Key questions concerning Kant’s Transcendental Deduction are: what is the method of proof? and why are two arguments needed? Karl Ameriks’s (Reference Ameriks1978) is the seminal work on the former, as is Dieter Henrich’s (Reference Henrich1969) on the latter. Thomas C. Vinci’s new book offers original answers. He builds on Ameriks’s contention that the Aesthetic and Deduction employ the same method. The method, for Vinci, is inference to the best explanation. The Aesthetic proposes a projectionism to explain the coincidence that bodies in empirical space and figures in pure space are Euclidean. The Deduction posits a prescriptivism to explain why empirical objects and intentional objects are categorial. Vinci accepts Henrich’s formulation of the problem of the two-steps-in-one-proof. While the first step treats ‘intuitions in general’ and the second ‘empirical intuitions’, the second must not trivially follow from the first. For Vinci, ‘intuitions in general’ are substance-accident unities, while ‘empirical intuitions’ are part-whole unities. Because these are disjoint classes of representations, each must be shown to be categorial.

Vinci’s Introduction argues that the Deduction’s project is to prove ‘nomic prescriptivism’, the two-fold thesis that (a) ‘the objective order must conform to the subjective conditions of thought’ and (b) the reason it must do so is that ‘the very existence of these objects depends on the existence of representations of them’ (p. 4). This is at odds with Kant’s own formulation, however. Kant states, ‘representation in itself … does not produce its object as far as its existence is concerned’ (Kant 1998: A92/B125). The categories, instead, make it possible ‘to cognize something as an object’ (ibid.).

Vinci’s treatment of the Deduction spans chapters 5–7, while chapters 1–4 treat Kant’s theory of space. Chapter 1 proposes a ‘container view’ (10), on which Kant’s thesis that space is an a priori form of intuition means that (a) space is a structure in which objects can be constructed and received, (b) space imparts its properties to objects in it and (c) objects in space impart nothing to space itself.

Chapter 2 addresses the ‘problem’ of ‘showing the connection between Kant’s claim that space is an a priori intuition and his claim that space is nothing more than a structure within … our minds’ (p. 23). There is some confusion here, though. Kant himself sees no problem with this connection. He writes, ‘[H]ow can an outer intuition inhabit the mind that precedes the objects themselves, and in which the concept of the latter can be determined a priori? Obviously not otherwise than insofar as it has its seat merely in the subject, as its formal constitution for being affected by objects’ (B41). Does the problem, as Vinci sees it, concern the empirical reality or the transcendental ideality of space? Is Vinci asking how Kant reasons from space being an a priori form of intuition to the conclusion that all appearances are in space, or to the conclusion that no things in themselves are? The latter would be the problem of the ‘neglected alternative’.

Vinci’s solution is this. Kant supposes that empirical intuitions and the objects of empirical intuitions alike are Euclidean. Finding this in need of explanation, Kant posits that the objects of empirical intuitions derive their properties from the properties of our representations. Now this is not a solution to the problem of the neglected alternative, since it leaves it open whether things in themselves might be spatial. Vinci’s solution seems, instead, to explain why appearances are spatial. His explanation differs from Kant’s own, however. Kant’s explanation, as I read it, is that, since space is an a priori form of our sensibility, and since objects can appear to us only by affecting our sensibility, space applies to all appearances (Kant 1998: A26–8/B42–4 and A89/B121–2). (For an extended discussion of this topic, see Shaddock Reference Shaddock2014: 43–4.)

Vinci considers Kant’s theory of intentionality as it relates to his projectionism in chapter 3. He argues that, for Kant, the objects of intuitions are intentional objects, which depend ontologically upon being intuited. He maintains that, for Kant, this is why their geometrical structure derives from the geometrical structure of our intuitions. Vinci is careful to distinguish transcendental idealism from phenomenalism, but he engages too superficially with Henry Allison’s (Reference Allison2004) powerful criticism of ontological interpretations.

Vinci reconstructs an argument of Kant’s regarding space in chapter 4, and it serves as his model for reconstructing the Deduction in chapter 5. The argument regarding space is this. Kant argues, on one hand, that figures constructed in pure intuition are Euclidean because the space of pure intuition is Euclidean and, on the other, that empirical objects are Euclidean because empirical space is Euclidean. Then Kant proposes to explain this coincidence with a projectionism according to which ‘pure intuition is the space in which empirical objects are situated’ (p. 95).

The argument of the Deduction, for Vinci, is this. Kant argues, on one hand, that the categories are ‘subjective conditions of thinking’, in that they are necessary for ‘intentionally objective content’, and, on the other, that they are ‘objectively valid’, in that they are needed for empirical objects (p. 116). To explain this, Kant posits a prescriptivism according to which we construct empirical objects using the categories. This is a very strong prescriptivism, on which ‘the categories are rules by means of which we create an objective world itself’ (pp. 212–13).

This prescriptivism does not fit well, however, with a crucial passage from section 13, in which Kant states that his Deduction will be inevitably difficult, and which Vinci discusses in chapters 5 and 6. In this passage, Kant explains that his Deduction will be more difficult than his Aesthetic, and his reason is that objects might appear without the categories (Kant 1998: A88/B121). As I read the passage, Kant’s explanation is that, while in the Aesthetic he could infer from the subjectivity of space and time to their empirical reality, in the Deduction he cannot draw a similar inference from the subjectivity of the categories to their objective validity. For, while it follows from space and time being subjective forms of sensibility that appearances are spatio-temporal, for all that follows from the categories being subjective forms of the understanding, it could well be that our application of the categories is an unjustified imposition and appearanes are not categorial (Shaddock Reference Shaddock2014: 44–5).

On Vinci’s interpretation of the passage, Kant affirms that intuitions can present us with objects independently of the categories, and his ‘concern’ is ‘with the absence of proof of the existence of … objects outside our representation of them’ (p. 102). For Vinci, Kant’s concern is that, at the outset of the Deduction, prescriptivism has not yet been established. This interpretation is unsatisfactory, however. Kant intends to contrast the Deduction with the Aesthetic, and indeed to identify a unique difficulty. The Deduction is not unique in that, before its conclusion is reached, an argument is needed. This same worry would arise at the outset of any philosophical proof, including, of course, the Aesthetic.

Vinci’s chapter 6 draws a key distinction for his solution to the problem of the two-steps-in-one-proof. The distinction is between two kinds of synthesis: connection and composition. Connection is the representation of an object in intuition as a substance–accident relation, where ‘the object is the subject and the property is the accident’ (p. 156). The result of this connection is an ‘intuition in general’ (p. 154), whose unity is ‘logical’ (p. 170), and which is implicitly a ‘judgement of experience’ (p. 168) according to Kant’s terminology at Prolegomena, 4: 298 (Kant 1997). Composition, by contrast, is the intuitive representation of an object as a part–whole relation in which the spatio-temporal manifold of sense is combined into an image. The result of composition, for Vinci, is an ‘aesthetically unified intuition’, which is ‘implicitly a judgement of perception’ (p. 171).

Here is Vinci’s solution. The Deduction’s first step argues that logically unified intuitions in general are categorial. The second argues that aesthetically unified empirical intuitions are categorial also. Vinci explains in chapter 7 that the reason both arguments are needed is that ‘intuitions in general’ and ‘empirical intuitions’ compose ‘disjoint classes’ (p. 197). Vinci denies that ‘intuitions in general’ means ‘all intuitions’, maintaining, instead, that ‘intuitions in general’ are intuitions ‘with the form but not the matter of empirical intuitions’ (p. 198). Vinci explains that, after the first conclusion, it remains open for a ‘hypothetical empiricist’ to deny that the matter of empirical intuitions is categorial (p. 196). Kant must prove, to the contrary, that ‘empirical intuitions … are not just aesthetically unified, they are also logically unified’ (p. 196).

Vinci recognizes a textual problem for his proposal. Kant’s first conclusion refers to ‘all sensible intuitions’ and ‘empirical intuitions’ (B143). There is a philosophical problem as well. Since form precedes and determines matter, for Kant, if intuitions in general are intuitions with the form of empirical intuitions, then, from the first conclusion that intuitions in general have categorial form, the second conclusion would immediately follow that the matter of empirical intuitions is categorial. Vinci thus trivializes the second step.

Vinci reconstructs the Deduction’s two arguments in chapter 7. His first reconstruction focuses on apperception. The power of apperception is our ‘second-order power’ ‘to be aware of our representations’ (p. 177). Vinci distinguishes the analytical power of apperception from the synthetic power. The analytic power ‘reveals the proposition-like structure of intuitions’ (p. 178), which is produced by the synthetic power (pp. 180–1).

Vinci’s focus on apperception nearly excludes the topic of judgement, which is problematic. Historically, one of Kant’s main revisions from 1781 to 1787 is his discussion of judgement, and in his 1786 Metaphysical Foundations of Natural Science he states that his proof ‘can almost be accomplished through a single inference from the precisely determined definition of a judgement in general’: 4: 475 (Kant 2004). More philosophically, as Beatrice Longuenesse (Reference Longuenesse1998) cogently argues, Kant’s treatment of judgement is necessary for his identification of the unity of apperception with the specific twelve categories.

Vinci finds ‘no argument’ in the Deduction’s second step ‘showing directly’ that empirical intuitions are categorial, though he reconstructs an ‘indirect proof’ (212–13). He argues that, for Kant, it is a condition of the possibility of ‘the ordinary illusion-reality distinction’ that all objects be in a ‘topologically unified space and time’ (p. 216). Vinci then argues that, for Kant, ‘all objects in our experience are connected in space in a way precisely analogous to that in which the theorems of applied geometry were demonstrated’ (p. 220). Vinci contends that Kant seeks to explain this coincidence by supposing that empirical intuitions are not just aesthetically but also logically unified.

This reconstructed argument is at odds with Kant’s concerns in the Deduction, however. As Stephen Engstrom (Reference Engstrom1994) convincingly argues, Kant is not concerned with the Cartesian sceptical worry that our experiences fail to be veridical, as illusions or dreams. He is concerned with the more radical sceptical worry that our experiences lack objectivity, that they are ‘less than a dream’ (A112).

I will conclude by briefly offering, as a contrast, my own solution to the problem of the two-steps-in-one-proof. On my reading, the first argument aims to show that the categories apply to the objects of our possible intuitions insofar as they can provide a rational basis for our knowledge. The second argues that the categories apply to the objects of our possible intuitions insofar as they can be located in space and time. The second step is not trivial since, from the first conclusion that the objects of our possible knowledge are categorial, the second conclusion does not trivially follow that objects in space and time are categorial. Indeed, Kant’s own view in his 1770 Inaugural Dissertation (Kant 1992) was that sensible objects in space and time and the intelligible objects of our rational knowledge compose two different worlds. Kant’s Deduction thus overturns his previous two-world view (see Shaddock Reference Shaddock2014: 48–54).