2. Subjective Necessity versus Objective Validity

Kant’s canonical formulations of his transcendental idealism are in the prefaces to the Critique of Pure Reason. In his 1781 preface, he describes his method of self-knowledge by comparing the Critique to a court of justice. He states that reason’s self-knowledge institutes this court, and that its decisions concern the justification and limitation of our metaphysical knowledge (Axi–xii). Kant describes his limitation of our knowledge to appearances in his 1787 preface. He draws two comparisons with Copernicus. First, while Copernicus denies that the apparent motions of celestial bodies are due to the movements of the bodies themselves, Kant denies that our cognition conforms to objects as they are in themselves. Second, Copernicus attributes the apparent motions of celestial bodies to the observer’s movement, and Kant asserts that our knowledge is of objects as appearances, which conform to our cognition (Bxvi).

A criterion of adequacy on any interpretation of Kant’s transcendental idealism is that it be compatible with his Transcendental Deduction. Kant formulates his Deduction’s problematic by asking the question quid juris (A84/B116). How can our application of concepts to objects be justified? He considers two ways: objects make our concepts possible, or our concepts make objects possible (A92/B125). He states that objects make our empirical concepts possible, but not our a priori concepts. He states that our practical concepts make the existence of objects possible as things in themselves, but our a priori concepts cannot.Footnote ² Instead, the categories can make the cognition of objects possible as appearances. Since Kant conceives of experience as the empirical cognition of objects (B147, B166 and A218/B176), his Deduction’s aim is to prove that the categories are ‘conditions of the possibility of experiences’ (A94/B126).

There is an ambiguity in this formulation. Is Kant’s aim to prove that the only way subjects such as ourselves can have any experiences at all is by applying the categories? Or is it to prove that the only way objects can be experienced at all is if the categories apply to them? The former, subjectivist interpretation has a long history,Footnote ³ and it is seldom sharply distinguished from the latter. I will argue that this is a crucial distinction for Kant, and that there is sufficient textual evidence for the latter.

I will begin by noting that Kant opposes Humean scepticism in his Deduction.Footnote ⁴ He interprets Hume as attributing a ‘subjective necessity’ to the concept of cause in particular and by extension the categories in general (B127–8).Footnote ⁵ For Kant, the Humean sceptic neither denies that we apply the categories to appearances, nor asserts that our application of the categories is contingent. The Humean sceptic maintains that our application of the categories is necessitated merely by our subjective habits of association.

Here is our criterion of adequacy. Kant’s method of self-knowledge and his limitation of our knowledge to appearances must be compatible with his proof that the categories are not merely subjectively necessary conditions we need for our experience, but objectively valid conditions necessary for objects to be appearances. I will clarify this criterion by considering some subjectivist interpretations.

3. Subjectivist Interpretations

I will argue that Patricia Kitcher’s and Henry Allison’s interpretations are subjectivist. Both respond to P. F. Strawson’s (Reference Strawson1966) attempt to reconstruct Kant’s transcendental arguments without his transcendental idealism.Footnote ⁶ According to Strawson, Kant’s arguments proceed by conceptual analysis. His Deduction argues that on any conception our experience must be categorial.Footnote ⁷ Kant’s transcendental idealism furnishes an explanation of this conclusion, according to Strawson. It states that the reason our experience must be categorial is because of a subjective imposition.Footnote ⁸ This results in a two-world interpretation. For Strawson, Kant posits a subjective, mind-dependent world of appearances and an objective, mind-independent world of unknowable things in themselves.Footnote ⁹

There is direct textual evidence against Strawson’s reconstruction, and there are more charitable interpretations of Kant’s transcendental idealism. I will present the text first. Kant explicitly denies that his method is conceptual analysis, stating that while ‘the usual procedure of philosophical investigations’ is that of ‘analyzing the content of concepts … and bringing them to distinctness’, the ‘proper business’ of ‘transcendental philosophy’ is ‘the much less frequently attempted analysis of the faculty of understanding itself’ (A65–6/B90–1).Footnote ¹⁰

Kitcher seeks to redeem Kant’s analysis of our cognitive faculty. She interprets Kant as arguing by way of the analysis of the cognitive operations we must perform in our experiences. Through this analysis, she maintains, Kant aims to specify the a priori constitution of our cognitive faculty. And it is through this specification of our a priori constitution, Kitcher contends, that Kant seeks to justify the categories. She writes, ‘[Kant’s] response to the quid juris on behalf of the a priori concepts … is, “We can do no other.”’ (Kitcher Reference Kitcher1990: 18).Footnote ¹¹ On Kitcher’s interpretation, then, Kant intends to justify the categories by proving that cognitive subjects constituted a priori such as ourselves cannot do otherwise than to apply the categories in our experiences.

There is textual evidence against Kitcher’s interpretation equal to that against Strawson’s. I will adduce this evidence by considering Kant’s criticism of pre-established harmony in his Deduction. His criticism is that pre-established harmony grants the sceptic’s wish for the ‘subjective necessity’ of the categories (B168).

Kant interprets pre-established harmony as the two-fold thesis that we must apply the categories because of the way God constitutes our cognitive faculty, and that objects must be categorial because of how God constitutes them. His criticism is this:

In this passage, Kant argues that, if our reason for applying the concept of cause were merely because of the way God constitutes our cognitive faculty, then we would be entitled to only the relatively weak claim that cognitive subjects constituted a priori such as ourselves cannot do otherwise than to connect appearances as cause and effect. For the concept of cause to be justified, however, Kant argues that we must be entitled to the stronger claim that appearances are causally related. This is Kant’s criticism. While pre-established harmony entitles us to only the weaker claim that we can do no other than to apply the categories to appearances, the justification of the categories requires that we be entitled to the stronger claim that appearances are categorial.Footnote ¹²

In this way, Kant posits a deep similarity between pre-established harmony and Humean scepticism. On Humean scepticism, our application of the categories to appearances is necessitated merely by our habits of association. On pre-established harmony, it is necessitated merely by our a priori constitution. But on either account it is necessitated merely by our subjectivity and so it is unjustified.

Now even if we are dissatisfied with Kant’s interpretations of Humean scepticism and pre-established harmony, and even if we are unimpressed by his cases against them,Footnote ¹³ the above passage is telling against Kitcher’s interpretation. She interprets Kant as intending to justify the categories by proving that cognitive subjects constituted a priori such as ourselves can do no other than to apply the categories to appearances. Kant’s argument against pre-established harmony, though, is that if this were our only reason for applying the categories, the sceptic would have what he wishes most. If all we could say on behalf of the categories were that we cannot do otherwise than to apply them to appearances, they would be merely subjectively necessary and unjustified.

This helps to clarify our criterion of adequacy. I argued above that Kant opposes a Humean sceptic who maintains that our application of the categories to appearances is necessitated merely by the way our subjectivity is constituted through habit. This can make it seem as though Kant may oppose scepticism by arguing that our application of the categories is necessitated by how our subjectivity is constituted a priori. We now see that Kant opposes this as well. Thus, while Kant’s method of self-knowledge does consist in his analysing our cognitive faculty rather than analysing our concepts, he does not argue only that cognitive subjects constituted a priori such as ourselves must apply the categories to appearances. This would be unacceptably subjectivist by Kant’s own lights.

Allison seeks to defend Kant’s transcendental idealism from subjectivism. He argues for a methodological or metaphilosophical, two-aspect interpretation against Strawson’s metaphysical, two-world interpretation. While for Strawson Kant’s limitation of our knowledge to appearances consists in his denying us objective knowledge, for Allison it consists in his reconceiving of objectivity. According to Allison, Kant maintains that objects have traditionally been conceived of independently of our cognition. Conceived of in this way, objects are things in themselves, and Kant argues that they are knowable not by us but only by God. Kant reconceives of the very same objects, according to Allison, in terms of the necessary conditions of our cognition. Conceived of in this way, objects are appearances, and Kant argues that our objective knowledge is of them. Allison writes that Kant ‘relativize[s] the concept of an object to the conditions (whatever they may be) of the representation of objects’ (Allison Reference Allison2004: 12).Footnote ¹⁴

Here is the difference between Allison’s interpretation and Kitcher’s. For Kitcher, all we can say on behalf of the categories is that we cannot do otherwise than to apply them to appearances. For Allison, we are entitled to say that appearances are categorial. We can say this, for Allison, because appearances are conceived of in terms of the necessary conditions of our cognition and Kant argues that the categories are such conditions.

This is no more than a verbal sleight of hand. Allison’s interpretation conceals the mere subjective necessity of the categories in the concept of an appearance. For him, appearances are categorial, but the only reason they are categorial is that they are conceived of in terms of the conditions necessary for our cognition and the categories are needed for our cognition. Allison is explicit that, whatever conditions may be needed for our cognition, the concept of an appearance is relativized to them. As a result, it is ultimately only because we need the categories for our cognition, according to Allison, that appearances are categorial. This prevents Allison from capturing Kant’s distinction between the categories being merely subjectively necessary conditions we need for our cognition and objectively valid conditions needed for objects to be appearances. This distinction makes all the difference, for Kant. It makes the difference between the sceptic having what he wishes most and the categories being justified.

We can again clarify our criterion of adequacy. We saw above that Kant intends to prove not merely that we need the categories for our cognition but that appearances are categorial. This could seem to leave it open how Kant intends do so. We now see that Kant does not leave this open. The reason appearances are categorial, for Kant, is not merely that we need the categories for our cognition. Thus, while Kant’s limitation of our knowledge to appearances surely consists in his reconceiving of objectivity rather than denying us objective knowledge, he does not simply relativize the concept of an appearance to the necessary conditions of our cognition. This would be unacceptably subjectivist, again, by Kant’s own lights.

Kant explains what it takes for the categories to be objectively valid in this passage from his Deduction:

Here Kant states that the reason appearances are categorial is not merely because of what we need for our cognition, but rather because of what objects are as appearances. The difficulty in interpreting this passage – and indeed the difficulty in interpreting Kant’s transcendental idealism generally – is in understanding how he can oppose subjectivism while avoiding transcendental realism. Kant opposes the subjectivist thesis that the categories apply to appearances simply because of us, whether because of our habituated or a priori constitution. He also rejects the transcendental realist thesis that the categories apply independently of us to things in themselves. Where is the middle ground? A satisfactory interpretation must explain how Kant conceives of appearances such that he makes reference to our cognitive faculty so as to avoid transcendental realism, yet does so without simply relativizing the concept of an appearance to the necessary conditions of our cognition, thus avoiding subjectivism.

In the next section I will outline my interpretation. I will do so by considering Kant’s theory of our cognitive faculties and his distinction between phenomena and noumena. I will fill in the details in the following section by reconstructing his Deduction’s proof.

4. Self-Knowledge and Phenomena

My interpretation centres on two claims. First, Kant’s method of self-knowledge consists in his determining what makes our cognitive faculty finite in contrast to God’s infinite cognitive faculty. Second, Kant’s limitation of our knowledge to appearances consists in his developing an account according to which appearances and our finite cognitive faulty are conceived of in terms of each other and in contrast to things in themselves and God’s infinite cognitive faculty. I will present these claims in turn.

While Kant denies that we can have knowledge of God, he adumbrates his theory of our cognitive faculty by drawing a contrast with God’s.Footnote ¹⁶ The difference is not in degree, for Kant, but in kind. It is not that God knows all things while we know only some. It is that God is an independent knower while we are dependent.

Kant defines cognition as the relation of representation to an object (B137). Since God’s cognitive faculty is independent, it relates to objects self-sufficiently. It does so by producing objects. Our cognitive faculty is not likewise productive for Kant. We therefore have two cognitive capacities rather than one. God has a single capacity to create and cognize objects in one act, while we have a receptive capacity through which objects are given to us and a spontaneous capacity through which we take them up. Kant calls our receptive capacity ‘sensibility’ and our spontaneous capacity ‘the understanding’.Footnote ¹⁷

It is not accidental, for Kant, that our cognitive faculty depends upon objects and comprises capacities of receptivity and spontaneity. Since Kant defines cognition as the relation of representation to objects, by determining how our finite kind of cognitive faculty relates to objects, he determines what it essentially is. Dependency and the cooperation of our receptivity and spontaneity thus make our finite cognitive faculty the kind of cognitive faculty it is.

Kant develops this theory of our cognitive faculty in his Aesthetic and Analytic. He characterizes our sensibility in his Aesthetic as a capacity to receive intuitions. Intuitions are singular representations that relate immediately to objects. Our intuitions are given to us through affection, and this results in sensations. Sensations provide the matter for our intuitions. Kant argues in his Transcendental Aesthetic that space and time are the forms.

Kant characterizes the understanding in his Analytic as a capacity to judge. In judging we spontaneously unify various intuitions under common concepts. The matter of our judgements is provided by the manifold of intuition in space and time. Kant argues in his Metaphysical Deduction that there are twelve logical forms of judgement, and he coordinates them with formal concepts, the categories.

Kant further develops this theory in his Transcendental Deduction. Before considering this development, I will introduce the second main claim of my interpretation. I will do so by considering the implications of Kant’s theory of our cognitive faculties for his concept of an appearance.

Since Kant defines cognition as the relation of representation to objects, in determining how our finite kind of cognitive faculty relates to objects, he also determines to what kind of objects our cognitive faculty relates. He does so, again, by contrasting us with God. As God’s infinite cognitive faculty is productive, the objects to which God’s cognition relates are the things God produces. By contrast, our finite cognitive faculty is dependent, and the objects to which our possible cognition relates are the things we depend upon. This is what appearances are, for Kant. More specifically, as we have capacities of sensibility and the understanding for receiving intuitions and making judgements, appearances are the things we depend upon for our possible intuitions and our possible judgements. As above, it is not accidental that appearances are objects of our possible intuitions and judgements. This is what makes appearances the kind of things they are.

Kant seeks to clarify this conception of an appearance by refining his two-fold distinction between appearances and things in themselves into a three-fold distinction among phenomena, noumena in the negative sense, and noumena in the positive sense (B306–9, A249–60). Kant defines phenomena as the things our finite cognitive faculty depends upon for our possible intuitions and judgements. Kant derives his definition of noumena in the negative sense by abstracting from the reference to our finite cognitive faculty in this definition of phenomena. Noumena in the negative sense are things otherwise than as our finite cognitive faculty depends upon them for our possible intuitions and judgements. Kant gives content to this abstraction by defining noumena in the positive sense as the things God’s infinite cognitive faculty produces.

It is therefore imprecise to cast Kant’s distinction between appearances and things in themselves as one between mind-dependent and mind-independent worlds, as Strawson does. This is for two reasons. First, phenomena are not simply mind-dependent. They are interdependent with our finite minds. Phenomena and our finite cognitive faculty are defined in terms of each other. Second, while noumena in the positive sense are independent of our finite minds, they are not wholly mind-independent. They are defined together with God’s infinite cognitive faculty. Only noumena in the negative sense are truly mind-independent. This is because their definition is derived by abstracting from the reference to our finite minds in the definition of phenomena. It is precisely for this reason that the definition of noumena in the negative sense is of no use to us in defining phenomena. We instead need to draw the contrast with noumena in the positive sense.

We are now in a better position to understand Kant’s method of self-knowledge, his limitation of our knowledge to appearances, and also his Deduction’s aim. Kant’s method of self-knowledge consists in his determining what kind of cognitive faculty ours is, in contrast to God’s. For Kant, our finite cognitive faculty is dependent upon objects in receiving intuitions and making judgements, while God’s infinite cognitive faculty produces objects.

Kant’s limitation of our knowledge to appearances consists in his determining what kind of things phenomena are, in contrast to noumena. For Kant, our knowledge is of phenomena, which are the things our finite cognitive faculty depends upon for our possible intuitions and judgements. We cannot have knowledge of things otherwise, for Kant, noumena in the negative sense. And we cannot have knowledge of things as God’s infinite cognitive faculty produces them, noumena in the positive sense.Footnote ¹⁸

I explained above that Kant’s aim in his Deduction is to prove that appearances are categorial not merely because of what we need for our cognition, but rather because of what objects are as appearances. I have now explained what objects are as appearances, for Kant. They are the things we depend upon for our possible intuitions and judgements. Thus Kant’s aim is to prove that appearances are categorial because of what they are as objects of our possible intuitions and judgements.

This in turn enables us to identify the middle ground Kant occupies between subjectivism and transcendental realism. Subjectivism is the thesis that the categories apply to appearances simply because of us. Kant rejects this. He seeks to prove that the categories apply to appearances not merely because of what we need for our cognition, rather because of what appearances are as the things we depend upon for our possible intuitions and judgements. The transcendental realist thesis is that the categories apply to objects independently of us as things in themselves. Kant opposes this as well. For him, the categories do not apply to things otherwise than as we depend upon them for our possible intuitions and judgements, nor to things as God produces them.

I will conclude this discussion by distinguishing my interpretation from Kitcher’s and Allison’s. For Kitcher and Allison, Kant’s analysis of our cognitive faculty is independent of his determination of what objects are as appearances. For Kitcher, Kant intends to justify the categories by proving that we need them for our experience, without regard to what objects are as appearances. For Allison, Kant relativizes the concept of an appearance to whatever conditions we may need for our cognition, so he can show that we need the categories for our cognition without reference to what objects are as appearances, and then infer that appearances are categorial because we need the categories for our cognition. On my interpretation, Kant does not relativize the concept of an appearance to the necessary conditions of our cognition. For one, he does not posit a unidirectional dependence of appearances on our cognition, but a bidirectional interdependence between them. Moreover, this interdependence is not between the concept of an appearance and the necessary conditions of our cognition. It is between the concept of an appearance and the very concept of our finite cognitive faculty. For this reason, Kant cannot analyse our cognitive faculty independently of determining what objects are as appearances, and nor can he infer that appearances are categorial because we need the categories for our cognition. He must prove that appearances are categorial because of what appearances are as objects of our possible intuitions and judgements. I will now turn to his proof.

5. The Transcendental Deduction

I will proceed by showing how my general disagreement with Allison bears on three points in the text of Kant’s Deduction: his sceptical opponent, his definition of judgement, and his treatment of space and time. I will focus on the 1787 edition, as does Allison.

Allison describes the threat of Kant’s sceptical opponent as ‘one of cognitive emptiness’ (Allison Reference Allison2004: 160). This sceptic doubts that the categories can be applied to sensibly given appearances. Allison cites a passage where Kant writes, ‘appearances could after all be so constituted that the understanding would not find them in accord with the conditions of its unity’ (A90–1/B123). On Allison’s interpretation, this is not Kant’s own view, rather his sceptical interlocutor’s worry. He writes, ‘The worry is that the deliverances of sensibility might not correspond to the a priori rules of thought’ (Allison Reference Allison2004: 160). To assuage this worry, Allison states, Kant must ‘establish the necessity of the categories’ (Allison Reference Allison2004: 160).

There are two problems here. The first is that Kant does not mention scepticism in the passage Allison cites. There are only two passages where Kant does refer to scepticism in his Deduction. I have already discussed both. In the first Kant opposes a Humean sceptic who contends that our application of the categories to appearances is necessitated merely by the way our subjectivity is constituted through habit. He criticizes pre-established harmony in the second for granting scepticism by maintaining that our application of the categories is necessitated merely by how our subjectivity is constituted a priori. Kant does not mean to express a sceptical interlocutor’s worry in the passage Allison cites. He means to explain his own previous claim that his Deduction will be ‘inevitably difficult’ (A88/B121).Footnote ¹⁹

The second problem is that Kant intends to prove a stronger conclusion against scepticism than the one Allison identifies. What Kant seeks to prove, on Allison’s interpretation, is the necessity of the categories. But Kant opposes a sceptic who grants the necessity of the categories, while denying their objective validity. The sceptical threat Kant seeks to avert is not one of ‘cognitive emptiness’ but of ‘subjective imposition’. It is not that the categories cannot be applied to appearances, but that even if we can and indeed must apply the categories to appearances, the reason we must do so might be only because of the way our subjectivity is constituted. To assuage this worry, Kant has to prove not merely the necessity of the categories but their objective validity. He has to prove that appearances are categorial not simply because of what we need for our cognition, but rather because of what objects are as appearances.

This first difference between my interpretation and Allison’s prepares us for the next two. Kant’s proof is divided into two arguments.Footnote ²⁰ The first concerns apperception and judgement, and the second treats the imagination and space and time. On Allison’s interpretation, each is meant to avert the sceptical threat of ‘cognitive emptiness’ by establishing the necessity of the categories. On mine, each is meant to demonstrate the objective validity of the categories, averting the threat of ‘subjective imposition’.

Allison interprets Kant’s first argument as proceeding in three steps. Kant discusses apperception to establish the necessity of synthesis, he defines objects in such a way as to prove that this synthesis is objective, and he treats judgement to prove that it is categorial. Kant’s apperception principle is, ‘The I think must be able to accompany all my representations’ (B131). According to Allison, this principle states that I must be able to become aware that I am the same subject of any of my individual representations and of all the component representations in any complex representation of mine (Allison Reference Allison2004: 164–5). Kant proceeds from this principle, according to Allison, by arguing that I can become aware of this self-identity only if I consciously synthesize each of my representations (Allison Reference Allison2004: 171). At this point in his reconstruction, Allison identifies two results that remain to be proved. First, Kant must prove that the synthesis presupposed by the apperception principle is objective, and second, he must prove that it is categorial (Allison Reference Allison2004: 173).

With the former point, Allison might seem to be on the right track. He might seem to recognize that Kant needs to prove not the merely subjective necessity of the synthesis presupposed by apperception but its objective validity. It becomes clear that Allison does not appreciate this difference as we follow his reconstruction. According to Allison, Kant defines ‘objects’ so that ‘whatever is represented through … a synthetic unity counts as an object’ (Allison Reference Allison2004: 173). The problem is that, if objects are defined in this way, then all it takes for a synthesis to be objectively valid is its necessity. There is then no difference between a merely subjectively necessary synthesis and an objectively valid one.

On my interpretation, Kant’s treatment of judgement is meant to prove that the synthesis presupposed by apperception is categorial and objectively valid. As Allison reads Kant on judgement, he seeks to prove that this synthesis is categorial. He does so, on Allison’s reading, by arguing that it is ‘nothing other than the act of judgment’ (Allison Reference Allison2004: 176). This reading is not supported by the text. Kant defines judgement as ‘the way to bring given cognitions to the objective unity of apperception’ (B141). He explains that a judgement is a relation of concepts in which the concepts ‘belong to one another in virtue of the necessary unity of the apperception in the synthesis of intuitions’ (B142). Kant’s claim here is not that the synthesis presupposed by apperception is itself a judgement. His claim is that this synthesis provides the basis for our judgements. Kant’s claim is that the necessary synthesis of our intuitions is that in virtue of which we relate concepts into a judgement. I will explain this further.

For Kant, a judgement is a relation between a subject concept and predicate concept. But it is not just any such relation. It is not an associative relation, for example. A judgement is a relation of concepts in which the concepts are related in virtue of, or on the basis of, the way in which objects are synthesized in intuition.Footnote ²¹ For example, if I relate the concepts ‘desk’ and ‘black’ and my basis for doing so is that this desk appears black in an intuition of mine, then I will have made a judgement. My judgement will be true or false depending on the actual colour of the desk that appears black in my intuition. By contrast, if I relate the concepts ‘ravens’ and ‘writing desks’ but do so without any basis in my intuition, then I will not have made a judgement, and truth and falsity will not be at issue. This is the difference between judgement and association, for Kant. The concepts related in a judgement are related on the basis of the way in which objects are synthesized in intuition, while merely associated concepts are not.

Here is how Kant’s definition of judgement figures in his Deduction’s first argument. I explained above that Kant begins his proof with a conception of our finite cognitive faculty as dependent upon objects in receiving intuitions and making judgements, and a conception of appearances as objects of our possible intuitions and judgements. By defining judgement, Kant furthers his analysis of our cognitive faculty. He specifies the precise way in which we depend upon objects in judging. Thereby, he determines precisely what appearances are as the objects of our possible judgements. On one hand, Kant shows that in judging we depend upon objects for the intuitional basis for our judgements. On the other, he shows that the objects of our possible judgements must be able to provide this basis. Now Kant infers directly from here to his conclusion that the objects of our possible judgements are categorial. What could license this inference?

While there is little to go on in the text, we can reconstruct Kant’s reasoning by considering the following analogy between judgement and inference. In an inference, the conclusion and the premises upon which the conclusion is based must have the same logical structure. Not just anything can serve as a premise in an inference, only something with the same logical structure as the conclusion. Much the same, Kant seems to reason, in order for objects synthesized in our intuitions to be able to provide the basis for the relation of concepts in judgement they must have the same logical structure as judgement. Since Kant defines the categories in his Metaphysical Deduction as concepts that correspond to the logical forms of judgement, he concludes that the objects of our possible judgements are categorial. This, then, is Kant’s first argument:

• P1. The objects of our possible judgements must be able to provide the basis in intuition for our judgements.

• P2. Whatever is able to provide the basis in intuition for judgement must have the same structure as judgement.

• P3. (From Kant’s Metaphysical Deduction) The categories are concepts that correspond to the logical forms of judgement.

• C. Therefore, the objects of our possible judgements are categorial.

It is crucial that this is neither transcendental realist nor subjectivist. Kant begins with the conception of appearances as objects of our possible judgements. This is not transcendental realist, since it refers to our cognitive faculty, specifically to the understanding, our capacity to judge. Nor is Kant’s conception of appearances subjectivist. It does not license the inference that appearances are categorial simply because we need the categories for judgement. For all that follows from Kant’s conception, it could well be that we need the categories for judgement, but that appearances need not be categorial to be objects of our possible judgements. This is what Kant has to prove. He has to prove that appearances are categorial because of what they are as objects of our possible judgements. His argument is that the objects of our possible judgements must be able to provide the intuitional basis for our judgements, and to be able to do so they must have the same structure as judgement, a categorial structure. Thus Kant’s conclusion is that appearances are categorial in virtue of being objects of our possible judgements.

My final point of disagreement with Allison concerns Kant’s treatment of space and time in his Deduction’s second argument. On Allison’s interpretation, this argument proceeds in three steps. Kant argues first that a synthesis of the imagination is necessary for our representations of space and time, next he argues that this imaginative synthesis is spontaneous, and finally he argues that it is categorial. Kant defines the imagination as ‘the faculty for representing an object even without its presence in intuition’ (B151). A synthesis of the imagination is necessary for the representation of space and time, on Allison’s interpretation, for the following reason. A determinate location in space or moment in time can be represented only by limiting the one infinite space or the single infinite time, according to Kant. Yet infinite space and time cannot be represented in intuition. So the imagination is required for the representation of infinite space and time, and hence for the representation of any determinate location in space or moment in time (Allison Reference Allison2004: 189–90). Allison contends that two results remain to be proved. It must be proved that the synthesis of the imagination is spontaneous, and that it determines empirical intuitions in accordance with the categories (Allison Reference Allison2004: 191, 193).

Allison finds no argument in either case. Regarding the former, he writes, ‘Unfortunately Kant’s treatment of this issue is extremely perfunctory. Instead of providing an argument, he simply asserts that the imaginative synthesis is an expression of the spontaneity of thought’ (Allison Reference Allison2004: 191). As for the latter, Allison reconstructs an argument, though he admits its key step is unsupported. The argument consists of two claims: first, since empirical intuitions are determined in space and time, they are subject to whatever conditions space and time themselves are subject to, and second, space and time are subject to the categories. Regarding this second claim, Allison laments, ‘Although obviously the key step since it links the synthesis of apprehension with the categories, Kant once again offers no argument. Instead, he simply asserts that the unity required for apprehension is an application to human sensibility of the unity of the manifold of an intuition in general that is required for apperception’ (Allison Reference Allison2004: 195).

I will now suggest that Allison fails to find the arguments he is looking for because he is looking for the wrong ones. Allison is looking for Kant to demonstrate the necessity of a spontaneous categorial synthesis for our representations of space and time, and hence for our empirical intuitions in space and time. As I have argued, Kant seeks to establish a stronger result. He aims to prove the objective validity of such a categorial synthesis. I will argue that this is precisely what Kant intends to do in his treatment of space and time.

Kant prefaces this discussion by restating the result of his Aesthetic, that space and time are the forms of our sensibility. This entails that the objects of our possible intuitions are in space and time, according to Kant. He then proceeds in two steps. First, he claims that space and time are not only forms of our intuitions but also formal intuitions. Second, he claims that everything in space and time is subject to whatever conditions space and time themselves are subject to. The first of these claims is what distinguishes my interpretation from Allison’s. Kant states it here:

Kant’s argument concerning space is given in this footnote:

While Kant’s point is easily obscured by his terminology, we can reconstruct his reasoning by considering the geometrical method of construction in pure intuition. According to Kant, we attain geometrical knowledge by constructing spatial figures in pure intuition. This is possible, according to Kant, because we have an intuition of space that provides the basis for our geometrical judgements. For example, we construct a triangle, extend the baseline, and draw a parallel line to one of the legs. We judge not merely that this triangle’s internal angles sum to 180 degrees, but that the internal angles of all triangles do. This is possible, Kant maintains, because space itself is represented in an intuition in our spatial construction, and our judgement is based on this intuitive representation of space. Kant’s reasoning regarding time is left tacit. It is implied that, just as we have an intuition of space that provides the basis for our geometrical judgements about space, we have an intuitive representation of time that provides the basis for our natural scientific judgements about rates of change over time.Footnote ²² Kant expresses this point by calling space and time ‘formal intuitions’. His point is not that space and time are represented by a synthesis of the imagination. It is that space and time provide an intuitional basis for our judgement.

Kant is now in a position to conclude that space and time themselves are subject to the categories. For his present result is that space and time provide an intuitional basis for our judgement. His previous result from his Deduction’s first argument was that whatever provides the intuitional basis for our judgement must have the same structure as judgement, a categorial structure. Kant’s next claim in his Deduction’s second argument is that everything in space and time is subject to whatever conditions space and time themselves are subject to. Allison notes this claim as well. Kant gives no argument, though his reasoning plausibly relies on transitivity. If space and time are determined by the categories, and if the objects of our possible intuitions are determined by space and time, then the objects of our possible intuitions are determined by the categories. From Kant’s conclusion in his Aesthetic that the objects of our possible intuitions are in space and time, he now draws the conclusion of his Deduction’s second argument, that the objects of our possible intuitions are categorial. This, then, is his argument:

• P1. Space and time are formal intuitions, which are able to provide the basis in intuition for judgements.

• P2. (From Kant’s first argument) Whatever is able to provide the basis in intuition for judgement must be categorial.

• P3. Everything in space and time is subject to whatever conditions space and time themselves are subject to.

• P4. (From Kant’s Aesthetic) The objects of our possible intuitions are in space and time.

• C. Therefore, the objects of our possible intuitions are categorial.

As above, this is neither transcendental realist nor subjectivist. Kant begins with the conception of appearances as objects of our possible intuitions. This is not transcendental realist, since it refers to our faculty of sensibility, our capacity to receive intuitions in space and time. Neither is it subjectivist. While it does follow from Kant’s conception of appearances as objects of our possible intuitions that appearances are in space and time, it does not follow that they are categorial. Kant has to prove that appearances are categorial because of what they are as objects of our possible intuitions. He seeks to do so by arguing that the objects of our possible intuitions are categorial in virtue of being in space and time. His argument is that space and time provide a basis in intuition for our judgements, so are categorial, and that everything in space and time is subject to the same conditions to which space and time themselves are subject. Kant’s conclusion is that appearances are categorial in virtue of being spatiotemporal objects of our possible intuitions.

Like his first argument, this second argument furthers his analysis of our cognitive faculty. Kant specifies the precise way in which we depend upon objects of our intuitions, and thereby he determines what appearances are as objects of our possible intuitions. Kant’s Aesthetic may have given the impression that our sensibility’s forms are independent of the understanding, and that our intuitions represent objects in space and time without the categories. Kant corrects this misleading impression in his Deduction’s second argument.Footnote ²³ By showing that space and time are subject to the categories, he shows that our sensibility’s forms are subject to the understanding. He expresses this point by saying, ‘the understanding determines the sensibility’ (B161n.). In addition, Kant’s argument shows that our intuitions depend upon the categories not only for becoming cognitions, but even for being intuitions at all. Here is why. In his Aesthetic, Kant defines intuitions as singular representations that relate immediately to objects, and he argues that our intuitions relate to objects in space and time. In his Deduction, Kant argues that our representations can relate to objects in space and time only under the categories. So our intuitions can be the representations they are, for Kant, only under the categories. He expresses this point: ‘If I take all thinking (through the categories) away … mere intuition … does not constitute any relation of such representation to any object at all’ (A253/B309).

I will briefly review the differences between my reconstruction and Allison’s. For Allison, Kant opposes a sceptic who doubts that the categories can be applied to appearances. Kant argues, first, that a categorial synthesis is presupposed by the apperception principle and, second, that a categorial synthesis is required for the representations of space and time. For me, Kant’s sceptical opponent grants that we can and must apply the categories to appearances, maintaining that the reason we must do so is merely because of the way our subjectivity is constituted. Kant argues, first, that appearances are categorial because of what they are as objects of our possible judgements, and second, that they are categorial because of what they are as objects of our possible intuitions. His first argument is that the objects of our possible judgements must be categorial in order to be able to serve as the intuitional basis for our relations of concepts in judgement. His second is that the objects of our possible intuitions must be categorial in order to be in space and time.

I will conclude this discussion by returning to the key difference between my interpretation and Allison’s. For him there is a unidirectional dependence of Kant’s concept of an appearance on the necessary conditions of our cognition, while for me there is a bidirectional interdependence between his concept of an appearance and his very concept of our finite cognitive faculty. Here is why this matters.

Allison’s unidirectional dependence thesis prevents him from capturing Kant’s distinction between the subjective necessity of the categories and their objective validity. If the concept of an appearance is relativized to the necessary conditions of our cognition, there is no difference between the categories being merely subjectively necessary conditions we need for our cognition and objectively valid conditions on objects being appearances. This can help us to diagnose the shortcomings in Allison’s reconstruction. Because he fails to recognize Kant’s distinction between the categories being merely subjectively necessary and objectively valid, he fails to appreciate the sceptical worry that the categories are merely subjectively necessary, and consequently he fails to reconstruct Kant’s proof of their objective validity.

My bidirectional interdependence thesis allows me to capture this crucial distinction of Kant’s. Because I do not render the concept of an appearance unidirectionally dependent upon the necessary conditions of our cognition, I leave room for the sceptical worry that, while we need the categories for our cognition, objects as appearances might not need to be categorial. On the other hand, I make room for Kant to answer this worry, and indeed to do so by analysing our cognitive faculty. This is because I represent Kant’s concept of an appearance and his very concept of our finite cognitive faculty as mutually interdependent for their intelligibility. Kant conceives of our finite cognitive faculty as dependent upon objects in making judgements and receiving intuitions in space and time, and he conceives of appearances as the objects of our possible judgements and the spatiotemporal objects of our possible intuitions. He proceeds in his Deduction by reflecting upon the act of judgement and our formal intuitions of space and time. Thereby, he argues that the objects of our possible judgements and the spatiotemporal objects of our possible intuitions must be categorial.

One might object that my interpretation fails to avoid subjectivism. I claim that appearances are categorial because of what they are as objects of our possible intuitions and judgements. But do I not claim that appearances are objects of our possible intuitions and judgements ultimately because we have capacities of sensibility for receiving intuitions and the understanding for making judgements? No, no more than I claim that we have capacities of sensibility and the understanding because appearances are objects of our possible intuitions and judgements. My claim is that because our cognitive faculty is finite, on one hand, we have capacities for receiving intuitions and making judgements and, on the other, appearances are objects of our possible intuitions and judgements. Of course, one might worry that this interdependence between our cognitive faculties and appearances is as objectionable as a dependence of appearances on the forms of our cognitive faculties. But the dogmatic insistence upon an independence of appearances from our cognitive faculties is transcendental realism. My aim has been to argue for an interpretation of Kant’s transcendental idealism that opposes transcendental realism while avoiding subjectivism.

The key point is that while on Allison’s interpretation Kant relativizes the concept of an appearance to the necessary conditions of our cognition, on mine Kant’s concept of an appearance refers to his concept of our finite cognitive faculty without being relativized to the conditions we need for our cognition. My interpretation thus leaves room for the sceptical worry that categories are merely subjectively necessary, while making room for Kant’s proof that they are objectively valid.