the Councils of Nicsea, of Constanti- 
 
 11* Eenouvier, Paychologie rationelle, Vol. Ill, p. 259. 
 ii5 76id., pp. 255 f. 
 
74 The Argument for a Finitist Theology. 
 
 nople, of Chalcedon, aflSnri, and modem theologians still ac- 
 cept, the multiplicity of divine persons. The Christian Trin- 
 ity is not a doctrine of the divine nnity."^^^ 
 
 It is true that Kenouvier suggests that " this polytheism is 
 far from being irreconcilable with the unity of God; . . . 
 for the one God would then be the first of the superhuman 
 persons, rex hominum et deorumJ''^'^'^ It is, however, perfectly 
 conceivable that there should be a number of superhuman per- 
 sons all finite in power, and that none of them should be 
 "king." Indeed, to anticipate the theoretical doubt which is 
 discussed in the next section, if all the members of such a 
 pantheon, whether it were monarchical or democratic in its 
 organization, could be known to be good, it is not evident that 
 the polytheistic conception would be religiously unsatisfying. 
 However, as remarked above, the issue does not present a " live 
 option," and it will be better to assume, in the further discus- 
 sion, that there is but one God. 
 
 (&) Is the Supreme Being Good? — ^It is true that the log- 
 ical motive for the doctrine that God is finite is the desire to 
 save his goodness. Our argument has been, God is good; the 
 world is, in part, evil ; therefore God's power is limited. His 
 finitude is thus an inference from his perfect goodness ; but it 
 is evident that the argument cannot be reversed. The perfect 
 goodness cannot be inferred from the finitude of the Deity. 
 
 If we divest ourselves of our prejudices, and forget the 
 affinity of the words good and God, it is possible to conceive 
 the existence of a being who is immeasurably more powerful 
 than all others, and yet is not good. Such a Supreme Being 
 might be defined as Power plus Intelligence plus Conscious 
 Purpose. But the purpose toward which the power is directed 
 need not include any concern for the pains and pleasures or 
 the ideal values of humankind. As a man intent upon the ac- 
 complishment of some end goes his way, and does not even 
 notice the ant-hill which his hurrying foot has demolished, so 
 
 lie Arnal, Philosophie Beligeuse de Charles Benouvier, pp. 148 £. 
 117 Psychologic rationcllc, III, 255. 
 
Concluding Reflections on Finitist Theology. 75 
 
 the Supreme Purpose might seek its own fulfilment wholly 
 regardless of the hopes and wishes of the denizens of our 
 planet. A consciously purposive Power wholly uninterested 
 in the affairs of men is, accordingly, a logically possible con- 
 ception of God. 
 
 Even the addition to this conception of that notion of an 
 interest in human doings and sufferings which, I have said, is 
 not necessarily included in the universal purpose, does not 
 bring us at once to the Christian thought of a Father-God. It 
 may indeed fall far short of it. The interest of the Supreme 
 Power in human affairs might be entirely non-moral. It might 
 be an interest in mundane happenings as a spectacle. Such 
 a God might take pleasure in the happiness of his creatures, 
 and also in their pains and disappointments, in their sorrows 
 as well as in their joys. In short God as thus defined might 
 be a Supreme Setebos, like him of whom Caliban muses in 
 Browning's verse : 
 
 Thinketh such shows nor right nor wrong in Him 
 Nor kind, nor cruel: He is strong and Lord. 
 'Am strong myself compared to yonder crabs 
 That march now from the mountain to the sea; 
 'Let twenty pass, and stone the twenty-first, 
 Loving not, hating not, just choosing so. 
 
 If, now, we add to our conception of a Supreme Being the 
 notion of moral quality, there still remains a horrible and 
 repulsive possibility ; for moral quality may be bad as well as 
 good. The Supreme Power might be malevolent. 
 
 A reversal of the traditional theodicy is not inconceivable. 
 Indeed the very argument by which men have sought to prove 
 that this is the best might be employed with a few alterations 
 to prove that it is the worst possible world. The elements of 
 goodness which mar the perfection of absolute evil might be 
 said to be required to set off the evil by contrast; or the 
 Supreme Fiend might be supposed to be limited in his man- 
 agement of the universe by a sort of " iron law of wages " : a 
 certain amount of pleasure might be necessary to insure the 
 continuance of the pain-economy. 
 
76 The Argument for a Finitist Theology, 
 
 To be sure, no one takes such a possibility very seriously; 
 yet, from the standpoint of mere logic and cold facts, it is not 
 unthinkable. The goodness of God cannot be proved. It can 
 only be believed; that is, assumed as a working principle of 
 human life. And, unless this assumption is made, the doc- 
 trine of a finite God has no religious value. 
 
 (c) Does the God of Finitist Theology Exist? — In a dis- 
 cussion of the adequacy of the idea of God the existential 
 question can not be wholly ignored. It is true that the value of 
 the idea is not wholly dependent upon its objective reality ;^^^ 
 yet, if a man were convinced that the idea of God is merely 
 an ideal, then for him its value would be seriously impaired. 
 If the existence of God is to be proved, the demonstration will 
 have to consist in an exhibition of the evidences of his pres- 
 ence in the world. But no one will maintain that the argu- 
 ment from design establishes more than the prohahility of 
 God's existence. Moreover, if, without evidence of his 
 presence, we could become convinced of his existence, mere 
 existence would not be enough. An entity that does nothing 
 (although the thought of such an entity might avail to relieve 
 one's loneliness) would not be completely adequate. From this 
 point of view the question of the existence of God merges in 
 that of his power. 
 
 We have criticized monistic idealism on the ground that, 
 by reason of its doctrine of the eternal perfection of the 
 Whole, it tends to quietism, to the mood of the "moral hol- 
 iday." But there is danger of reaching a similar position 
 from the opposite direction. The finite God may be so limited 
 in our thought of him as to make it doubtful whether he can 
 in any significant sense be said to be supreme. Thus the same 
 modification that makes the traditional doctrine of God the- 
 oretically tolerable threatens to destroy its practical value. 
 For if men should be convinced that, while there is a God, 
 his power and intelligence are not adequate to the task of 
 world redemption, they would fall into despair; and nothing 
 
 118 Mill, Autobiography; Vaihinger, Die Philosophie des als Ob, 
 
Concluding Reflections on Finitist Theology. 77 
 
 so completely paralyzes action as despair. There is inspiration 
 for strong natures in the thought of cooperation with a God 
 who actually needs our help ; but not all are strong, and even 
 the strongest and most daring spirits have their hours of de- 
 pression, when they need to feel that there is sufficient power 
 on their side to assure the ultimate victory of the Eight. From 
 this point of view the question of God's existence is equivalent 
 to a question about the salvability of the world. It may, ac- 
 cordingly, be rephrased thus: Is there, in this world of ours, 
 sufficient power and intelligence in the service of good will, to 
 assure the realization and preservation of the values that wd 
 hold dear? 
 
 4. Finitist Theology and the Bight to Believe, — By Wil- 
 liam James finitist theology is combined with a doctrine of 
 the " will to believe." The existence of God can not be proved 
 by scientific methods of demonstration. Considered jas a 
 hypothesis it is, indeed, not inconsistent with the facts; but 
 neither is the contrary hypothesis. 'Now, says James, this is 
 a case where we ought to practise the will to believe. " Our 
 passional nature not only lawfully may, but must, decide an 
 option between propositions, whenever it is a genuine option 
 that cannot by its nature be decided on intellectual grounds."^^® 
 In other words, though James nowhere puts it in just this 
 way, we are at liberty to act as if we were certain of God' 9' 
 existence, even if we have no intellectual grounds, or have only 
 insufficient grounds, for certainty. 
 
 There are, however, obvious objections to this procedure. 
 It seems to encourage the all too common tendency to super- 
 ficial thinking, where one's own interests and prejudices are 
 involved ; and there appears to be a suggestion of intellectual 
 dishonesty in the proposal to believe when there is not sufficient 
 evidence to convince the reason. In my opinion, however, 
 these objections are based upon a failure to distinguish be- 
 tween different senses of the word " believe." It must be ad- 
 
 ii» The Will to Believe, p. 27. 
 
78 The Argument for a Finitist Theology. 
 
 mitted, I fear, that James himself is partly responsible for 
 these confusions. 
 
 There are at least three kinds of "believing.'' In the first 
 place, one may be said to believe when he feels that he knows. 
 Secondly, belief may be understood in a wholly practical 
 sense. One shows his faith by his works; and it is easy to 
 pass from this principle to the view that faith, or belief, is 
 the action which would normally accompany or result from 
 belief in the first sense. It is this second sense of believing, 
 the acting as if one knew, which James seems to have chiefly 
 in mind when he speaks of a " will to believe." 
 
 There is, however, a third sense of the word "believe," 
 which seems to be implied, though not clearly distinguished 
 from the others, in James's exposition. It differs from our 
 first sense in being without real or supposed theoretical jus- 
 tification; and from the second in being an affair of feeling, 
 rather than of will or action. If the first kind of believing 
 is the '^ feeling that one knows," and the second, "the acting 
 as if one hnew/' the third may be said to be "the feeling 05 
 if one knew/' 
 
 That this third kind of belief is psychologically possible 
 is a matter of everyday experience. Our feelings are seldom 
 quite appropriate to the theoretical situation. The passenger 
 on the railway train who is nervous and ill at ease because of 
 the fear of a wreck is permitting emotion to outrun the evi- 
 dence. But the same is true of the passenger who has no 
 feeling of anxiety whatever; for there is some danger. And, 
 while the probability of a wreck is not sufficiently great to 
 justify the fears of the one, it is not so small as to justify the 
 utter calm of the other. Belief, in the third sense, the feeling 
 as one would feel if one had theoretical knowledge which he 
 does not have, is thus illustrated by our usual freedom from 
 emotional disturbance on a rapidly moving train. We know 
 that a thousand and one things might happen, any one of 
 which might plunge us to almost instant death; we may be 
 theoretically persuaded that there are a given number of 
 
Concluding Reflections on Finitist Theology. 79 
 
 chances in ten million that we will on this particular day be 
 killed in a wreck ; we may even allow our minds to dwell upon 
 these chances of destruction ; and yet feel as we should feel if 
 the chance were absolutely nil. 
 
 This sort of belief is even better illustrated in our social 
 relations. Here, too, the degree of certainty which we feel is 
 not usually the exact degree that would be logically appro- 
 priate to the situation. We cannot, prove that the bank will 
 not fail; that people are telling us the truth; that our best 
 friends will not play us false ; that the Causes to which we de- 
 vote ourselves are really worthy of our devotion. We can have 
 no intellectual certainty in regard to these matters; and yet 
 we not only act but also feel as we should act and feel if we 
 were intellectually certain. In a word, our faiths and loyal- 
 ties habitually outrun the evidence. 
 
 In the same way, although we do not hnow that there is a 
 God, or that the world is moving toward a worthy goal, and 
 cannot therefore be said to believe in the existence of God or 
 in the salvability of the world in the first of our three senses 
 of the word " believe," we have the right to believe in the other 
 two senses. We are justified in accepting the existence of 
 God as an assumption in accordance with which to plan our 
 lives; and also in feeling a greater degree of certainty with 
 reference to his existence than is theoretically warranted. 
 
BIBLIOGKAPHY. 
 
 Aenal, Andre. La Philosophie Religieuse de Charles Renouvier. 
 Paris, 1907. 
 
 B'OWNE, B. p. Metaphysics: A Study in First Principles. New 
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 Bradley, F. H. Appearance and Reality: A Metaphysical Essay. 
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 Cantor, Georg. Beitrage zur Begriindung der transfiniten Mengen- 
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 Clarke, W. N. The Christian Doctrine of God. New York, 1909. 
 
 CounjRAT, Louis. De L'Infini Mathematique. Paris, 1896. 
 
 Dedekind, Richard. Statigkeit und Irrationale Zahlen, and Was 
 Sind und Was Sollen die Zahlen? Translated by W. W. Bemait 
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 FiSKE, John. The Idea of God as Affected by Modem Knowledge. 
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 Hocking, W. E. The Meaning of God in Human Experience: A 
 Philosophical Study of Religion. New Haven, 1912. 
 
 HowisoN, G. H. The Limits of Evolution. New York, 1901. The 
 Conception of God. New York, 1897. See Royce. 
 
 James, Willl^m. The Will to Believe and Other Essays in Popular 
 Philosophy. New York, 1899. A Pluralistic Universe: Hibbert 
 Lectures at Manchester College on the Present Situation in Phi- 
 losophy. London, 1909. Some Problems in Philosophy: A Be- 
 ginning of an Introduction to Philosophy. New York, 1911. 
 
 Kant, Immanuel. Kritik der Reinen Vemunft. Translated by F. 
 Max Mueller. London, 1907. 
 
 Keyser, C. J. The New Infinite and the Old Theology. New York, 
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 80 
 
Bibliography, 
 
 81 
 
 McTaggart. Studies in Hegelian Cosmology. Cambridge, 1901. 
 
 Mansel, H. L. The Limits of Religious Thought. Oxford, 1858. 
 
 Mezes. The Conception of God. See Royce. 
 
 Mill, J. S. Autobiography. New York, 1873. Three Essays on 
 Religion. New York, 1874. 
 
 Newman, J. H. An Essay in Aid of a Grammar of Assent. Lon- 
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 PoiNCARE, Henri. Science et Methode. Paris, 1909. 
 
 Renotjvier, Charles. Essais de Critique Generale. Four volumes. 
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82 The Argument for a Finitist Theology. 
 
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 IX. 
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VITA. 
 
 Eay Harbaugh Dotterer was born in Westmoreland County, 
 Pennsylvania, Aug. 4, 1880. He attended the public schools, 
 and taught two terms. In 1902, he was graduated at the Cen- 
 tral State !N'ormal School, Lock Haven, Pa.; in 1906, at 
 Franklin and Marshall College; in 1909, at the Theological 
 Seminary of the Eeformed Church, Lancaster, Pa. From 
 June, 1909, to January, 1913, he was pastor of a Reformed 
 Church at Eockwood, Pa., and from 1913 to the present, in 
 Baltimore, Md. In 1910, he completed a graduate course, and 
 received the degree of Ph.M. from Franklin and Marshall Col- 
 lege. Since October, 1913, he has been a student in the Johns 
 Hopkins University. His subjects have been Philosophy, 
 Psychology, and Education. In 1916 he received the degree 
 of Master of Arts, having submitted an essay on " The Philos- 
 ophy of the ' As If ' in its Application to Theology.'' 
 
 88 
 
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