¹ Readers of part I of this article (Kantian Review, 3, 1999) will recall that I use the term ‘psychologism’ to designate a method of determining the meaning, and delimiting the scope of application, of certain key meta-physical concepts by means of a psychological account of their origin as representations in the mind.

² The reading outlined in this section derives primarily from chs 4A and 5E of my book, Hume's Theory of Consciousness (HTC) (Cambridge: Cambridge University Press, 1994)Google Scholar.

³ The essential element of an idea of a causal relation is the idea of a necessary connection (see A Treatise of Human Nature (THN) 407 and An Enquiry Concerning Human Understanding (EHU) VIII/i. 74). Its impression original consists of two elements: (i) the facility affect in terms of which Hume psychologistically explicated the notion of a relation between distinct perception (facility is the ‘essence’ or ‘nature’ of relation: THN 99, 204, 220, 260), and (ii) the vivacity affect in terms of which Hume psychologistically explicated the notion of real existence, especially the real existence of anything lying beyond the memory and senses (THN97, 107–10, 184, and EHU VI/ii). For an extended treatment of the role of facility affect in Hume's theory of the understanding, see my article, ‘The point of Hume's skepticism with regard to reason: the primacy of facility affect in the theory of human understanding’, Hume Studies, 24/2 (Nov. 1998), 235–74. For a discussion of vivacity affect, and the role of affect in Hume's associationalism generally, see HTC.

⁴ Hume did allow that there are ‘philosophical relations of cause and effect’ which do not incorporate in them the idea of a customary transition of thought. However, he deemed such relations parasitic on the ‘natural relations of cause and effect’ which do include it (see THN 94). This is because the necessity component ‘makes an essential part of causation’ (THN 407), and the idea of a necessary connection has its source in customary transitions of thought.

⁵ ‘[S]pace, no less than time, inheres in us as a pure form of our sensibility before perception of experience and makes possible all intuition of sensibility, and therefore all appearances’ (Ak. 17: §4673; see also A26/B42, A30/B45, A42/B59, A115–16, B162 , A378; Ak. 20: 266; and Ak. 22:43).

⁶ See B67, A89–90/B122–3, A92–3/B125–6, A111, A124, B145.

⁷ If, as most scholars suppose, Kant denied the (extra-logical, that is, mathematical) possibility of non-Euclidean geometry, then he would have been claiming more than he could prove from transcendental philosophical grounds, and, indeed, his claim would be contrary to them. For Euclidean space is a constructed space, made in accordance with the concepts that enter into its definitions, axioms and postulates, whereas Kantian metaphysical space is possible prior to and independently of all concepts. In general, Kant is clear that nothing transcendental implies or entails any mathematical or empirical truth; and so his transcendental philosophy should, it seems, be completely non-committal about what the particular axioms of geometry are to be. What then is the import of the transcendental principle of Axioms of Intuition (A162–6/B202–7)? It seems to me that virtually everything Kant says about Euclidean geometry can be reconciled with the thesis that no mathematical truths of any kind — axioms or any other — can be derived from the transcendental principle without supplementation by properly mathematical principles exhibited (constructed) in intuition. In particular, the transcendental principle of axioms may amount to nothing more than this: whatever axioms of geometry we may succeed in constructing — whether by 400 BC, 1780, 3750, or whatever date — have validity in relation to the a priori nature (formal constitution) of appearances. If so, Kant's emphasis on Euclidean geometry may simply have been due to the fact that no other rigorously defined, genuinely mathematical axioms of space existed in his lifetime. That is, it may never have been Kant's intention to declare that Euclidean axioms are immune to being subsumed or superseded by subsequent developments in mathematics; his concern may rather have been to render these, together with any axioms geometers may succeed in constructing, invulnerable to the assaults of his own extension of Humean scepticism to mathematics (see Critique of Practical Reason (CPrR) 52; also A165/B206). Although we can probably never be completely certain on the basis of the available textual evidence, it seems to me highly probable that a philosopher who recognized that ‘mathematics … always progresses without end’ (Ak. 20: 259) would not have given so vulnerable a hostage to fortune as a meta physically based defiance of all future geometers to devise rigorously defined, fully mathematical non-Euclidean axioms.

⁸ Confusingly, Kant sometimes writes of the concepts of space and time when he means the pure intuitions. In this sense, it is part of the concept of space and time that they are not concepts at all (most notably, in the sections of the Aesthetic that carry the subheadings ‘metaphysical expositions of this concept [of space, of time]’; see also A85/B118 and A107).

⁹ See n. 8 above.

¹⁰ See my Kant's Model of the Mind (Oxford: Oxford University Press, 1991), pp. 56–56.Google Scholar Kant did not hesitate to go so far as to deny even so much as the possibility that space and time might exist as things in themselves or as features (properties, relations) of things in themselves (see A42–4/B59–62 and Prolegomena to Any Future Metaphysics (PFM) §52b, Ak. 4: 341–2; also A38/B55, B149, A358–9, A375–6, and A385). The question is on what ground could Kant make such an affirmation? Psychologism, I believe, is the only tenable answer.

¹¹ This idea is present in a less developed form in the A Deduction: ‘the numerical unity of this apperception thus underlies a priori all concepts’ (A107). In the A edition of the Critique, the role of apperception in making thought itself possible is more evident in the Paralogisms than in the Deduction: ‘the concept, or if one prefers, the judgment: I think … is the vehicle of all concepts in general, thence also of transcendental concepts, and thus that it is always conceived along with these too and is just as transcendental as they’ (A341/B399). See also A341/B399, A346/B404, A348/B406, A350, A354–5, and A381–2 (it is also clearly in evidence in Ak. 18: §5203 from the second half of the 1770s). Only in the 1787 Deduction did Kant see fit to devote an entire section to the relation of representations to the identity of the subject of thought, quite apart from any question of their relation to an object in cognition.

¹² An extended account can be found in my article, ‘Kant and the possibility of thought: universals without language’, Review of Metaphysics (June 1995), 809–59.

¹³ For further discussion, see n. 12 and my article, ‘What are Kant's Analogies about?’, Review of Metaphysics (Sept. 1993), 63–114.

¹⁴ Kant seems to have excluded singular representations from the province of pure general logic proper: see A71/B96. Since it is difficult to conceive of any calculus, including that of truth-functions, as being possible in the absence of singular referring expressions, one may see in this evidence that Kant would have been likely to regard post-Fregean mathematical logic as a branch of pure mathematics rather than as pure general logic.

¹⁵ Although number (the schema of the categories of quantity, see A142–3/B182), as well as the transcendental principle of Axioms of Intuition, do enter into mathematics in much the same way as the pure cogito enters into logic, Kant held that it is impossible to abstract absolutely from their sensible conditions (time and space) so as to rely merely on the (unschematized) categories for purposes of mathematics. Why he held this to be so even in the cases of arithmetic and algebra is far from certain, yet that he did so seems beyond question. Kant states that arithmetic attains its concepts of numbers by successive addition in time at PFM §10, and, while admitting that ‘the science of numbers, notwithstanding the succession that every construction of quantity requires, is a pure intellectual synthesis’, still insists that it would be impossible to specify quantities (or quanta) in accordance with this science except by subjecting the pure manifold of thought ‘to the time condition’ (letter to Schultz, 25 Nov. 1788). Kant even appears to have believed pure space to be necessary to concepts of number as well, thereby seeming to extend to their schema his remark about the principles of quantity at B293:

We cannot represent any number except through successive enumeration (Aufzählung) in time and then the comprehension (Zusammennehmen) of this plurality in the unity of a number. But this cannot occur otherwise than that I place them next to one another in space; for they must be thought as given simultaneously, i.e. as comprehended into one representation; otherwise, this many (Viele) does not constitute a quantitative magnitude (number); however, simultaneity is not possible to cognize other than that I can apprehend (not merely think) the plurality as given forwards and backwards outside of my act of composition. Thus, an intuition must be given in which the manifold is represented outside one another and [simultaneously represented] next to one another, i.e. an intuition of space which makes possible spatial representation in perception in order to determine [existence] my own existence in time, i.e. an existence outside of me that underlies the determination of my own existence, i.e. the empirical consciousness of my self. (Ak. 18: §6314, c.1790–1; see also Kant's letter to Rehberg, 25 Sept. 1790).

Evidently, Kant supposed three things not derivable from intellect (logic) to be essential to all consciousness of number: (i) a manifold of a priori intuition in general; (ii) the ability to run through a manifold successively; and (iii) the ability to represent this successive manifold cumulatively at each instant (so that the preceding elements are not lost from thought: cf. A101–2). The special form for this last, in beings whose sensibility is constituted like ours, is space, as making possible the juxtaposition of a manifold in mathematical and empirical intuition (‘juxtaposition’ is a term found rarely in the Critique but often in the Reflexionen and Opus Postumum). For one must be careful to keep in mind that inner sense and its pure form (time) only make possible one kind of intuition of manifoldness, or distinctness (Verschiedenheit), among sensible representations: succession. Without a different mode of distinctness, it would be impossible for us to exhibit intuitively to ourselves how predecessors in a series can be added to their successors so as to make possible the (categorial) representation of a totality — not excepting the adding up of distinct times to constitute a determinate magnitude of time (i.e. ‘time itself’ as generated ‘in the apprehension of the intuition’, A143/B182; also, Kant's insistence that time cannot be represented in intuition except by drawing a line in space, A33/B50 and B154–5). Thus, for Kant, space, as an infinite given magnitude that precedes and makes possible the juxtaposition of a manifold of elements (howsoever many), ipso facto also makes possible all determinate (that is, concept-based) representations of magnitudes, be they purely abstract and intellectual (numbers) or inner and immediately sensible (insofar as Kant treats time as the permanent substrate of succession, as at B224, space/juxtaposition is just as indispensable to this representation as time/succession).

¹⁶ No such proof is possible, according to Kant, for their relation to objects as things in themselves. As we saw in part I, section 4, demonstrating the impossibility of such a proof is Kant's ‘main purpose’ (Axvi) in the Critique.

¹⁷ The passage in Kant's response to Eberhard discussed in n. 21 of part I of this article has sometimes been invoked (e.g. by D. Henrich) as evidence in support of the anti-psychologistic reading of quid juris, since there Kant borrows another notion from the theory of right: original acquisition. But there is nothing about the phrase itself that implies that Kant deemed the genetic and the normative senses of the notion in any way incompatible. Moreover, when one considers the use to which it is put by Kant, there can be no doubt that he is primarily, indeed exclusively, concerned with the genetic sense (that is, the origin of pure intuitions and pure concepts in the mind): he argues against innatism and against empiricism in favour of a third mode of origin, made possible by his doctrine of pure sensibility (‘Original acquisition’). Indeed, for all intents and purposes, original acquisition is the same as the patently genetic notion of an ‘epigenesis of pure reason’ discussed in the B transcendental deduction (see also n. 19 of part I). Thus, we should be wary of reading too much into Kant's predilection for legal analogies: it tells us nothing, either way, about the context or the content of transcendental philosophy.

¹⁸ Insofar as transcendental idealism is part and parcel of Kant's doctrine of pure sensibility, and so, too, of his psychologiem, this dependence may be supposed to extend to his practical philosophy as well:

The system of the critique of pure reason turns on two cardinal points: as system of nature and of freedom, one leading with necessity to the other. The ideality of space and time and the reality of the concept of freedom, the first leading inexorably and analytically to the second. According to the one, synthetic-theoretical cognition a priori; according to the other, synthetic-practical, likewise completely a priori. (Ak. 18: §6353: 1796–8)

Without the transcendental psychological foundation laid in the first Critique, Kant's principle of morality (=the maxim of one's action should also be able to be considered a universally legislated principle for all wills: CPrR 30–l) would collapse into a mere formula, lacking the special grounding in the nature of our minds which alone saves it from a dependence on the passions (as aroused by exhortation, threats of punishment, etc.) to draw us to obedience. The recent tendency to downplay or altogether neglect the first Critique's subjective-transcendental dimension in considerations of Kant's moral philosophy is highly regrettable, since it can only obscure the nature and sources of reason's inherently practical vocation. Nor can one hope to understand the historical course philosophy took in the years after Kant (Fichte, Hegel, Schopenhauer, et al) if one does not grasp the transition from the negative freedom conceived by means of the theoretical reason of the first Critique to the positive freedom made conceivable by the practical reason of the second.