Chapter XI: Introduction (2)

Paulsen is justified in maintaining that Kant, in both editions of the _Critique_, recognises the validity of mathematics and pure natural science. The fact of their validity is less explicitly dwelt upon in the first edition, but is none the less taken for granted. The sections transferred from the _Prolegomena_ to the _Introduction_ of the second edition make no essential change, except merely in the emphasis with which Kant’s belief in the existence of valid _a priori_ synthetic judgments is insisted upon. As has already been stated, only by virtue of this initial assumption is Kant in position to maintain that there is an alternative to the strict synthetic method. The _problem_ from which he starts is common to both methods, and for that reason the formulation used in the _Prolegomena_ can also be employed in the _Introduction_ to the _Critique_. Only in their manner of solving the problem need they differ.[180] Kant’s Critical problem first begins with this presupposition of validity, and does not exist save through it.[181] He does not first seek to discover whether such judgments are valid, and then to explain them. He accepts them as valid, but develops a method of argument which suffices for proof as well as for explanation. The argument being directed to both points simultaneously, and establishing both with equal cogency, it may legitimately be interpreted in either way, merely as explanation, or also as proof. Kant does not profess or attempt to keep exclusively to any one line of statement. Against the dogmatists he insists upon the necessity of _explaining_ the validity of _a priori_ synthetic judgments, against the sceptics upon the possibility of _proving_ their validity. And constantly he uses ambiguous terms, such as ‘justification’ (_Rechtfertigung_), ‘possibility,’ that may indifferently be read in either sense. But though the fundamental demand which characterises the synthetic method in its distinction from the analytic thus falls into the background, and is only occasionally insisted upon, it is none the less fulfilled. So far as regards the main argument of the _Critique_ in either edition, the validity of synthetic _a priori_ judgments is not required as a premiss. It is itself independently proved.

The manner in which Kant thus departs from the strict application of the synthetic method may be illustrated by an analysis of his argument in the _Aesthetic_.[182] Only in the arguments of the first edition in regard to space and time is the synthetic method employed in its ideal and rigorous form. For the most part, even in the first edition, instead of showing how the _a priori_ character of pure and applied mathematics follows from conclusions independently established, he assumes both pure and applied mathematics to be given as valid, and seeks only to show how the independently established results of the _Aesthetic_ enable him to explain and render comprehensible their recognised characteristics. This is not, indeed, any very essential modification of the synthetic method; for his independently established results suffice for deducing all that they are used to explain. The validity of mathematics is not employed as a premiss. Kant’s argument is, however, made less clear by the above procedure.

Further difficulty is caused by Kant’s occasional employment, even in the first edition, of the analytic method. He several times cites as an argument in support of his view of space the fact that it alone will account for the existing science of geometry. That is to say, he employs geometry, viewed as valid, to _prove_ the correctness of his view of space.[183] Starting from that science as given, he enquires what are the conditions which can alone render it possible. These conditions are found to coincide with those independently established. Now this is a valid argument when employed in due subordination to the main synthetic method. It offers welcome _confirmation_ of the results of that method. It amounts in fact to this, that having proved (by application of the transcendental method) the mathematical sciences to be valid, everything which their validity necessarily implies must be granted. Kant’s reasoning here becomes circular, but it is none the less valid on that account. This further complication of the argument is, however, dangerously apt to mislead the reader. It is in great part the cause of the above division among Kant’s commentators. The method employed in the _Prolegomena_ is simply this form of argument systematised and cut free from all dependence upon the transcendental method of proof.[184]

The whole matter is, however, still further complicated by the distinction, which we have already noted, between real and ideal possibility. Are the given synthetic _a priori_ judgments valid? That is one question. Can the Critical philosophy discover, completely enumerate, and prove in a manner never before done, all the possible synthetic _a priori_ principles? That is a very different problem, and when raised brings us to the further discussion of Kant’s transcendental method. The question at issue is no longer merely whether or not certain given judgments are valid, and how, if valid, they are to be accounted for. The question is now that of discovering and of proving principles which have not been established by any of the special sciences. This shifting of the problem is concealed from Kant himself by his omission to distinguish between the undemonstrated axioms of the mathematical sciences and their derivative theorems, between the principles employed by the physicist without enquiry into their validity and the special laws based upon empirical evidence.

As regards the mathematical axioms, the problem is fairly simple. As we shall see later, in the _Aesthetic_, they do not require a deduction in the strict transcendental sense. They really fall outside the application of the transcendental method. They require only an “exposition.” But in regard to the fundamental principles of natural science we are presented with the problem of discovery as well as of proof. Unlike the axioms of the mathematician, they are frequently left unformulated. And many postulates, such as that there is a _lex continui in natura_, are current in general thought, and claim equal validity with the causal principle. Kant has thus to face the question whether in addition to those principles employed more or less explicitly by the scientist, others, such as might go to form an immanent metaphysics of nature, may not also be possible.

B. (_a_)[185] =Psychological and logical possibility.=--Both have to be recognised and accounted for. Let us consider each in order.

(1) =Psychological possibility.=--What are the _subjective_ conditions of _a priori_ synthetic judgments? _Through what mental faculties_ are they rendered possible? Kant replies by developing what may be called a transcendental psychology. They depend upon space and time as forms of sensibility, upon the _a priori_ concepts of understanding, and upon the synthetic activities by which the imagination schematises these concepts and reduces the given manifold to the unity of apperception. This transcendental psychology is the necessary complement of the more purely epistemological analysis.[186] But on this point Kant’s utterances are extremely misleading. His Critical enquiry has, he declares, nothing in common with psychology. In the _Preface_ to the first edition we find the following passage: “This enquiry ... [into] the pure understanding itself, its possibility and the cognitive faculties upon which it rests ..., although of great importance for my chief purpose, does not form an essential part of it.”[187] The question, he adds, “how is the faculty of thought itself possible?... is as it were a search for the cause of a given effect, and therefore is of the nature of an hypothesis [or ‘mere opinion’], though, as I shall show elsewhere, this is not really so.” The concluding words of this passage very fairly express Kant’s hesitating and inconsistent procedure. Though he has so explicitly eliminated from the central enquiry of the _Critique_ all psychological determination of the mental powers, statements as to their constitution are none the less implied, and are involved in his epistemological justification alike of _a priori_ knowledge and of ordinary experience. If we bear in mind that Kant is here attempting to outline the possible causes of given effects, and that his conclusions are therefore necessarily of a more hypothetical character than those obtained by logical analysis, we shall be prepared to allow him considerable liberty in their formulation. But in certain respects his statements are precise and definite--the view, for instance, of sensations as non-spatial, of time as a form of inner sense, of the productive imagination as pre-conditioning our consciousness, of spontaneity as radically distinct from receptivity, of the pure forms of thought as not acquired through sense, etc. No interpretation which ignores or under-estimates this psychological or subjective aspect of his teaching can be admitted as adequate.[188]

(2) =Logical or epistemological possibility.=--How can synthetic _a priori_ judgments be _valid_? This question itself involves a twofold problem. How, despite their synthetic character, can they possess truth, _i.e._ how can we pass from their subject terms to their predicates? And secondly, how, in view of their origin in our human reason, can they be objectively valid, _i.e._ legislate for the independently real? How can we pass beyond the subject-predicate relation to real things? This latter is the Critical problem in the form in which it appears in Kant’s letter of 1772 to Herz.[189] The former is the problem of synthesis which was later discovered.

(_b_) (1) =Possibility of explanation and= (2) =possibility of existence.=--(1) How can synthetic _a priori_ judgments be _accounted for_? How, despite their seemingly inconsistent and apparently paradoxical aspects, can their validity (their validity as well as their actuality being taken for granted) be rendered _comprehensible_? (2) The validity of such judgments has been called in question by the empiricists, and is likewise inexplicable even from the dogmatic standpoint of the rationalists. How, then, can these judgments _be possible at all_? These two meanings of the term ‘possible’ connect with the ambiguity, above noted, in the term ‘how.’ The former problem can be solved by an analytic method; the latter demands the application of the more radical method of synthetic reconstruction.

(_c_) =Real and ideal possibility.=[190]--We have to distinguish between the possible validity of those propositions which the mathematical and physical sciences profess to have established and the possible validity of those principles such as that of causality, which are postulated by the sciences, but which the sciences do not attempt to prove, and which in certain cases they do not even formulate. The former constitute an actually existent body of scientific knowledge, demonstrated in accordance with the demands of scientific method. The latter are employed by the scientist, but are not investigated by him. The science into which they can be fitted has still to be created; and though some of the principles composing it may be known, others remain to be discovered. All of them demand such proof and demonstration as they have never yet received.[191] This new and ideal science is the scientific metaphysics which Kant professes to inaugurate by means of the _Critique_. In reference to the special sciences, possibility means the conditions of the actually given. In reference to the new and ideal metaphysics, possibility signifies the conditions of the realisation of that which is sought. In view of this distinction, the formula--How are synthetic _a priori_ judgments possible?--will thus acquire two very different meanings. (1) How are the existing _a priori_ synthetic judgments to be accounted for? (2) How may all the really fundamental judgments of that type be exhaustively discovered and proved? Even in regard to immanent metaphysics Kant interprets the formula in both ways. This is due to his frequent confusion of immanent metaphysics with the principles of natural science. Its propositions are then regarded as given, and only their general validity calls for proof. It is, however, in the problem of ideal possibility that the essential problem of the _Critique_ lies; and that is a further reason why it cannot be adequately dealt with, save by means of the synthetic method.

* * * * *

=Experience.=--Throughout the _Introduction_ the term _experience_[192] has (even at times in one and the same sentence) two quite distinct meanings, (1) as product of sense and understanding acting co-operatively, and (2) as the raw material (the impressions) of sense. Considerable confusion is thereby caused.

=Understanding and reason=[193] are here, as often elsewhere in the _Critique_, used as equivalent terms. Throughout the entire two first sections of the _Introduction_ to the second edition the term reason does not occur even once. As first mentioned,[194] it is taken as the source of metaphysical judgments.

=General (a priori) truths have an inner necessity and must be clear and certain by themselves.=[195]--These statements are not in accordance with Kant’s new Critical teaching.[196] They have remained uncorrected from a previous way of thinking. This must be one reason for the recasting of this paragraph in the second edition.

=Even with (unter) our experiences there is mingled knowledge which must be of a priori origin.=[197]--Kant is here distinguishing the _immanent a priori_, such as that involved in any causal judgment, from the _transcendent a priori_ dwelt upon in the next paragraph. The latter is expressed through metaphysical judgments, such as ‘God exists,’ ‘the soul is immortal.’

=Original concepts and judgments derived from them.=[198]--Cf. B 5-6.

=Pure.=--In the title of the section the term _pure_[199] (_rein_) is, as the subsequent argument shows, taken as exactly equivalent to _a priori_. As Vaihinger notes, the adjective _apriorisch_ had not yet been invented. The opposite of pure is here empirical (_empirisch_).[200]

=All our knowledge begins with experience.=[201]--This is a stronger statement than any in the corresponding paragraphs of the first edition. Had Kant proceeded to develop its consequences, he would have had to recast the entire _Introduction_, setting the problem of empirical knowledge alongside that of the _a priori_.[202] As it is, he is forced[203] to subdivide the absolutely _a priori_ into the pure and the mixed.[204]

=By objects which affect (rühren) our senses. The raw material of sensuous impressions.=[205]--These incidental statements call for discussion. Cf. below, pp. 80-8, 120-1, 274 ff.

=A knowledge of objects which we call experience.=[206]--Kant does not keep to this definition. The term experience is still used in its other and narrower sense, as in the very next paragraph, when Kant states that knowledge does not, perhaps, arise solely from experience (= sense impressions).

=In respect of time.=[207]--This statement, taken as an account of Kant’s teaching in the _Critique_, is subject to two reservations. In the _Aesthetic_[208] Kant sometimes claims a temporal antecedence for the _a priori_. And secondly, the _a priori_ is not for Kant merely logical. It also possesses a dynamical priority.[209]

=Even experience itself is a compound.=[210]--The “even” seems to refer to the distinction drawn in A 2 between the immanent and the transcendent _a priori_.[211]

=It is therefore a question whether there exists such knowledge independent of experience.=[212]--This question was not raised in the first edition.[213] The alternative methods, analytic and synthetic, are discussed above, p. 44 ff.

=Such knowledge is called a priori and is distinguished from empirical knowledge.=[214]--Throughout the _Introduction_, in both editions equally, Kant fails to state the problems of the _Critique_ in a sufficiently comprehensive manner. He speaks as if the _Critique_ dealt only with the absolutely _a priori_, in its two forms, as immanent scientific knowledge and as transcendent speculation. It also deals with the equally important and still more fundamental problem of accounting for the possibility of _experience_.[215] Our empirical knowledge involves an _a priori_ element, and may not therefore be opposed to _a priori_ knowledge in the manner of the passage before us.

=This term a priori is not yet definite enough.=[216]--It is frequently employed in a merely relative sense. Thus we can say of a person who undermines the foundations of his house that he might have known _a priori_ that it would collapse, that is, that he need not wait for the experience of its actual fall. But still he could not know this entirely _a priori_; he had first to learn from experience that bodies are heavy, and will fall when their supports are taken away. But as dealt with in the _Critique_ the term _a priori_ is used in an absolute sense, to signify that knowledge which is independent, not of this or that experience only, but of all impressions of the senses. Thus far Kant’s position is comparatively clear; but he proceeds to distinguish two forms within the absolutely _a priori_, namely, mixed and pure. The absolutely _a priori_ is mixed when it contains an empirical element, pure when it does not. (“Pure” is no longer taken in the meaning which it has in the title of the section.[217] It signifies not the _a priori_ as such, but only one subdivision of it.) Thus after defining absolutely _a priori_ knowledge as independent of all experience, Kant takes it in one of its forms as involving empirical elements. The example which he gives of an absolutely _a priori_ judgment, which yet is not pure, is the principle: every change has its cause. “Change” is an empirical concept, but the synthetic relation asserted is absolutely _a priori_. In the next section[218] this same proposition is cited as a _pure_ judgment _a priori_--“pure” being again used in its more general meaning as synonymous with _a priori_. This confusion results from Kant’s exclusive preoccupation with the _a priori_, and consequent failure to give due recognition to the correlative problem of the empirical judgment. The omitted factor retaliates by thus forcing its way into Kant’s otherwise clean-cut divisions. Also, it is not true that the relative _a priori_ falls outside the sphere of the Critical enquiry. Such judgment expresses necessity or objectivity, and for that reason demands a transcendental justification no less urgently than the absolutely _a priori_. The finding of such justification is, indeed, the central problem of the _Analytic_.[219]

The subdivisions of the _a priori_ may be tabulated thus:

{ Relative, _e.g._ every unsupported house must
{ fall.
_A priori_ knowledge{ { Mixed, _e.g._ every change has its cause.
{ Absolute { Pure, _e.g._ a straight line is the shortest
{ { distance between two points.

The term _pure_ (_rein_) thus acquires a second meaning distinct from that defined above.[220] It is no longer employed as identical with _a priori_, but as a subdivision of it, meaning _unmixed_. Its opposite is no longer the empirical, but the impure or mixed. Owing, however, to the fact that “pure” (in its first meaning) is identical with the _a priori_, it shares in all the different connotations of the latter, and accordingly is also employed to denote that which is _not relative_. But “pure” has yet another meaning peculiar to itself. The phrase “independent of experience” has in reference to “pure” an ambiguity from which it does not suffer in its connection with “_a priori_” (since mathematical knowledge, whether pure or applied, is always regarded by Kant as _a priori_). It may signify either independence as regards _content and validity_, or independence as regards _scope_. The latter meaning is narrower than the former. By the former meaning it denotes that which originates, and can possess truth, independently of experience. By the latter it signifies that which is not only independent of sense but also applies to the non-sensuous. In this latter meaning pure knowledge therefore signifies transcendent knowledge. Its opposite is the immanent. The various meanings of “pure” (four in number) may be tabulated as follows:

(_a_) (1) _A priori_: independent of experience as regards origin
and validity. (Its opposite = empirical.)

{ (2) Absolutely independent of experience. (Its
{ opposite = relative.)

{ (3) Unmixed with experience. (Its opposite =
{ impure or mixed.)

(_b_) (4) Independent of experience as regards scope = transcendent.
(Its opposite = immanent.)

All these varied meanings contribute to the ambiguity of the title of the _Critique_. Kant himself employs the title in all of the following senses:

1. Critique of absolutely pure _a priori_ knowledge, determination of its sources, conditions, scope and limits.

2. Critique of all _a priori_ knowledge, relative as well as absolute, in so far as it depends upon _a priori_ principles, determination, etc.

3. Critique of all knowledge, whether _a priori_ or empirical, determination, etc.

4. Critique of transcendent knowledge, its sources and limits.

Further meanings could also be enumerated but can be formulated by the reader for himself in the light of the ambiguities just noted.[221] The special context in each case can alone decide how the title is to be understood. If a really adequate definition of the purpose and scope of the _Critique_ is sought by the reader, he must construct it for himself. The following may perhaps serve. _The_ Critique _is an enquiry into the sources, conditions, scope and limits of our knowledge, both a priori and empirical, resulting in the construction of a new system of immanent metaphysics; in the light of the conclusions thus reached, it also yields an analysis and explanation of the transcendental illusion to which transcendent metaphysics, both as a natural disposition and as a professed science, is due._

Kant further complicates matters by offering a second division of the absolutely _a priori_,[222] viz. into the original and the derivative. Also, by implication, he classes relative _a priori_ judgments among the propositions to be reckoned with by the _Critique_; and yet in B 4 he speaks of the proposition, all bodies are heavy, as merely empirical.[223]

=A criterion.=[224]--Necessity and universality are valid criteria of the _a priori_ (= the non-empirical). This follows from Kant’s view[225] of the empirical as synonymous with the contingent (_zufällig_). Experience gives only the actual; the _a priori_ alone yields that which cannot be otherwise.

“Necessity and strict universality are thus safe criteria of _a
priori_ knowledge, and are inseparable from one another. But since
in the employment of these criteria the empirical limitation of
judgments is sometimes more easily shown than their contingency,
or since, as frequently happens, their unlimited universality can
be more convincingly proved than their necessity, it is advisable
to use the two criteria separately, each being by itself
infallible.”[226]

Now Kant is here, of course, assuming the main point to be established, namely, that experience is incapable of accounting for such universality and necessity as are required for our knowledge, both ordinary and scientific. We have already considered this assumption,[227] and have also anticipated misunderstanding by noting the important qualifications to which, from Kant’s new Critical standpoint, the terms ‘necessity’ and ‘universality’ become subject.[228] The very specific meaning in which Kant employs the term _a priori_ must likewise be borne in mind. Though negatively the _a priori_ is independent of experience, positively it originates in our human reason. The necessity and universality which differentiate the _a priori_ distinguish it only from the humanly accidental. The _a priori_ has no absolute validity. From a metaphysical standpoint, it is itself contingent. As already stated,[229] all truth is for Kant merely _de facto_. The necessary is not that which cannot be conceived to be otherwise, nor is it the unconditioned. Our reason legislates only for the world of appearance. But as yet Kant gives no hint of this revolutionary reinterpretation of the rationalist criteria. One of the chief unfortunate consequences of the employment in this _Introduction_ of the analytic method of the _Prolegomena_ is that it tends to mislead the reader by seeming to commit Kant to a logical _a priori_ of the Leibnizian type.

=To show that, if experience is to be possible, [pure a priori propositions] are indispensable, and so to prove their existence a priori.=[230]--At first sight Kant would seem to be here referring to the alternative synthetic method of procedure, _i.e._ to the _transcendental_ proof of the _a priori_. The next sentence shows, however, that neither in intention nor in fact is that really so. He argues only that _a priori_ principles, such as the principle of causality, are necessary in order to give “certainty” to our experience; such a principle must be postulated if inductive inference is to be valid. Experience could have no [scientific] certainty, “if all rules according to which it proceeds were themselves in turn empirical, and therefore contingent. They could hardly be regarded as first principles.” There is no attempt here to prove that empirical knowledge _as such_ necessarily involves the _a priori_. Also the method of argument, though it seeks to establish the _necessity_ of the _a priori_, is not transcendental or Critical in character. It is merely a repetition of the kind of argument which both Hume and Leibniz had already directed against the sensationalist position.[231] Very strangely, considering that these sentences have been added in the second edition, and therefore subsequent to the writing of the objective deduction, Kant gives no indication of the deeper problem to which he finally penetrated. The explanation is, probably, that to do so would have involved the recasting of the entire _Introduction_. Even on the briefest reference, the hard-and-fast distinction between the _a priori_ and the empirical, as two distinct and separate classes of judgment, would have been undermined, and the reader would have been made to feel the insufficiency of the analysis upon which it is based.[232] The existence of the deeper view is betrayed only through careless employment of the familiar phrase “possibility of experience.” For, as here used, it is not really meant. “Certainty of experience”--a very different matter--is the meaning that alone will properly fit the context.

=Reason and understanding.=[233]--They are here distinguished, having been hitherto, in A 1-2, employed as synonymous. The former carries us beyond the field of all possible experience; the latter is limited to the world of sense. Thus both _Reason_ and _understanding_ are here used in their narrowest meaning.

=These inevitable problems of pure Reason itself are God, freedom, and immortality. The science which, with all its methods, is in its final intention directed solely to the solution of these problems, is called metaphysics.=[234]--These sentences are characteristic of the second edition with its increased emphasis upon the positive results of the _Critique_ on the one hand, and with its attitude of increased favour towards transcendent metaphysics on the other. The one change would seem to be occasioned by the nature of the criticisms passed upon the first edition, as, for instance, by Moses Mendelssohn who describes Kant as “the all-destroyer” (_der alles zermalmende_). The other is due to Kant’s preoccupation with the problems of ethics and of teleology. The above statements are repeated with even greater emphasis in B 395 _n_.[235] The definition here given of metaphysics is not strictly kept to by Kant. As above noted,[236] Kant really distinguishes within it two forms, immanent and transcendent. In so doing, however, he still[237] regards transcendent metaphysics as the more important. Immanent metaphysics is chiefly of value as contributing to the solution of the “inevitable problems of pure Reason.”

=A 3-4 = B 7-8.=--The reasons, here cited by Kant, for the failure of philosophical thinking to recognise the difference between immanent and transcendent judgments are: (1) the misunderstood character, and consequent misleading influence, of _a priori_ mathematical judgments; (2) the fact that once we are beyond the sensible sphere, experience can never contradict us; (3) natural delight in the apparent enlargement of our knowledge; (4) the ease with which logical contradictions can be avoided; (5) neglect of the distinction between analytic and synthetic _a priori_ judgments. Vaihinger points out[238] that in the _Fortschritte_[239] Kant adds a sixth reason--confusion of the concepts of understanding with the Ideas of Reason. Upon the first of the above reasons the best comment is that of the _Methodology_.[240] But the reader must likewise bear in mind that in B xvi Kant develops his new philosophical method on the analogy of the mathematical method. The latter is, he claims, _mutatis mutandis_, the true method of _legitimate_ speculation, _i.e._ of immanent metaphysics. The one essential difference (as noted by Kant[241]), which has been overlooked by the dogmatists, is that philosophy gains its knowledge from concepts, mathematics from the construction of concepts.

=Remain investigations only.=[242]--Cf. _Prolegomena_, § 35.

=The analysis of our concepts of objects.=[243]--Vaihinger’s interpretation, that the concepts here referred to are those which we “form _a priori_ of things,”[244] seems correct.[245] The rationalists sought to deduce the whole body of rational psychology from the _a priori_ conception of the soul as a simple substance, and of rational theology from the _a priori_ conception of God as the all-perfect Being.

=Analytic and synthetic judgments.=[246]--“All analytic judgments
depend wholly on the law of contradiction, and are in their nature
_a priori_ cognitions, whether the concepts that supply them with
matter be empirical or not. For the predicate of an affirmative
analytic judgment is already contained in the concept of the
subject, of which it cannot be denied without contradiction. In the
same way its opposite is necessarily denied of the subject in an
analytic, but negative, judgment by the same law of
contradiction.... For this very reason all analytic judgments are
_a priori_ even when the concepts are empirical, as, for example,
gold is a yellow metal; for to know this I require no experience
beyond my concept of gold as a yellow metal: it is, in fact, the
very concept, and I need only analyse it, without looking beyond it
elsewhere.... [Synthetic judgments, _a posteriori_ and _a priori_]
agree in this, that they cannot possibly spring solely from the
principle of analysis, the law of contradiction. They require a
quite different principle. From whatever they may be deduced, the
deduction must, it is true, always be in accordance with the
principle of contradiction. For that principle must never be
violated. But at the same time everything cannot be deduced from
it.”[247]

In A 594 = B 622 analytic judgments are also spoken of as identical; but in the _Fortschritte_[248] this use of terms is criticised:

“Judgments are analytic if their predicate only represents clearly
(_explicite_) what was thought obscurely (_implicite_) in the
concept of the subject, _e.g._ all bodies are extended. Were we to
call such judgments identical only confusion would result. For
identical judgments contribute nothing to the clearness of the
concept, and that must be the purpose of all judging. Identical
judgments are therefore empty, _e.g._ all bodies are bodily (or to
use another term material) beings. Analytic judgments do, indeed,
ground themselves upon identity and can be resolved into it; but
they are not identical. For they demand analysis and serve for the
explanation of the concept. In identical judgments, on the other
hand, _idem_ is defined _per idem_, and nothing at all is
explained.”

Vaihinger[249] cites the following contrasted examples of analytic and synthetic judgments:

_Analytic._--(_a_) Substance is that which exists only as subject in which qualities inhere.[250] (_b_) Every effect has a cause.[5] (_c_) Everything conditioned presupposes a condition.

_Synthetic._--(_a_) Substance is permanent. (_b_) Every event has a cause.[251] (=c=) Everything conditioned presupposes an unconditioned.

=B 11-12.=--The first half of this paragraph is transcribed practically word for word from the _Prolegomena_.[252] The second half is a close restatement of an omitted paragraph of the first edition. The chief addition lies in the concluding statement, that “experience is itself a synthetic connection of intuitions.” This is in keeping with statements made in the deduction of the categories in the second edition,[253] and in the paragraph inserted in the proof of the second analogy in the second edition.[254] The _x_ has strangely been omitted in the second edition in reference to empirical judgments, though retained in reference to synthetic _a priori_ judgments.

=The proposition: everything which happens has its cause.=[255]--As we have already observed,[256] Hume influenced Kant at two distinct periods in his philosophical development--in 1756-1763, and again at some time (not quite definitely datable) after February 1772. The first influence concerned the character of concrete causal judgments; the second related to the causal axiom. Though there are few distinctions which are more important for understanding the _Critique_ than that of the difference between these two questions, it has nowhere been properly emphasised by Kant, and in several of the references to Hume, which occur in the _Critique_ and in the _Prolegomena_, the two problems are confounded in a most unfortunate manner. The passages in the _Introduction_[257] are clear and unambiguous; the influence exercised by Hume subsequent to February 1772 is quite adequately stated. The causal axiom claims to be _a priori_, and is, as Hume asserts, likewise synthetic. Consequently there are only two alternatives, each decisive and far-reaching. Either valid _a priori_ synthesis must, contrary to all previous philosophical belief, be possible, or “everything which we call metaphysics must turn out to be a mere delusion of reason.” The solution of this problem is “a question of life and death to metaphysics.” To this appreciation of Hume, Kant adds criticism. Hume did not sufficiently universalise his problem. Had he done so, he would have recognised that pure mathematics involves _a priori_ synthesis no less necessarily than do the metaphysical disciplines. From denying the possibility of mathematical science “his good sense would probably have saved him.” Hume’s problem, thus viewed, finds its final and complete expression in the formula: How are synthetic _a priori_ judgments possible?

In A 760 = B 788 the account differs in two respects: first, it discusses the metaphysical validity of the causal axiom as well as its intrinsic possibility as a judgment; and secondly, reference is made to the conception of causality as well as to the axiom. The implied criticism of Hume is correspondingly modified. Otherwise, it entirely harmonises with the passages in the _Introduction_.

“Hume dwelt especially upon the principle of causality, and quite
rightly observed that its truth, and even the objective validity of
the concept of efficient cause in general, is based on no insight,
_i.e._ on no _a priori_ knowledge, and that its authority cannot
therefore be ascribed to its necessity, but merely to its general
utility in the course of experience and to a certain subjective
necessity which it thereby acquires, and which he entitles custom.
From the incapacity of our reason to make use of this principle in
any manner that transcends experience he inferred the nullity of
all pretensions of reason to advance beyond the empirical.”

Now so far, in these references to Hume, Kant has had in view only the problems of mathematical and physical science and of metaphysics. The problems involved in the possibility of empirical knowledge are left entirely aside. His account of Hume’s position and of his relation to Hume suffers change immediately these latter problems are raised. And unfortunately it is a change for the worse. The various problems treated by Hume are then confounded together, and the issues are somewhat blurred. Let us take the chief passages in which this occurs. In A 764 = B 792 ff. Kant gives the following account of Hume’s argument. Hume, recognising the impossibility of predicting an effect by analysis of the concept of the cause, or of discovering a cause from the concept of the effect, viewed all concrete causal judgments as merely contingent, and therefrom inferred the contingency of the causal axiom. In so doing Hume, Kant argues, confuses the legitimate and purely _a priori_ inference from a given event to _some_ antecedent with the very different inference, possible only through special experience, to a _specific_ cause. Now this is an entire misrepresentation of Hume’s real achievement, and may perhaps be explained, at least in part, as being due to the fact that Kant was acquainted with Hume’s _Treatise_ only through the indirect medium of Beattie’s quotations. Hume committed no such blunder. He clearly recognised the distinction between the problem of the validity of the causal axiom and the problem of the validity of concrete causal judgments. He does not argue from the contingency of concrete causal laws to the contingency of the universal principle, but shows, as Kant himself recognises,[258] that the principle is neither self-evident nor demonstrable _a priori_. And as necessity cannot be revealed by experience, neither is the principle derivable from that source. Consequently, Hume concludes, it cannot be regarded as objectively valid. It must be due to a subjective instinct or natural belief. (The two problems are similarly confounded by Kant in A 217 = B 264.)

In the _Introduction_ to the _Prolegomena_ there is no such confusion of the two problems, but matters are made even worse by the omission of all reference to Hume’s analysis of the causal axiom. Only Hume’s treatment of the concept of causality is dwelt upon. This is the more unfortunate, and has proved the more misleading, in that it is here that Kant makes his most explicit acknowledgment of his indebtedness to Hume. In §§ 27 ff. of the _Prolegomena_ both problems reappear, but are again confounded. The section is preceded by sentences in which the problem of experience is emphasised; and in keeping with these prefatory remarks, Kant represents “Hume’s _crux metaphysicorum_” as concerning only the concept of causality (viewed as a synthetic, and professedly _a priori_, connection between concrete existences). Yet in § 30 the causal axiom is also referred to, and together they are taken as constituting “Hume’s problem.”

Now if we bear in mind that Hume awakened Kant to both problems--how _a priori_ knowledge is possible, and how experience is possible--this confusion can easily be understood. Kant had already in the early ‘sixties studied Hume with profound admiration and respect.[259] In the period subsequent to 1772 this admiration had only deepened; and constantly, as we may believe, Kant had returned with fresh relish to Hume’s masterly analyses of causality and of inductive inference. It is not, therefore, surprising that as the years passed, and as the other elements in Hume’s teaching revealed to him, through the inner growth of his own views, their full worth and significance, he should allow the contribution that had more specifically awakened him to fall into the background, and should, in vague fashion, ascribe to Hume’s teaching as a whole the specific influence which was really due to one particular part. By 1783, the date of the _Prolegomena_, Kant’s first enthusiasm over the discovery of the fundamental problem of _a priori_ synthesis had somewhat abated, and the problem of experience had more or less taken its place. This would seem to be the reason why in the _Prolegomena_ he thus deals with both aspects of Hume’s problem, and why in so doing he gives a subordinate place to Hume’s treatment of the causal axiom. But though the misunderstanding may be thus accounted for, it must none the less be deplored. For the reader is seriously misled, and much that is central to the Critical philosophy is rendered obscure. The influence which Kant in the _Prolegomena_ thus ascribes to Hume was not that which really awakened him from his dogmatic slumber, but is in part that which he had assimilated at least as early as 1763, and in part that which acted upon him with renewed force when he was struggling (probably between 1778 and 1780) with the problems involved in the deduction of the categories. It was Hume’s treatment of the causal axiom, and that alone, which, at some time subsequent to February 1772, was the really effective influence in producing the Copernican change.[260]

=Purely a priori and out of mere concepts.=[261]--Vaihinger’s comment seems correct: Kant means only that neither actual experience nor pure intuition can be resorted to. This does not contradict the complementary assertion,[262] that the principle, everything which happens has its cause, can be known _a priori_, not immediately from the concepts involved in it, but only indirectly[263] through the relation of these concepts to possible experience. “Possible experience,” even though it stands for “something purely contingent,” is itself a concept. Vaihinger[264] quotes Apelt upon this “mysterious” type of judgment.

“Metaphysics is synthetic knowledge from mere concepts, not like
mathematics from their construction in intuition, and yet these
synthetic propositions cannot be known from bare concepts, _i.e._
not analytically. The necessity of the connection in those
propositions is to be apprehended through thought alone, and yet is
not to rest upon the form of thought, the principle of
contradiction. The conception of a kind of knowledge which arises
from bare concepts, and yet is synthetic, eludes our grasp. The
problem is: How can one concept be necessarily connected with
another, without also at the same time being contained in it?”

The paragraphs in B 14 to B 17 are almost verbal transcripts from _Prolegomena_, § 2 _c_, 2 ff.

=Mathematical judgments are one and all (insgesammt) synthetic.=[265]--This assertion is carelessly made, and does not represent Kant’s real view. In B 16 he himself recognises the existence of analytic mathematical judgments, but unduly minimises their number and importance.

=All mathematical conclusions proceed according to the principle of contradiction.=[266]--To the objection made by Paulsen that Kant, in admitting that mathematical judgments can be deduced from others by means of the principle of contradiction, ought consistently to have recognised as synthetic only axioms and principles, Vaihinger replies as follows:[267]

“The proposition--the angles of a triangle are together equal to
two right angles--Kant regards as synthetic. It is indeed deduced
from the axiom of parallels (with the aid of auxiliary lines), and
to that extent is understood in accordance with the principle of
contradiction.... The angles in the triangle constitute a special
case of the angles in the parallel lines which are intersected by
other lines. The principle of contradiction thus serves as vehicle
in the deduction, because once the identity of A and A´ is
recognised, the predicate _b_, which belongs to A, must also be
ascribed to A´. But the proposition is not for that reason itself
analytic in the Kantian sense. In the analytic proposition the
predicate is derived from the analysis of the subject concept. But
that does not happen in this case. The synthetic proposition can
never be derived _in and by itself_ from the principle of
contradiction; ... but only with the aid of that principle _from
other propositions_. Besides, in this deduction intuition must
always be resorted to; and that makes an essential difference.
Without it the identity of A and A´ cannot become known.”

=Pure mathematics.=[268]--“Pure,” as thus currently used, is opposed only to applied, not to empirical. Kant here arbitrarily reads the latter opposition into it. Under this guise he begs the point in dispute.

7 + 5 = 12.[269]--Though 7 + 5 = 12 expresses an identity or equality, it is an equality of the _objects_ or _magnitudes_, 7 + 5 and 12, not of the concepts through which we think them.[270] Analysis of the concepts can never reveal this equality. Only by constructing the concepts in intuition can it be recognised by the mind. This example has been already cited in the first edition.[271] It is further elaborated in the _Prolegomena_, § 2 _c_, and is here transcribed. Kant’s mode of stating his position is somewhat uncertain. He alternates between “the representation of 7 and 5,” “the representation of the combination of 7 and 5,”[272] and “the concepts 7 and 5.”[273] His view would seem to be that there are _three_ concepts involved. For the concept of 7 we must substitute the intuition of 7 points, for the concept of 5 the intuition of 5 points, and for the concept of their sum the intuitive operation of addition.

=Call in the assistance of intuition, for instance our five fingers.=[274]--This statement, repeated from the _Prolegomena_,[275] does not represent Kant’s real position. The views which he has expressed upon the nature of arithmetical science are of the most contradictory character,[276] but to one point he definitely commits himself, namely, that, like geometrical science, it rests, not (as here asserted) upon empirical, but upon pure intuition.[277] Except indirectly, by the reference to larger numbers, Kant here ignores his own important distinction between image and schema.[278] The above statement would also make arithmetic dependent upon space.

=Segner: Anfangsgründe der Arithmetik=,[279] translated from the Latin, second edition, Halle, 1773.

=Natural science (physica) contains synthetic a priori judgments.=[280]--There is here a complication to which Vaihinger[281] has been the first to draw attention. In the _Prolegomena_[282] Kant emphasises the distinction between physics and pure or universal science of nature.[283] The latter treats only the _a priori_ form of nature (_i.e._ its necessary conformity to law), and is therefore a propaedeutic to physics which involves further empirical factors. For two reasons, however, this universal natural science falls short of its ideal. First, it contains empirical elements, such as the concepts of motion, impenetrability, inertia, etc. Secondly, it refers only to the objects of external sense, and not, as we should expect in a universal science, to natural existences without exception, _i.e._ to the objects of psychology as well as of physics.[284] But among its principles there are, Kant adds, a few which are purely _a priori_ and possess the universality required: _e.g._ such propositions as that _substance is permanent_, and that _every event has a cause_. Now these are the examples which ought to have been cited in the passage before us. Those actually given fall entirely outside the scope of the _Critique_. They are treated only in the _Metaphysische Anfangsgründe_. They belong to the relatively, not to the absolutely, pure science of nature. The source of the confusion Vaihinger again traces to Kant’s failure to hold fast to the important distinction between immanent and transcendent metaphysics.[285] His so-called pure or universal natural science (nature, as above noted, signifying for Kant “all that is”) is really _immanent metaphysics_, and the propositions in regard to substance and causality ought therefore to be classed as metaphysical. This, indeed, is how they are viewed in the earlier sections of the _Prolegomena_. The distinction later drawn in § 15 is ignored. Pure natural science is identified with mathematical physics, and the propositions which in § 15 are spoken of as belonging to pure universal natural science are now regarded as metaphysical. “Genuinely metaphysical judgments are one and all synthetic.... For instance, the proposition--everything which in things is substance is permanent--is a synthetic, and properly metaphysical judgment.”[286] In § 5 the principle of causality is also cited as an example of a synthetic _a priori_ judgment in metaphysics. But Kant still omits to draw a distinction between immanent and transcendent metaphysics; and as a consequence his classification of synthetic _a priori_ judgments remains thoroughly confused. They are taken as belonging to three spheres, mathematics, physics (in the relative sense), and metaphysics. The implication is that this threefold distinction corresponds to the threefold division of the _Doctrine of Elements_ into _Aesthetic_, _Analytic_, and _Dialectic_. Yet, as a matter of fact, the propositions of mathematical physics, in so far as they are examples of applied mathematics, are dealt with in the _Aesthetic_, and in so far as they involve concepts of motion and the like fall entirely outside the scope of the _Critique_, while the _Analytic_ deals with those _metaphysical_ judgments (such as the principle of causality) which are of immanent employment.[287]

As the new paragraphs in the _Introduction_ to the second edition are transferred without essential modification from the _Prolegomena_, they are open to the same criticism. To harmonise B 17 with the real teaching of the _Critique_, it must be entirely recast. Instead of “natural science” (_physica_) we must read “pure universal natural science [= immanent metaphysics],” and for the examples given we must substitute those principles of substance and causality which are dealt with in the _Analytic_. The next paragraph deals with metaphysics in its transcendent form, and accordingly states the problem peculiar to the _Dialectic_.

=Metaphysics.=[288]--This paragraph deals _explicitly_ only with transcendent judgments, but as the terms used are ambiguous, it is possible that those of immanent metaphysics are also referred to. The paragraph is not taken from the _Prolegomena_. The corresponding passage[289] in the _Prolegomena_ deals only with the judgments of immanent metaphysics.

=The real problem of pure reason is contained in the question: How are synthetic a priori judgments possible?=[290]--Cf. above, pp. 26 ff., 33 ff., 43 ff.

=David Hume.=[291]--Cf. above, pp. 61 ff.

=A theoretical knowledge.=[292]--_i.e._ Kant explicitly leaves aside the further problem, whether such judgments may not also be possible in the practical (moral) and other spheres.

=How is pure natural science possible?=[293]--The note which Kant appends shows that he is here taking natural science in the relative sense.[294] The same irrelevant instances are again cited.

=As these sciences really exist.=[295]--Cf. below, p. 44 ff.

=The poor progress which metaphysics has hitherto made.=[296]--Cf. _Preface_ to the second edition; _Prolegomena_, § 4, and A 175 ff.

=How is metaphysics as a science possible?=[297]--We may now consider how this and the three preceding questions are related to one another and to the various divisions of the _Critique_.[298] The four subordinate questions within the main problem--How are synthetic _a priori_ judgments possible?--are here stated by Kant as:

1. =How is pure mathematics possible?=

2. =How is pure natural science possible?=

3. =How is metaphysics as natural disposition possible?=

4. =How is metaphysics as science possible?=

There is little difficulty as regards 1 and 2. The first is dealt with in the _Aesthetic_, and the second[299] in the _Analytic_, though, owing to the complexity of the problems, the _Aesthetic_ and _Analytic_ are wider than either query, and cannot be completely separated. Applied mathematics is dealt with in the _Analytic_ as well as in the _Aesthetic_, and in both the determination of the limits of scientific knowledge is equally important with that of accounting for its positive acquisitions. The third and fourth questions raise all manner of difficulties. Notwithstanding the identical mode of formulation, they do not run on all fours with the two preceding. The first two are taken as referring to actually existing and valid sciences. It is the ground of their _objective validity_ that is sought. But what is investigated in the third question falsely lays claim to the title of science; we can enquire only as to the ground of its _subjective_ possibility. In the fourth question, the problem takes still another form. Kant now seeks to determine _whether_ a new, not yet existing, science of metaphysics is possible, and _in what manner_ it can be validly constructed. The manifoldness of the problems is thus concealed by the fixity of the common formula.[300] Now with what divisions of the _Critique_ are the two last questions connected? It has been suggested[301] that the third question is dealt with in the _Dialectic_ and the fourth in the _Methodology_, the four questions thus corresponding to the four main divisions of the _Critique_. But this view is untenable, especially in its view of the fourth question. The division of the _Critique_ is by dichotomy into _doctrine of elements_ and _doctrine of methods_, the former including the _Aesthetic_ and _Logic_, and the _Logic_ being again divided into _Analytic_ and _Dialectic_. Its problems stand in an equally complex subordination; they cannot be isolated from one another, and set merely side by side. Secondly, it has been maintained[302] that the third question is dealt with in the introduction to the _Dialectic_ (in its doctrine of Ideas), and the fourth in the _Dialectic_ proper. This view is fairly satisfactory as regards the third question, but would involve the conclusion that the fourth question refers only to transcendent metaphysics, and that it therefore receives a negative answer. But that is not Kant’s view of metaphysics _as a science_. The _Critique_ is intended to issue in a new and genuine body of metaphysical teaching.