CHAPTER FIVE

1. The Source of the Ideas of Pure Reason and of Absolute Metaphysical Judgements

WE can say of the a priori principles which Kant has now shown to be necessary conditions for the objective character of a type - not, as I have argued, of every type - of objective empirical judgement, that they are genuine metaphysical pro- positions. They are valid in that they are presuppositions of Newtonian science and of 'commonsense' objective experience. The term' presupposition' is a vague one, and has been greatly misused; but its use in referring to Kant's position should be harmless, once the main theses of the Analytic have been understood.

Metaphysical presuppositions, whether of science, of mathematics, or of any other theory, must be distinguished from absolute metaphysical propositions. The latter are not necessary conditions of the objective character of a non-metaphysical theory, but apparently constitute the body of an autonomous science. They are not about the possibility of objective experience, but apparently about some peculiar subject matter of their own.

The task of Kant's Transcendental Dialectic is (1) to show that belief in such absolute metaphysical principles arises from the very nature of our thinking about matters of fact; (2) to give a complete list of these principles and of the a priori notions which are involved in them; (;) to demonstrate that their claim to give us knowledge of matters of fact is illegitimate; and lastly (4) to explain their proper and legitimate function in our theoretical endeavour. The strategy is analogous to that of the Analytic. To the method used in the Analytic for discovering the Categories there corresponds here in the Dialectic a method for discovering the Ideas of Reason, i.e. a priori notions which are neither abstracted from nor applicable to experience. To the transition in the Analytic from the allegedly complete list of Categories to the synthetic a priori Principles of the pure Understanding there corresponds in the Dialectic the transition from the Ideas to the a priori Principles of Reason, i.e. the absolute metaphysical principles. There is, however, no Transcendental Deduction of the Ideas. Instead Kant shows that their application to (alleged) matters of fact is unjustified. In other words to the Transcendental Deduction of the Categories there corresponds in the: Dialectic the proof that there can be no such deduction of the Ideas. This proof - or disproof - Kant regards as highly important. Absolute metaphysics (the term is not Kant's own, but conveys his meaning) is no ordinary illusion which can be removed with sufficient logical care. It can be recognized as illusion but it is irremovable. 'The transcendental illusion does not vanish even when it has been detected and when its illusory character stands clearly revealed by transcendental criticism (for instance, the illusion in the proposition: The world' must have ~ beginning in time).'

Kant's claim to have found a clue for listing all the Ideas of Reason and consequently all absolute metaphysical principles is again based on his confidence in the completeness of the traditional logic - its completeness this time in listing all the possible forms not of judgement but of mediate inference. He holds that just as the Categories are embodied in the judgement-forms, so the Ideas are embodied in the forms of inference. For us it is again important to distinguish between his large claim, to have discovered all possible Ideas and absolute metaphysical principles, and the more moderate claim, implied in the other, that he has discovered at least some of them. It would indeed be foolish to let the neatly, for some tastes too neatly, systematic presentation of the Transcendental Dialectic blind us to the importance of the thoughts which it conveys. They are hardly less relevant to contemporary philosophical issues than are the thoughts contained in the equally neat and rigid system of the Transcendental Analytic.

Kant calls the power of mediate inference' reason' in a narrow sense of the term in which it is distinguished from understanding, which is the power of ffiJ1king objective perceptual judgements by the application of the Categories. Since syllogistic inference is for him the only mediate inference, 'reason' can also be said to be the power of syllogistic inference. The only type of inference other than this which Kant recognizes, is that called' immediate'; in which the conclusion follows directly from one premise as, e.g., 'Some men are mortal' or 'No men are immortal' follows from' All men are mortal'. Immediate inference is always assigned to the under- standing.

In a mediate or syllogistic inference, e.g. from' All men are mortal' and ' All scholars are men' to the conclusion' There- fore all scholars are mortal' there must always be two premises. The premise which contains the predicate of the conclusion, 'mortal' in our example, is called the major. The one which contains the subject of the conclusion, in our example 'scholar', is called the minor. Kant distinguishes between three kinds of mediate, syllogistic inferences, or as he also calls them 'inferences of reason'; namely that in which the major premiss is always a categorical, that in which it is a hypothetical, and that in which it is a disjunctive judgement, i.e. he divides inferences according to the so-called' relation' of the major premise.

In a mediate inference we do not make any new objective empirical judgement but state the deductive relationship between given judgements. In particular, if a certain judgement is given we look for two others which could serve as premisses from which it follows as their conclusion. Since the premises themselves are only used in the inference and not proved by It we must, if we want to prove them, look for further premisses from which they can be deduced. In order in this way to prove our major premises 'All men are mortal' we should have to show it as following from some more general proposition, say 'All animals are mortal' which, if we can add 'All men are animals', would prove it.  

Now 'All animals are mortal' is a common major premiss not only with respect to the conclusion 'All men are mortal " but also with respect to 'All tigers are mortal',  ‘All fish are mortal', and so on. It thus connects all these propositions and gives them a systematic unity which they do not possess if regarded as separate judgements. Such unity among our judgements increases with every further such arrangement of them into syllogistic form and in particular with any further demonstration that the major premiss of a given syllogism is itself a conclusion which follows from more general premisses.

We have been speaking of syllogistic inference and with it of reason, which is the faculty of such inference; and we can see two characteristics of it which are of importance for the understanding of Kant's argument in the Transcendental Dialectic. 'First, the inference of reason is not concerned with perceptions by bringing them under rules (as is the under- standing with its Categories), but with concepts and judgements,' Secondly, in giving systematic unity to judgements through arranging them in syllogistic order, it tries to find a more general major premiss for every one of its syllogistically arranged judgements, and thus the ultimate premiss in every chain of syllogisms. It tries, in Kant's somewhat obscure words 'to the conditional knowledge of the understanding, to find the unconditioned', ~order to 'bring the former to completion'.

Kant, however, makes his meaning quite clear by a distinction between the logical maxim of syllogistic arrangement and the fundamental principle of pure reason. The maxim is a piece of logical advice and could be formulated as follows: If you want to give systematic unity to your judgements by arranging, them syllogistically, you must find to every condition or pre- miss a further condition or premiss, and try to proceed in that way towards the ultimate condition, which, being itself dependent on no further condition, would be unconditioned or absolute. It is important to note that this useful maxim does not imply that there is any ultimate, unconditioned condition. In this respect it reminds us of the moral maxim that we should all try to become saints, a maxim which, however valuable it may be, certainly does not imply that if we set out to follow it 'We shall or possibly can become saints.

As contrasted with this logical maxim of pure reason its fundamental principle is the assumption that the chain of premisses or conditions actually has a last unconditioned or absolute member and is, therefore, able to be completed and so, in a sense, completely given. The transition from the maxim to the principle is analogous to the transition from the maxim that we should try to become saints, to the assumption that we can. It is equally unwarranted in both cases.

'The logical maxim cannot become a fundamental principle of pure reason unless we assume that if the conditioned is given, the whole sequence of subordinate conditions, which consequently is itself unconditioned, is also given. . . Whether this principle that the sequence of conditions. . . reaches the un- conditioned is or is not objectively valid; and what consequences follow from this for the empirical use of reason. . . will be our business in the Transcendental Dialectic, which we now intend to develop from its sources which are deeply hid- den in human reason.'

The fundamental principle of reason thus assumes as given completely that systematic unity in all the judgements of our understanding, towards which the logical maxim only bids us to strive. Claiming in this sense to confer the unity of a perfect logical order on our judgements, it reminds us of the fundamental principle of the Understanding, the unity of pure ap- perception, which claims to confer synthetic unity on the manifold of perception, as though our judgements furnished Reason with a kind of manifold of its own. But while the subjective claim of the unity of pure apperception was shown to be rightful, Kant means to demonstrate that the subjective claim of this so-called fundamental principle of reason is the source of antinomies and other fallacies and, therefore, wholly spurious and unjustified.

Kant's sharp distinction between a maxim saying how the next member in an ascending syllogistic chain is found and the assumption that the links in their totality are given, shows striking similarity to a highly important distinction in the modem theory of sets and the foundations of mathematical analysis. I refer to the distinction between a rule which allows us to construct the next member of an ' infinite' sequence and the assumption that the whole sequence is given in its totality. The need for the distinction lies in the logical antinomies or contradictions implicit in systems where this assumption is made. It is another tribute to Kant's remarkable penetration that many philosophical logicians consider the assumption of infinite yet completely given totalities as illegitimate for reasons very similar to those which he put forward against the fundamental principle of pure reason.

The principle that 'if the conditioned is given, the whole sequence of subordinate conditions... is also given' leads according to Kant to three sources of fallacy, due to the assumption of three types of completed sequence corresponding to the three possible forms of syllogistic inference. If we ascend along a syllogistic chain from premiss to higher premiss by means of categorical syllogisms, then the fundamental principle of pure reason demands that we arrive at length' at a subject which is not itself a predicate'. H the ascent takes place by means of hypothetical syllogisms, then the principle demands an ultimate' presupposition which itself presupposes nothing else '. Lastly if the journey is undertaken by way of disjunctive syllogisms, the principle demands 'an aggregate of the members of the (disjunctive) division, - such as requires no more in order to complete the division of the concept'.

The fundamental principle of reason thus demands three kinds of absolute or unconditioned unity. Kant identifies them

with three Transcendental Ideas: ‘first the absolute (unconditioned) unity of the thinking subject, second the absolute unity of the sequence of the conditions of the appearance, third the absolute unity of the condition of objects of thought in general. The thinking subject is the subject matter of (speculative) psychology, the totality of appearances (the world) that of (speculative) cosmology, and the entity which contains the highest condition of the possibility of everything which can be thought (the entity of all entities), that of theology .'

The logical maxim of syllogistic order which demands that we should, step by step, proceed from premiss to higher pre- miss can be followed within the field of the understanding, that is to say, for any, limited or unlimited, set of objective perceptual judgements. The assumption of the completed pro- cess cannot be realized in this field and is indeed the source of antinomies. It transcends all possible experience or is, as Kant puts it, transcendent. Consequently no object of experience can possibly correspond to any of the three Ideas.

 2. The Illusions of Speculative Psychology  

Many philosophers before Kant and some philosophers after him, for example his one-time disciple Fichte, believed in the possibility of a science of the self which can be developed, like pure mathematics or logic, in a purely a priori fashion without recourse to any empirical observation or experiment. This putative a priori psychology went under the names of speculative or rational psychology. The very thought of such a ‘science’ seems strange to us who have seen the birth and will, as I believe, continue for a long time to see the perpetuation, of an experimental psychology so obstinately experimental that some of its exponents think proper to frown upon introspection even when introspecting in pursuance of their inquiry. Rational Psychology is a thing of the past. Its fallacies, how- ever, like all the others examined in the Dialectic, have lost none of their vitality, sometimes even being hailed nowadays as new and profound discoveries.

Thus the theme which Heidegger, in what seems to me pro vocatively Kantian terminology, calls 'the Analytic of Existence (Dasein)' is no more than a variation of the old theme of rational psychology. In the first chapter of the first part of his Sein und Zeit (the long tide of which duly contains the term 'Transcendental') he says that 'the existent, the analysis of which is our task. is we ourselves. The being of this existent is always mine. In its being this existent concerns itself with its own being.' There are other examples of rational psychology to be found in contemporary philosophical works, but I should hardly expect to find many presented so precisely in terms which Kant used as key-terms in the Critique of Pure Reason.

In the Analytic of Concepts Kant has drawn a sharp distinction between the' I think which must be capable of accompanying all my presentations',  thereby giving them synthetic unity, and the empirical, introspected, self which is itself a presentation. To be truly a priori rational psychology must have for its subject the former, i.e. the self of pure self-consciousness. This however is not, according to Kant, an object of experience. It is a necessary condition of objective experience and so of the applicability of the Categories. It is not an instance of any Category.

Now rational psychology consists in the 'application' of Categories - in particular the Category pf substance - to a pure self which is assumed to be free from any empirical admixture. It does this mainly by means of a fallacious syllogism. The fallacy consists in using the terms 'subject' and 'substance' in two different senses. In the major premiss of the syllogism 'subject' is used in the purely logical sense of 'subject of a categorical judgement'. In the minor premiss it is usedirl'the sense of the I think of pure self-consciousness. 'Substance' similarly, is used in the major premiss in the logical sense of 'that which can be the subject but not the predicate of categorical judgements', and in the minor in the sense in which only a (thinkable and perceivable) object of experience can be a substance. The logical sense of' subject' and' substance' will be distinguished by capitals in the sequel, for the sake of clearness.

Kant expresses the fundamental fallacy as follows: (1) 'What cannot be thought except as a SUBJECT also does not exist except as a SUBJECT and is therefore SUBSTANCE'; (2) 'A thinking being considered merely as such cannot be thought except as a subject.' Therefore (3) 'A thinking being only exists. . . as substance.' The fallacy is evident; and, as Kant shows by considering the premisses and the conclusion separately, the fallacy can also be seen clearly if we notice that the premisses are analytic juagements which merely elucidate the meanings of SUBJECT, SUBSTANCE, and subject, while the conclusion is synthetic. From analytic premisses a synthetic conclusion cannot be legitimately inferred. If this were possible we could create matters of fact by suitably defining our terms.

If the thesis of rational psychology that the self or soul is a , substance is an illusion of absolute metaphysics, then the same must be true of the theses (1) that it is simple substance; (2) that it is a substance which remains numerically identical throughout the passage of time; and (3) that it stands in relation to possible objects in space, in particular to its own body.

3. The lllusions of Speculative Cosmology

If the world or cosmos is conceived as the sum total of all things in space and time, speculative or rational cosmology will be that branch of absolute metaphysics which consists of such synthetic a priori propositions as are about 'the world'. Kant shows that this alleged a priori science too must lead to fallacies - this time to antinomies which only the critical philosophy can resolve.

By an antinomy is understood a pair of propositions, apparently contradictory, which follow from the same set of assumptions. An antinomy is resolved either (a) by showing: that the apparently contradictory propositions are in fact contradictories and follow from a certain internally inconsistent assumption, or (b) by showing that the apparently contradictory propositions are not in fact contradictory at all but mutually compatible. A trivial example of the first type of antinomy would be the propositions' A square circle is round' and ' A square circle is not round '. It is resolved by showing that they follow from the self-contradictory assumption that a circle is square. A trivial example of the second type of antinomy is found in the apparently incompatible propositions' The end of life is death' and' The end of life is not death '. It is resolved by showing that 'end' is used for termination in the one case and for purpose in the other - two different senses.

An antinomy the source of which is hidden is particularly invidious and worrying. While other fallacies disguise from us the fallaciousness of our reasoning and may thereby give us a certain - however undeserved - peace of mind, antinomies the

source of which is undiscovered incessantly remind us of our shortcomings as thinkers. Such are the cosmological antinomies which possess the highest degree of the salutary capacity 'to arouse philosophy from its dogmatic slumber and move it to the difficult business of the critique of reason itself'. Kant believed that a popularization of his theory of knowledge ought profitably begin by drawing attention to the antinomies of rational cosmology. This could be done, he says in a letter to Marcus Herz (11.5:1781), 'in a very flourishing way' and would excite 'the reader's desire to probe beneath the sources of this conflict'. But characteristically he adds that 'first academic philosophy (die Schule) must be given its due, only afterwards can one properly permit oneself to amuse the world '.

Within the limits of this Introduction I can do little more than reproduce the cosmological antinomies and show the method by which Kant resolves them. Once again, the cosmological antinomies are divided according to the table of the Categories as - for so we might call them - the antinomies of quantity, of quality, of relation, and of modality respectively. The first antinomy has for its thesis: 'The world has a beginning in time and is also limited in space' and for its antithesis: 'The world has no temporal beginning and no limits in space; with respect to both time and space it is infinite.' The second antinomy has as its thesis: 'In the world every composite substance is composed of simple parts; nothing exists anywhere except it either is simple or is composed of simple parts' and as its antithesis, 'In the world no composite thing consists of simple parts and there exists nowhere in the world anything simple.'

The third antinomy has as its thesis: 'Causality according to laws of nature is not the only kind of causality from which the phenomena of the world can be derived. It is necessary, in order to explain. them, to assume a causality through freedom ', i.e. to assume uncaused causes. Its antithesis is: 'There is no freedom; everything in the world takes place solely in accordance with laws of nature.' Lastly the fourth antinomy states as its thesis, 'There belongs to the world as a part of it or as its cause, something which exists as an absolute necessary being.' Its antithesis is, 'There exists nowhere an absolutely necessary being as the world's cause, either in it or out of it.'

Each and every one of these conflicting propositions can be found among the central assumptions of on~ or more meta- physical systems. The first antinomy is relevant to any metaphysical theory which asserts or denies, explicitly or implicitly, that the world has been created at a point in time. The second is relevant to any metaphysical theory which asserts or denies the existence of atoms or monads of any kind. The third op- poses determinism to indeterminism and thus indirectly, as Kant believes, opposes natural science to the foundation of ethics. The last antinomy expresses the conflict between meta- physical theories which try to prove and those which try to disprove the existence of God from premisses about the world.

Kant insists that the proofs which he offers of each antithesis and its thesis are not mere' barristers' proofs' but are strictly valid. The proofs turn mainly on the nature of infinite aggregates. Their structure, since Kant's time, has been made the subject of an elaborate mathematical theory by Cantor and his successors. This does not mean that what Kant has to say on the matter is wholly superseded and belongs to the dark ages of logical superstition. Indeed Hilbert acknowledges his debt to Kant by saying expressly that he regards the notion of an infinite totality as a Kantian Idea of Reason.

On the other hand the Kantian arguments do seem to stand in need of modification in the light of developments in the logic of infinite aggregates subsequent to Cantor's work. To give one example: to Kant's assertion! that 'no aggregate is greatest' there corresponds a theorem in the modern theory of aggregates, but his reason for asserting it would now be rejected, namely that 'to every aggregate one or more units can be added '.8 It IS an express theorem that the addition of a finite number of units to an infinite aggregate does not increase its number. I cannot hold with any attempt to 'modernize' Kant's proofs of the antinomies. It would, as I think, end in mere idle speculations as to the sort of answer which Kant would have given to questions which simply could not have occurred to him.

Such speculations fortunately are .not necessary for the understanding of Kant's main point about the cosmological antinomies. He sets about the demonstration that every single one of the cosmological a priori propositions, while claiming, to be an absolute metaphysical truth, embodies a logical mistake. This demonstration, although prompted by the proofs of the antinomies, is not dependent for its validity on the correct- ness of these proofs.

The first antinomy concerns' the magnitude of the world of space and time'. In stating that a volume of space or a stretch : of time has a certain magnitude we assume that a process of measurement (the successive addition of units) can be completed and that its completion can be experienced. Now the process of measuring the world in space and time cannot be completed in experience. The concept of its completion is thus an Idea to which ~g in experience can correspond. The statement that the world in space or time is finite or that it is infinite in magnitude is thus exactly similar to the statements that a square circle is round and that it is not round. Kant would probably not have been greatly disturbed by the claims of contemporary scientists to be able to estimate the magnitude of the world in space or time. He would merely have considered that the theorists were using concepts of measurement quite different from his.

The Second Antinomy concerns the division of  appearances '. To the Idea of completing the unlimited division of a thing no experience can possibly correspond. The statement, however, that every substance consists of indivisible parts '(or does not so consist) assumes that a process of division can be completed in experience which cannot in fact be so completed. Kant, here, is using the notion of a physical division which is assumed to be unlimited in principle - a division which, in particular, is not limited by available laboratory techniques or by the implications of a physical theory. The antinomies are contradictory pairs of absolute metaphysical propositions such as Democritus or Leibniz might have asserted, and not consequences of a physical theory based on experiment and observation.

In the first and second antinomies' the falsity of the assumption consisted in that what contradicts itself in a concept (namely appearance as thing in itself) was presented as compatible'. Indeed the idea of the completion of an unlimited process is that of a non-phenomenon, intelligible or thing in itself. In the third and fourth antinomies' the falsity of the assumption consists in that what is compatible is presented as incompatible'.

The third antinomy concerns the question whether there is or is not freedom, i.e. are there or are there not uncaused cause? It is resolved by showing that the thesis - that all phenomena are subject to 'causality according to laws of nature' - is compatible with the antithesis that a different kind of causality, allowing of uncaused causes, exists for noumena or things in themselves. The latter kind of causality is, of  course, only an Idea - the Idea of freedom - which according to Kant is necessary to account for the experience of moral obligation. This experience is quite different from any objective experience which falls within the scope of the natural ' sciences, and is the theme of the Critique of Practical Reason.

The fourth antinomy concerns the existence or otherwise of an absolutely necessary being. Kant resolves it by distinguishing between a cause within the phenomenal world and an ' intelligible cause - a thing in itself - such as might be the cause of phenomena. The following two propositions are, then, compatible: the thesis that there is no absolutely necessary cause of the world of phenomena in accordance with laws of nature I and the antithesis' that this world is nevertheless connected with a necessary being as its cause (a different kind of cause and one according to a different law) '.

Kant's resolution of the cosmological antinomies is evidence, if not of the truth, at least of the impressive logical force of the critical philosophy and of the theory of transcendental idealism as developed in Kant's Aesthetic and Analytic.  The distinction between phenomena and noumena or the corresponding distinction, which to me seems preferable, between :' Ideas and other concepts helps to divest absolute metaphysics of its unlawful theoretical claims and prepares us for a recognition of the proper function of its Ideas and principles.

4. The illusions of Speculative Theology

God, the subject of speculative theology, is conceived as .an ' individual and the bearer of all possible perfections. A 'perfection' is not only a positive predicate into whose definition negation cannot enter; it is unlimited in the sense that it cannot be incompatible with any other positive predicate. No empirical predicate, therefore, can be a perfection. Any positive empirical predicate, e.g. 'red' or 'square', is incompatible with some other such predicate, say' green' or 'triangular'. The perfections of this most perfect being, or ens realissimum or God, can thus only be grasped 'by analogy'.

In assuming the applicability of an Idea of Reason (e.g. the soul conceived as the absolute unity of the thinking subject) we assume that an unlimited aggregate is given as completed. In assuming the existence of God we assume not only that the unlimited aggregate of all possible perfections is given as completed, but beyond this, that it applies to a single individual and that this individual is a person. Since the completion of an infinite aggregate cannot be an object of experience, the assumption that there is such an object is logically impossible. The thesis that God can be an object of experience, in the same sense in which objects which fall within the scope of natural science are, must therefore be rejected for the same reasons as the theses of speculative psychology and the theses and anti- theses of speculative cosmology.

Yet just as the Ideas of the absolute unity of the thinking subject and of the absolute unity of the world may have a function and may even be necessary in our thinking about what ... ought to be and what is our duty, so the notion of God may have its proper and necessary place in moral thought. Notions to which nothing in objective experience can correspond can have no direct use in theoretical inquiries and their application :after the fashion of a posteriori concepts and of the Categories must lead to confusion and fallacy. Yet our thinking about moral obligation cannot be limited to notions to which objective experience corresponds. This would be to equate what ought to be with what in fact is. The manner in which the notions of the soul, of freedom and of God are, according to Kant, connected with moral judgement is not, however, at present our concern.

Since the notion of God implies not only the completion of an infinite aggregate of predicates but also individuality and indeed personality, Kant calls it not only an 'Idea', but also an 'Ideal '. Since, unlike the notion of a perfectly wise man and; other such ideals, which - at least partly - are the result of the imaginative combination of empirical concepts, the notion of God contains no empirical element, Kant calls it 'the Ideal of pure reason' or 'the transcendental Ideal '.

Although the concept of the existence of a bearer of all possible perfections must be rejected as a possible object of experience (it would be incompatible with the findings of the Transcendental Analytic, which was the exposition of the concept 'object of experience ') Kant still proceeds to consider the main theoretical proofs for the existence of God which have been put forward. These are the so-called ontological, cosmological and physico-theological arguments.

The ontological argument consists in an alleged deduction from conceivability to existence; from the statement that a most perfect being can be conceived to the statement that he exists. The argument is intended as a reduction ad absurdam. If, it says, there were a most perfect being who did not exist, there would be a still more perfect being. There would be one who in addition to all the perfections of the former would have the added perfection - the predicate of existence. A most perfect being who does not exist is a contradiction in terms.

Kant's objection to this argument consists in pointing out that 'existence' is not a predicate. 'Whatever, and however much, our concept of an object contains [i.e. logically implies], we must go beyond it in order to ascribe existence to it', that is to say, in order to judge correctly that it is not empty. 'The conception of a supreme being is in many respects a very useful Idea; because, however, it is a mere Idea, it is quite incapable by itself alone of extending our knowledge of that which exists.' Kant's objection can also be put in a slightly different way. The premiss of the ontological argument states the fact that we are capable of defining the notion of a supreme being. The definition, like every definition, is formulated by an analytic statement. No analytic statement logically implies a synthetic statement. Yet the conclusion of the argument is synthetic. The cosmological argument has as its premiss the synthetic statement that something exists, e.g., I myself do. It concludes - an equally synthetic statement - that an absolutely necessary being exists. Kant finds many logical flaws here. Perhaps the most fundamental is the assumption, the making of which in his view IS the root of all the mistakes of absolute metaphysics, that an unlimited sequence (here a sequence of causes) is completable in experience. It is worth noting that the cosmological argument by itself does not prove the existence of God, but at

most the existence of an absolutely necessary being. The Physico-theological argument or, as it is often called, the argument from design, has as its premiss a specific experience, "namely that of apparent design. 'Everywhere do we see a chain of effects and causes, of ends and means, regularity in the way in which things come into being and cease to be', and it is indeed very intelligible that we should feel inclined to conclude that there must be a creator or, at least, a builder of the world. Kant shows a certain tenderness for this argument, which has been fairly frequently propounded, even after the Critique of Pure Reason had become part of general philosophical education, and this by philosophers who clearly separated their religious from their philosophical convictions. Yet an unlimited sequence of ends and means can, just as little as an unlimited sequence of causes and effects, be assumed to be completed in experience. In any case neither the argument from design nor the cosmological argument can prove the existence of the ens realissimum; since the former, if successful, would prove at most a world-builder, the latter at most an absolutely necessary being. The fallacious character of the effort by the three theoretical arguments criticized to show that the Ideal of pure reason exists as an object of possible experience would not imply that " no valid theoretical arguments existed unless the three arguments really exhausted all the possibilities. But Kant believes himself to have shown this also. Whether or not he has done so hardly matters, inasmuch as the impossibility that the transcendental Ideal should be an object of experience is implied by the general principles of the Transcendental Logic.

On the other hand a theoretical disproof of the existence of a supreme being, i.e. a disproof of his existence as a noumenon, is, if we adopt Kant's position, equally impossible. Indeed' the same grounds on which the inability of human reason to assert the existence [of a supreme being] has been demonstrated, are necessarily sufficient to demonstrate also the invalidity of any counter-assertion '. Moreover, if per impossibile such a theoretical disproof could be given (one to the effect that God exists neither as a phenomenon nor as a noumenon) then the very proof

of his existence on which Kant himself relies - his necessary existence as an Idea of practical reason - cannot, he believes, possibly be produced. Such a proof as this latter Kant himself believes possible, and produces in the Critique of Practical Reason.

5. The Legitimate Use of the Ideas of Pure Reason

 The misuse of the Ideas to which nothing in experience can correspond consists in their spurious application to alleged objects of experience. It consists in using them after the fashion of a posteriori concepts which are applicable to experience be- cause they are abstracted from it; or after the fashion of the Categories, which are applicable to experience because their applicability is a condition of there being objective experience, because, in other words, they are constitutive of objects.

Although the Ideas of reason cannot be applied to what is given in perception, they have in the field of theoretical thinking still an 'excellent and unavoidably necessary regulative use, namely to direct the understanding to a certain goal. . . which serves the purpose of giving the greatest unity and the greatest breadth at the same time'. To understand this their legitimate function, we must recall the difference between the logical maxim of syllogistic ordering and the fundamental principle of pure reason (§ I). The former enjoins us to ascend from premiss to premiss in a series of categorical, hypothetical, or disjunctive syllogisms, which has no last term. The latter demands that there be a last term and that the series be complete, and thus leads to the formation of the Ideas of the soul, the world, and God.

Thus far, it has not led to any of the mistakes of absolute metaphysics. These mistakes have their source in a further principle which might be called' the fundamental principle of dialectical reason', namely that the series of conditions has a last term and is thus complete in experience. Only if we accept the last principle, which is very easily and naturally done, do we seem committed to the principles of absolute metaphysics.

If we only follow the logical maxim we achieve a progressive systematic ordering of our legitimate judgements. In Kant's representation of the matter we look for the genus of different species; for different species falling under the same genus; and for continuous transitions from one species to another. Kant calls these principles of ordering' the principles of homogeneity, of specification, and of affinity '. These principles are principles of ordering judgements and of classifying concepts. They are not themselves judgements and are not incompatible with each other since they can all be applied together 'up to a point'. In an analogous way a political society can be ordered by the interplay of the democratic, the aristocratic, and the monarchic principles.

Kant's maxim of syllogistic ordering is, of course, too restricted in scope - a result of his dependence on the traditional theory of deductive inference. We should recognize a much wider maxim of deductive ordering nowadays, the maxim which is conformed to when we systematize the results of scientific inquiry by means of so-called hypothetico-deductive systems. This type of deductive ordering differs from Kant's syllogistic systematization in using many more types of deductive reasoning and in starting from axioms which for any given theory are regarded as being fundamental and not deducible from higher principles. Yet Kant's idea of a system of judgements is still recognizably similar to contemporary ideas of the' systematic character of a scientific theory.

The Ideas of Reason themselves have also a further systematic or rather systematizing use if we consider them not as applicable in experience but rather as indicating unreachable goals which yet we can approxin1ate; in other words if we use them as ideal standards, analogously to the way in which, in applied mathematics, limits are used which for various purposes it is sufficient to approxin1ate to within this or that specified margin.

Thus in psychology it may be extremely useful  to connect all appearances, actions and the receptivity of our mind . . . as if it were a simple substance, which endowed with personal identity (at least during life) permanently exists, while its states, to which those of the body belong only as external conditions, continuously change'. In a similar way we may use the Idea of the totality of all things, or the world, or the Ideal of the ens realissimum. Far from being harmful this use of the Ideas may have not only great systematic but also great heuristic usefulness.

This as-if' justification of the Ideas of pure reason may be separated from the rest of the transcendental logic and elevated into a supreme maxim of method. We may decide in our theoretical endeavour to disregard the applicability or emptiness of concepts altogether and to employ only those which serve our purposes when treated as if they were applicable. We should then be methodological pragmatists. We might easily then be led to go further and consider the usefulness pf a concept as the criterion of its applicability. Our pragmatism would then be epistemological or metaphysical. The writings of pragmatist philosophers often make it difficult to distinguish whether their pragmatism is merely methodological or something more. What at first seems to be a pragmatist theory of truth or of the universe frequently turns out to be no more than the spirited proclamation of a methodological decree.

C. S. Peirce, one of the fathers of modern pragmatism, 'devoted two hours a day to the study of Kant's Critique of Pure Reason for more than three years until [he] almost knew the whole book by heart, and had critically examined every section of it . . .'  As a result of his study he rejects the arguments of the Analytic but finds a great deal that is worth while in the Dialectic. Kant, he says, subjects the Ideas of God, freedom, and immortality ',to a different kind of examination, and finally admits them upon grounds which appear to the seminarists more or less suspicious, but which in the eyes of the laboratorists are infinitely stronger than the grounds upon which he has accepted space, time, and causality'..

It would be difficult to estimate how far Kant's philosophy of knowledge has 'influenced' Peirce. There can be no doubt in the case of Vahinger’s pragmatism in his Philosophy of the As-If. Vaihinger not only acknowledges his debt to the Transcendental Dialectic and other parts of Kant's critical philosophy but tries at great length to show how

in his opinion it had anticipated his own variant of pragmatism. The organized wealth of original and profound conceptions and of subtle analyses which is the Critique of Pure Reason contains, of course, the seeds of many modern philosophies. Concentration on the positive doctrine of the Dialectic to the exclusion of most other theses of the Kantian system leads, as we have seen, to pragmatism. Concentration on the doctrine of the Transcendental Logic as a whole to the exclusion of Kant's ethical works leads to a non-phenomenalist (non-Berkeleian) empiricism or positivism - provided the table of the Categories is not taken too literally. Twisting the Dialectic into a logic of truth leads- to metaphysical systems of the Hegelian type. Even phenomenology and existentialism contain many recognizably Kantian elements. They certainly at least abound with Kantian terms. The fundamental theses of the Kantian theory of knowledge are contained in the Transcendental Aesthetic, the Transcendental Logic and the Transcendental Dialectic which together form the first main part of the Critique of Pure Reason called the Transcendental Doctrine of Elements. Its second part, the Transcendental Doctrine of Methods, adds, as I believe, no important ideas which are both new and not to be found in Kant's later works - in particular the Critique of Practical Reason. A reader who has grasped the doctrine of the first part will find the second comparatively easy reading. For our purpose it is neither possible nor really necessary to consider it in any detail.