1.1 The Metaphysical and Transcendental Deductions

What is the goal of Kant’s transcendental deduction of the pure concepts of the understanding?Footnote ¹ Many different accounts have been offered, ranging from the modest or “regressive” account that the deduction is meant to establish only the conditional that if we have any empirical knowledge, then we must use certain a priori concepts, to the more radical anti-skeptical account that the deduction is supposed to establish that we have self-consciousness, yet that self-consciousness is possible only if we have knowledge of objects that exist independently of our representations of them, thus that we have such knowledge of objects.Footnote ² Kant himself offers what seems to be a clear statement of his intentions in the introductory paragraphs to the “Deduction,” in a formulation that could be traced back to his original conception of the problem of a critique of pure reason in his famous letter to Marcus Herz of February 21, 1772: he states that the task of the transcendental deduction of the pure concepts of the understanding is to demonstrate that certain concepts, which are not only a priori, that is, independent of any empirical origin, but also have an origin that has no obvious connection with the spatial and temporal form of our experience, nevertheless necessarily apply to all of our experience of objects and events in space and time. In Kant’s words,

The goal of the deduction is to prove that the pure concepts of the understanding apply to all our “objects of sensible intuition” even though these concepts are not any part of the form in or by which these objects are given. The forms in or by which objects of sensible intuition are given, according to the “Transcendental Aesthetic,” the first part of the Critique’s “Doctrine of Elements,” are space and time, the essential structure of which is characterized by mathematics; the concepts in accordance with which such objects must be thought are derived from logic; the task of the deduction is therefore to show that categories associated with the essential concepts of logic necessarily apply to the objects of sensible intuition the forms of which are described by mathematics.Footnote ⁴

This statement, simple as it is, has important implications for some of Kant’s most cherished philosophical doctrines. But before we can consider such implications, we must also recognize that, simple as it appears, this statement nevertheless masks at least one considerable obscurity. Throughout this statement and its context, Kant refers collectively to an indeterminate group of concepts of the pure understanding. In an antecedent section of the Critique, entitled “On the Clue to the Discovery of All Pure Concepts of the Understanding” (A 66–83/B 91–116) and only in the second edition retrospectively referred to as the “metaphysical deduction [of] the origin of the a priori categories in general” (B 159), however, Kant had identified twelve distinct “logical function[s] of the understanding in judgments” (A 70/B 95) and corresponding to them twelve categories for conceiving of objects (A 80/ B 106). This fact naturally raises the question: What is the transcendental deduction supposed to prove with regard to the necessary applicability of each of the twelve categories to objects of sensible intuition? By proving that the categories en bloc apply to objects of sensible intuition, is the deduction supposed to prove only that at least one of the twelve categories applies to each object of sensible appearance? Or is it supposed to prove that each of the categories must apply to at least some object of sensible intuition? Or is it, finally, supposed to prove that all of the categories must be applied to all objects of sensible intuition, that is, that in some way each of the categories must apply to each object of sensible intuition?

Ultimately, it would seem, Kant could accomplish his philosophical objectives only by proving something like the last of these alternatives. Certainly to refute Hume by proving the objective validity of the universal principle of causation,Footnote ⁵ Kant has to prove not just that some of the twelve categories apply to some or all objects of sensible intuition, but that the specific category “Of Causality and Dependence” applies to all such objects. Likewise, to refute Leibniz’s monadology, Kant has to prove that not just some category or other but the specific category “Of Community (of reciprocity between agent and patient)” applies to all objects in space and time. These two cases alone, of course, do not prove that each of the categories must be shown to apply to all objects of sensible intuition; nevertheless, it seems fairly clear that Kant intends to prove that each of the categories necessarily applies to all objects of sensible intuition, or at least to all objects within one of the two most fundamental classes of objects of sensible intuition.Footnote ⁶ But this surely cannot be established by showing simply that the categories en bloc necessarily apply to objects of sensible intuition en bloc.

The chief argument of this Introduction, as the background for the chapters in Parts I and II of this volume, will be that Kant divides the “Transcendental Analytic” into two parts, the “Analytic of Concepts” and the “Analytic of Principles,” in order to address precisely this problem. The “Analytic of Concepts,” which is what is in turn divided in the second edition of the Critique into the “metaphysical” and “transcendental” deductions of the categories, is what is meant to prove that the categories en bloc apply to the objects of sensible intuition; while the “Analytic of Principles,” primarily in its middle chapter, the “System of All Principles of Pure Understanding,” is what is meant to establish that each of the categories necessarily applies to objects of sensible intuition, indeed that each of the categories necessarily applies to each object of sensible intuition, although not in precisely the same way.

Further, I will argue that this fact has important philosophical consequences for Kant and perhaps for any attempt to revive Kant’s supposed method of transcendental argumentation. For what close examination of the “System of All Principles” reveals is that the proof that each of the categories is a necessary condition of the possibility of experience cannot be accomplished by appeal to the resources of logic alone, but depends on explicit appeal to the spatial and temporal structure of our experience. Kant usually fails to acknowledge this fact within the confines of the “Transcendental Deduction” proper, although his remark in the first edition of the “Deduction” that “all of our cognitions are in the end subjected to the formal condition of inner sense, namely time, as that in which they must all be ordered, connected, and brought into relations” (A 99) is one exception to this rule. But this fact is nevertheless important, for while Kant likes to argue that for purposes of the practical use of reason, that is, our moral thought, the categories can be used to think objects that cannot be presented in space and time and thus cannot be known by means of them, namely, human freedom and immortality and the existence of God, his arguments for the necessity of each of the categories, and certainly for the crucial categories of causality and community, are inextricably tied to the spatio-temporality of our experience. While the distinction between intuitions and concepts is certainly Kant’s most fundamental philosophical distinction, his complete deduction of the categories depends as much on the forms of intuition as on the forms of thought. This may place crucial limits on some of Kant’s most cherished ulterior objectives.

My account thus far suggests a certain division of labor between the “Analytic of Concepts” and the “Analytic of Principles.” What is the division of labor within the “Analytic of Concepts,” the division represented by what in the second edition of the Critique Kant labeled the distinction between the “metaphysical” and “transcendental” deductions of the pure concepts of the understanding? In an important article, Rolf-Peter Horstmann has argued that this question has been neglected, and has also proposed a solution to it.Footnote ⁷ Horstmann argues that we can begin thinking about this question by means of the distinction between the metaphysical and transcendental expositions of the concepts of space and time in the “Transcendental Aesthetic,” which is also a distinction introduced in the second edition (Horstmann Reference Horstmann and Tuschling1997, pp. 62–3). A metaphysical exposition is one that “exhibits” the concept in question “as given a priori” (B 38), whereas a transcendental exposition is “the explanation of a concept as a principle from which insight into the possibility of other synthetic a priori cognitions can be gained” (B 40). If this distinction were applied directly to that between the metaphysical and transcendental deductions of the pure concepts of the understanding, then the metaphysical deduction would show that these concepts are given a priori while the transcendental deduction would show that they are the condition of the possibility of other synthetic a priori cognitions. However, this distinction cannot be applied immediately to the distinction between the metaphysical and transcendental deductions. The first reason for this conclusion, which Horstmann stresses (p. 63), is that Kant subsequently seems to insist that any deduction must be a demonstration of the objective reality or instantiation of the concept at issue (A 84–5/B 116–17), and thus the metaphysical deduction cannot merely exhibit its concept as given a priori without also making at least some contribution to the proof of the objective reality or legitimacy of the relevant concepts. The second reason for rejecting this interpretation, which Horstmann does not mention, is that its account of the role of the transcendental deduction would then blur the distinction between the latter and the “Analytic of Principles,” the function of which seems to be precisely to show that the a priori yet objective reality of the categories is the condition of the possibility of other synthetic a priori cognition, such as the synthetic a priori cognition of the universal law of causation and the principle of interaction.

So Horstmann argues for a different interpretation. Appealing to Kant’s characterization of the transcendental deduction of the categories as “the explanation of the way in which concepts can relate to objects a priori” (A 85/B 117), he argues that the metaphysical deduction must establish what such an explanation presupposes, namely, that the concepts it exhibits as given a priori are also conditions of the possibility of cognition of objects at all:

Horstmann then argues that the metaphysical deduction accomplishes this goal by means of its well-known argument that the same function of the understanding that combines intuitions into the representation of an object also combines the latter into a judgment, and thus that the functions of thought that are available for the formulation of judgments are also involved in the representation of objects themselves, and are thus a necessary condition for the possibility of any reference to them (A 79/B 104–5; Horstmann Reference Horstmann and Tuschling1997, p. 72).

The problem with this approach is that instead of neglecting the function of the metaphysical deduction, it seems to exaggerate it, inflating the role of the metaphysical deduction – which after all the first edition of the Critique called nothing more than a “clue to the discovery” of the categories – until it takes in most of the function of the transcendental deduction as Kant described that in our opening quotation, that is, showing that the categories are the conditions of the possibility of the “objects of sensible intuition” becoming “objects for us” (A 90/B 122–3), while at the same time reducing the function of the transcendental deduction to that of what Kant called in the first edition its “subjective” side, which concerns not the demonstration of the “objective validity of its concepts a priori” but only the “possibility” of “the understanding itself” and “the powers of cognition on which it itself rests,” which, Kant there asserts, is not essential to his chief end at all (A xvi–xvii)! Horstmann does not argue that the transcendental deduction should be reduced to its subjective side, nor should he. So we must recapture what Kant considers the chief end of the transcendental deduction, without losing sight of the important implications of the aspect of the transcendental deduction to which Horstmann has drawn attention.

I suggest that we do this in the following way. First, Horstmann is correct to argue that the so-called metaphysical deduction is meant to establish that the categories are the conditions of the possibility of cognition of objects. But that leaves entirely open the question of whether we have any cognition of objects, or how much of such knowledge we have. The “chief end” of the transcendental deduction is then to make a transition from possibility to actuality, or to prove that we do have cognition of objects and indeed in a sense to determine how much we have, by arguing that all self-consciousness involves the categories and can thus be considered cognition of objects, and indeed also that all sensible intuition or all representation of objects in space and time can also be considered cognition of objects, thus requiring the necessary application of the categories as required by A 89–90/B 122–3. At the same time, the proof that the categories apply to all intuitions in space and time is also, as Horstmann’s account suggests, the explanation of how the categories apply to the objects of our cognition, namely, through our representations of them as occupying regions of space and time, and this in turn is what prepares the way for the argument of the “Analytic of the Principles” that each of the categories has a necessary role in human cognition: it is through the appeal to specific features of intuition in space and time that the necessity of each category can be demonstrated. Thus the transcendental deduction does have a double function, as Kant’s initial account suggests (A xvi–xvii), though not quite the particular function that this account suggests: the transcendental deduction first establishes that the categories apply to all of our sensible intuition en bloc, but this in turn lays the foundation for the subsequent proof that each of the categories necessarily applies to sensible intuition.

1.2 Functions and Categories

On the account that I propose, the role of the metaphysical deduction of the pure concepts of the understanding then is to establish that the use of those categories en bloc is the condition of the possibility of any cognition of objects, or that if we are to have anything that counts as objective cognition, it must involve the use of the categories. The gist of Kant’s argument lies in the claims that to bring a multitude of representations into connection with each other, or to synthesize them, is to bring them under a single representation that stands for the multitude of them by representing something common to them, in other words, a concept; that concepts in turn, however, provide cognition only by being linked to each other in judgments; and thus that the characteristic functions by means of which concepts can be related to each other in judgments, the various combinations of which yield the various forms of judgments, are the structures by means of which any synthesis of a multitude of representations at all must take place. There are three keys to this argument: the assumption that synthesis always involves the subsumption of lower-order representations under higher-order ones that is characteristic of the subsumption of instances under concepts, the assumption that these higher-order representations yield cognition only when they are in turn linked together in judgments, and the assumption that there is a determinate number of ways in which the latter can be done.

It could well be argued that Kant does not sufficiently defend any of these three assumptions. His famous claim that “The same function that gives unity to the different representations in a judgment also gives unity to the mere synthesis of different representations in an intuition, which expressed generally, is called the pure concept of the understanding” (A 79/B 104), does not seem to explain the basis of his inference at all, for it does not state explicitly that even to combine partial representations into a complex but whole intuition must involve subsuming the partial representations under the concept of some feature they have in common, as would be done, for instance, when the parts of a square are recognized as all parts of a square. Perhaps Kant comes closer to suggesting this basic explanation at the outset of the section, when he argues that while “All intuitions, as sensible, rest on affections, concepts,” by contrast, rest “on functions,” where by a function, in turn, he means “the unity of the action of ordering different representations under a common one” (A 68/B 93). This at least suggests that while individual parts of a complex intuition – for example, the various lines and corners of a (represented) square – might be passively received or perceived, any recognition of them as constituting a whole requires the subsumption of these different representations under a common one, for example, the recognition of them as parts of a square.

Kant goes to slightly greater length to establish that “the understanding can make no other use of these concepts than that of judging by means of them” (A 68/B 93). Here he argues that since only intuitions relate immediately to objects, and concepts never do, concepts must always be related to something, namely, to an intuition or to another concept that is in turn related to an intuition, in order to yield cognition of an object; but for a concept to be related either to another concept or to an intuition is precisely for it to be used in a judgment. Kant’s illustration of his claim actually makes clear that judgments always consist of combinations of concepts that are more and less immediately related to objects rather than of concepts and intuitions themselves: thus, in the judgment “All bodies are divisible” he treats the concept of the divisible as a more general concept that is related to intuitions through the concept of body, which “in turn is related to certain appearances that come before us” (A 69/B 93), although one might have thought that divisibility could have been considered as one of the more immediate properties of intuitions through which the more complex concept of body can be predicated of them.Footnote ⁸ Either way, however, the general point seems clear that to have any cognition of an object at all is to judge that several intuitions manifest a hierarchy of properties in virtue of which they can be subsumed under a hierarchy of concepts: thus, several intuitions each of which can be subsumed under the concept “line” can also be subsumed collectively under the concept “rectangle” when it is seen that there are four of them and that they intersect at right angles; those lines and another group of three intersecting ones can both be subsumed under the concept “plane figure” when the number of them and the size of the angles at which they intersect is ignored, and so on.Footnote ⁹ The arguments that synthesis always involves concepts and that concepts are always used in judgments do not seem too hard to make.

The argument that seems harder to make, and to which both Kant and his commentators have devoted more ink – the latter vastly more than the former – is the argument that there is a fixed and determinate number of functions of judgment, which would give rise to a fixed and determinate number of forms of judgment, and that also determines the fundamental forms of the concepts of objects by determining how objects must be conceived if it is to be possible to make judgments about them by means of these functions of judgment. First, just to sort out the terminology: by a “function” of judgment Kant seems to mean something like an aspect of a judgment, for example, that it has a quantity, like being about all or some objects in some extension; that it has a quality, like asserting or denying something of the object it is about; and that it expresses a relation, as when it asserts or denies a predicate connecting several objects.Footnote ¹⁰ A fixed number of such functions would then give rise to a number of forms of judgment in the sense categorized by ordinary logic (what Kant calls “general logic”): from the functions mentioned, you could generate particular affirmative predicative judgments, particular negative predicative judgments, universal affirmative predicative judgments, and so on. Kant does not pause to make this inference explicit, although it seems obvious. What Kant does make explicit is the claim (the basis of what he calls “transcendental logic”) that the various functions of judgment (and thus the various logical forms of judgment) can only be applied to objects if our concepts of objects have certain fundamental forms: thus, if we are to make judgments about one, some, or all of the objects in a group there must be some way in which we can conceive of the objects themselves as a unity, a plurality, or a totality; if we are to make affirmative or negative judgments, there must be some way in which we conceive of objects as realities or not; if our judgments are to assert or deny predicates of subjects, then we must be able to carve reality up into subjects that can have properties; and so on. It is this assumption that leads from the functions of judgment to the pure concepts of the understanding, or the categories: the categories are the forms that govern the construction of particular concepts of objects so that those concepts can be used to make judgments about objects.

There has been little attempt to question Kant’s assumption that if there is a determinate set of functions by means of which judgments can be formed, then there must also be determinate sets of forms by means of which the concepts of objects themselves can be constructed. A tremendous amount of ingenuity has instead been devoted to the question of how Kant thought he could derive the twelve functions of judgment, grouped under four headings, from which the twelve categories for the conception of objects are derived.Footnote ¹¹ I have given only a partial list of these functions of judgment thus far: the complete list maintains that judgments can have three quantities, universal, particular, or singular; three qualities, affirmative, negative, or infinite; that they can manifest three relations, the categorical, hypothetical, or disjunctive relations; and that they can have three modalities, problematic, assertoric, or apodictic. The problem is that while Kant attempts to explain why there are always three items in each group, where in some cases traditional (and contemporary) logic would only recognize two, he makes no effort at all to explain why judgment must be understood in terms of his four main headings in the first place. But I will not attempt to solve this problem; in fact, Kant eventually admits that he could no more prove that any logic must contain all and only these functions of judgment, and hence give rise to all and only these categories, than he could actually prove that space and time are the only two possible forms for human intuition (B 145–6). Instead, the only type of “completeness proof” that Kant actually attempts is the demonstration that we must use each and every one of these categories suggested by the functions of formal logic. But he does not attempt to construct this completeness proof on the basis of resources offered by logic alone. Instead, taking it for granted that logic affords these categories to us, what Kant argues is that it is only by appeal to the spatio-temporal character of human experience that we can prove that we must use each and every one of these categories. The only completeness proof that Kant attempts to give is to be found, in other words, not in the “metaphysical deduction” at all, but in the “Analytic of Principles.”

1.3 The Application of the Categories en bloc

Before Kant attempts to prove the necessity of each of the categories in our experience, of course, he attempts to prove that at least some of the categories, or the categories en bloc, apply to all of our experience. This is the task of the “Transcendental Deduction.” I will confine my comments here to some general observations about the structure of this proof. In the most general terms, Kant’s strategy is to show that any conscious experience at all involves the kind of synthesis or combination that can only be produced through judgment, and therefore involves the use of the categories, thus that the categories are the conditions of the possibility of the objects of all experience because they are the conditions of the possibility of all experience as such (see A 94/B 127). I will not concern myself here with the details of Kant’s claim that synthesis always involves judgment.Footnote ¹² Instead, I will restrict my attention to the issue of the scope of the application of the categories. Dieter Henrich famously proposed that in the second-edition version of the “Deduction,” Kant argues for the necessary application of the categories to all possible experience in two distinct steps. First, he contends, Kant argues that the categories are the conditions of the possibility of any unified or unitary consciousness, without any specification of how often we might have unified or unitary consciousness or what the scope of such consciousness might be. Then, he claims, Kant adds the necessary specification, or removes the restriction on the first stage of his argument, by observing that all of our consciousness is representation of objects and/or states of affairs in space and/or time; that space and time themselves are unities; that their unity must, like any unity, depend on the use of the categories; and thus that the categories must apply to all of our sensible intuition – what Kant set out to prove at A 90/B 123 – because for something to be a sensible intuition at all is for it to be part of a unified space and/or time.Footnote ¹³ A key piece of evidence for Henrich’s account is Kant’s statement in §21 of the second-edition “Deduction” that “in the above proposition [i.e., §20] the beginning of a deduction of the pure concepts of the understanding has been made”; only a beginning, apparently, because what has been proven is that “the empirical consciousness of a given manifold of one intuition stands under a pure a priori self-consciousness,” which can be achieved only through the use of the categories (B 144), where the word “one” is given a special emphasis by being capitalized (Einer) instead of being left uncapitalized like an ordinary indefinite article (einer).Footnote ¹⁴ Kant then announces his intention to lift this restriction in §26 when he writes that “Now the possibility of cognizing a priori through categories whatever objects may come before our senses, not as far as the form of their intuition but rather as far as the laws of their combination are concerned … is to be explained” (B 159), although the proof of this unrestricted claim depends precisely on showing that what we might previously have assumed is simply given by the form of intuition, namely, the unity of space and/or time, is not simply given at all, but is instead a product of synthesis and therefore involves the exercise of judgment and the use of the categories.

Henrich does not observe that the proof of the transcendental deduction in the first edition of the Critique also appears to involve a similar transition from a restricted to an unrestricted assertion of the scope of the application of the categories. In that version, Kant begins by analyzing what is involved in the cognition of any randomly chosen object, arguing that such cognition requires a threefold synthesis culminating in the recognition of the unity of the object under a concept (A 98–103). This recognition is in turn analyzed as an assertion of necessary connection among the parts of the object (A 104–5) that requires a “transcendental condition as its ground” (A 106), which Kant argues can be nothing other than “transcendental apperception,” the necessary numerical identity of the self in all of its different states or “that unity of consciousness that precedes all data of the intuitions, and in relation to which all representation of objects is alone possible” (A 107). Kant’s claim is then that this unity itself depends on the use of the categories (A 108), and if any consciousness at all is consciousness of part of a unity that requires the use of the categories, then of course the consciousness of any particular object also requires the use of the categories (see A 110).

There is good reason for Henrich not to have drawn a parallel between the structure of the first- and second-edition proofs of the deduction, however, for to have done so would have undermined his interpretation of the second. The expansion of the scope of the categories from cognition of an arbitrarily chosen object to all consciousness as such in the first edition does not depend on appeal to the unity of space and/or time at all, but solely on the claim that all self-consciousness as such is already a form of unity regardless of any objects the representations of which one is self-conscious might ultimately be taken to represent. Yet Kant begins the second-edition “Deduction” with precisely the same claim. The starting point of this argument (in its §16) is that “The I think must be able to accompany all my representations” and is “also the original apperception, since it is that self-consciousness which, because it produces the representation I think,… must be able to accompany all others” (B 132). Kant then argues that “this thoroughgoing identity of the apperception of a manifold given in intuition contains a synthesis of the representations, and is possible only through the consciousness of this synthesis” (B 133). In the following sections (§§17–20), Kant will attempt to show, with questionable success, that this synthesis necessarily involves the use of the categories, but once again, we will ignore the details of this argument; our present concern is only his conclusion that “Synthetic unity of the manifold of intuitions, as given a priori, is thus the ground of the identity of apperception itself, which precedes a priori all my determinate thought” (B 134). Here, just as he did in the first edition, Kant draws the inference that the categories must be involved in any cognition of particular objects because they are already involved in our recognition of our representations of the object as our own which precedes our recognition of what those representations represent.

When Kant reminds us of the unity of all sensible intuitions in space and/or time in §26, it thus cannot be to prove for the first time that the categories apply to all possible sensible representations, because that has already been established by the argument of §16 that all self-consciousness as such involves synthesis followed by that attempted in §§17–20 that this synthesis involves the use of the categories. So if it is not to remove a restriction that never existed, what is Kant’s point in §26? Two things suggest themselves. First, Kant could mean to tell us that, in spite of any appearance to the contrary that might have been created by the “Transcendental Aesthetic,” the unity of space and/or time is not a source of unity independent of synthesis in accordance with the categories that could undermine the claim that the unity of apperception as such depends on that synthesis, but rather that spatio-temporal unity itself depends on that synthesis. This would be a natural reading of his claim that “even unity of the synthesis of the manifold, outside or within us” – that is, in space or in time – “can be none other than that of the combination of the manifold of a given intuition in general in an original consciousness, in agreement with the categories, only applied to our sensible intuition” (B 161). Second, Kant could mean to explain how the use of the categories produces the unity of consciousness, and in so doing also explain in what sense the categories are the conditions of the unity even of space and time, by starting the argument that the categories are the conditions of assigning determinate positions to objects in space and states of affairs in time, which are in fact the most basic features of the unity of consciousness itself. This is at least what Kant’s examples of the function of the categories in establishing the unity of space and/or time suggest. Kant’s first example is that “the category of the synthesis of the homogeneous in an intuition in general, i.e., the category of quantity,” is the condition of the possibility of making “the empirical intuition of a house into perception through apprehension of its manifold” (B 162). This suggests that the use of the category of quantity (and also, one might add, the relational category of substance), even if not obviously a condition of the possibility of the representation of empty space as such, is the condition of the possibility of the representation of an object as filling a determinate region of space, and a fortiori of a system of objects as determinately occupying all positions or filling all regions of space. Kant’s second example is that “If … I perceive the freezing of water, I apprehend two states (of fluidity and solidity) as ones standing in a relation of time to each other,” which in turn requires “the category of cause” in order to “determine everything that happens in time in general as far as its relation is concerned” (B 162–3). In other words, Kant claims, although of course he does not yet prove, that the concept of causation is required in order to make determinate the sequence of two states of affairs, such as the same substance being liquid and being solid, in time. Again, the category of causation might not be required to represent the unity of empty time as such, whatever precisely that would mean, but is alleged to be required in order to assign a determinate sequence to any two states of affairs, a fortiori to all states of affairs, in time. In other words, the unity of space and time introduced in the final stage of the transcendental deduction is actually the unity of space and time filled with objects and events, and Kant’s argument is then that the use of the categories is the condition of the possibility of this unity in space and time.

On this approach, Horstmann’s account of the relation between the metaphysical and transcendental deductions is partly wrong but partly right. If he means to argue that the metaphysical deduction establishes that the use of the categories is the condition of the possibility of all cognition of objects and that the transcendental deduction is only meant to explain how the categories apply to objects of experience, he omits the crucial role of the transcendental deduction in establishing that the categories apply to all possible experiences. Yet if by pointing out that the transcendental deduction does explain how the categories apply to experience he means to elucidate the role of the introduction of the unity of space and time in the categories, then his account is better than Henrich’s. For as we have seen, the appeal to the unity of space and time in the transcendental deduction cannot be to remove a restriction in the argument that never existed, but rather must be to point out the medium through which the categories apply to all possible consciousness, and thereby prepare the way for the extended argument of the “Analytic of the Principles,” which will show not merely that the categories in general but that each of the categories necessarily applies to our experience, by showing that each of the categories has a specific role to play in establishing the unity of objects and events in filled space and/or time.

1.4 The Application of Each of the Categories to All of Our Experience

My task now will be to show that Kant’s strategy in the “Analytic of Principles” is to show that the use of each of the categories is necessitated by a specific feature of the spatial and/or temporal structure of human sensible intuition. Once again, I will have to proceed at a high level of generality.Footnote ¹⁵

The constructive work of the “Analytic of Principles” is carried out in its first two chapters, “On the Schematism of the Pure Concepts of the Understanding” and the “System of All Principles of Pure Understanding”; the third chapter, “On the Ground of the Distinction of All Objects in General into phenomena and noumena,” prepares for the critique of traditional metaphysics that will be carried out in detail in the ensuing “Transcendental Dialectic.” The purpose of the “Schematism” is to make the categories of the understanding, which thus far have the purely logical content they have derived from the logical functions of judgment, applicable to sensible intuition, as the “Transcendental Deduction” has shown they must be, by associating them with structures or relations that can be found in sensible intuition, in particular, with determinations of time, since only the latter can be found in all sensible intuitions – on Kant’s view, only some representations, those of outer sense, represent spatial relations, but since all representations, “wherever” they “may arise,” “as modifications of the mind … nevertheless belong to inner sense, … all of our cognitions are in the end subjected to the formal condition of inner sense, namely time, as that in which they must all be ordered, connected, and brought into relations” (A 98–9). The “Schematism” thus assigns a temporal schema to each category: for example, the “schema of substance is the persistence of the real in time” and the schema of causality “consists in the succession of the manifold insofar as it is subject to a rule” (A 144/B 183). The “Schematism” clearly takes its clue from the “Metaphysical Deduction,” starting with the list of twelve categories under four headings provided there and seeking a temporal interpretation or correlate of each of those categories.Footnote ¹⁶

That being so, one might expect that the argumentation of the “System of All Principles” would begin with the several schemata identified in the preceding chapter and somehow generate the principles to be established from those schemata. In fact, the argumentation moves in the opposite direction. Instead of presupposing the concept of substance and somehow proving that substance is conserved in all change, or presupposing the concept of cause and then showing that every event has a cause, what Kant does instead is to argue that there is something about the structure of time itself that requires the existence of something permanent through all change, which is only then identified with substance, and likewise that there is something about the nature of time that requires that states of affairs succeed one another in accordance with a rule, and therefore requires the use of the concept of causation. More generally, the “Schematism” makes the categories available for use in a form applicable to sensible intuition; the “System of All Principles” appeals to specific features of the structure of sensible intuition that requires the use of principles of judgment that in turn require the use of all the categories in the form made available by the “Schematism.”

Indeed, what the “System of All Principles” attempts to show is that the structure of sensible intuition is such as to require the use of each of the categories, and in fact at least one of the categories under each of the four headings of each intuition that we can have. The second of these claims may not be obvious in the case of the first two sections of the principles, the “Axioms of Intuition” and the “Anticipations of Perception,” in each of which Kant attempts to prove only a single principle of judgment. However, his argument actually suggests that in each case in order to apply the single principle involved all three of the relevant categories will be needed. Thus, in these two cases as well as the more obvious cases of the “Analogies of Experience” and “Postulates of Empirical Thinking in General,” Kant’s argument shows why each of three categories under the relevant general heading must be used, which was not attempted in the original “Metaphysical Deduction.”

(i) The principle to be demonstrated under the title of “Axioms of Intuition” is that “All appearances are, as regards their intuition, extensive magnitudes” (A 161), where extensive magnitudes are magnitudes that can be represented as composed of an aggregation of distinguishable homogeneous parts or units.Footnote ¹⁷ But Kant does not appeal to anything about the logical categories of one, some, and all to establish this point. Instead, he appeals immediately to the form of intuition: his argument is simply that since all intuitions, whether pure or empirical, are given through the form of space and time, and space and time themselves can be represented as composed of aggregations of homogeneous parts, therefore the intuitions of objects in space and time must also be represented as composed of homogeneous parts:

It is the principle that appearances are always produced by the synthesis of homogeneous parts that then requires the use of general concept of magnitude: “Now the consciousness of the homogeneous manifold in intuition in general, insofar as through it the representation of an object first becomes possible, is the concept of a magnitude (Quanti)” (B 203). Kant’s argument thus does not presuppose that any purely logical consideration has established the necessity of the use of the general concept of quantity; instead, his argument shows that the spatio-temporal structure of intuition requires the use of this category that logic merely makes possible. A note that Kant added to his own copy of the first edition of the Critique makes this point particularly clear: “One must subsume the perceptions under the categories. But one can infer nothing from those categories themselves, but only from the possibility of perception, which can only happen through the determination of time and in time” (Erdmann LXVI, 23:28; in Kant Reference Kant, Guyer and Wood1998, p. 287).

Now in this section Kant does not make an explicit argument for the necessary use of all three categories of quantity – unity, plurality, and totality – but the argument is not far beneath the surface. Indeed, perhaps the argument for the necessity of the first two categories of quantity is at the surface: Kant argues that because all appearances are in space and time, they “can only be cognized through successive synthesis (from part to part),” and this is enough to imply that in making any judgments about intuitions at all we must use both the categories of unity and plurality because we must represent both parts and wholes: “All appearances are accordingly already intuited as aggregates (multitudes of antecedently given parts)” (A 163/B 204). So all that would need to be added would be an explicit argument for the necessary use of the third category of quantity, totality, and perhaps this would not be hard to construct: since Kant has argued in the “Transcendental Aesthetic” that any space and time is always bounded by more space and time, and thus can be represented only as part of a single, all-encompassing space or time, he could argue that in judging of objects in intuition we could not be limited to the use of the concepts of parts and aggregates of parts, but must always be able in turn to conceive of any aggregation of parts as itself part of a larger whole, namely, the totality of space or time itself, or perhaps filled space and time. Again, the crucial point would be that it is not logic but the structure of space and time that dictates that we must be able to use not just two but three categories of quantity.

(ii) Why there are three rather than two of what Kant calls the categories of “quality” may be the biggest puzzle about the original tables of the logical functions of judgment and categories. We can perhaps analyze the very possibility of judgment at all as involving the possibilities of either affirming or denying a predicate of a subject, and thus see that judgment has both affirmative and negative forms which in some sense correspond to reality and negation in the object of judgment. But why should there be a third function of quality, an “infinite” form of judgment that corresponds to “limitation” in the object? Kant’s argument in the “Anticipations of Perception” does not answer all of the questions of what he means by the infinite form of judgment, but it does explain why we must be able to apply the concept of limitation as well as those of reality and negation: it is not a matter of logic but of the form of intuition that qualities in objects are not simply present or absent, but are present in a variety of degrees or intensities, indeed a continuum of degrees or intensities, any one of which can be represented as a limitation of a greater one. Indeed, as Kant’s argument at least suggests, the necessity of three rather than two categories pertaining to the qualities in objects on the basis of which we affirm or deny their reality derives not from the structure of pure intuition, but in this case from the structure of empirical intuition. In the second-edition version of the argument, Kant begins precisely by drawing attention to the empirical aspect of intuition:

It is this fact – what Kant pretty clearly represents as an empirical fact about the nature of human perception – that requires us to have a concept for degrees of sensation and corresponding degrees of intensity in the qualities we sense, and not just concepts of their mere absence or presence: “between reality and negation there is a continuous nexus of possible realities, and of possible smaller perceptions” (A 169/B 211). One could of course dispute Kant’s empirical premise, and indeed it may be that he puts himself in the peculiar position of trying to argue for the empirical premise that any kind of sensation can come in a continuum of intensity by treating pure intuition and empirical intuition as if they were part of a single scale, rather than treating pure intuition as the mere form of empirical intuition which is not itself a possible kind of empirical intuition. However, there is no mistaking the general structure of his argument: he does not appeal to logic to establish that there must be at least three positions on the scale of empirical intuition; rather, he appeals to the structure of intuition to argue that we must be able to avail ourselves of all the possibilities that logic affords by way of concepts of quality.

(iii) Under the rubric of “Analogies of Experience,” Kant explicitly argues for three distinct principles of judgment and for the necessity of using the particular category of relation associated with each. While there is much obscurity in the details of Kant’s argument, again the general structure of his method is clear: he does not appeal to logic to argue that we must be able to make three different kinds of time-determination, but instead appeals to three different time-determinations that we indisputably make in order to establish the necessity of using the three categories of relation: “The three modi of time are persistence, succession, and simultaneity. Hence three rules of all temporal relations of appearances … precede all experience and make it possible” (A 177/B 219).

(1) In the first “Analogy,” Kant argues that the “persistence of substance,” indeed a principle of conservation that dictates that “In all change of appearance substance persists, and its quantum is neither increased nor diminished in nature” (B 224), is a condition of the possibility of a fundamental determination of time. Once again, his argument proceeds directly from a feature of time to a principle that requires the use of one of the categories, rather than from a presupposition of the necessity of the category to the validity of the correlated principle. What makes the first “Analogy” tricky is that during the course of its exposition Kant actually appeals to two different claims about time to make his point. At the outset of his argument, following his suggestion that persistence is a mode of time itself, he argues that there needs to be some object other than time itself that persists as long as time does in order to represent the persistence of time. This is a dubious argument that presupposes the problematic epistemic principle that a representation of any property F must itself have property F, a principle that Kant himself elsewhere abjures when he states that “The representation of something persisting in existence is not the same as a persisting representation” (B xli n). But Kant also suggests a different argument, an argument that it is not the persistence of time but rather the determinate representation of alteration in time that requires the representation of something that endures through the alteration, the conception of which would in turn require the concept of substance. Kant at least asserts the existence of such an argument when he maintains that

The interpretation of this remark that I and others have suggested is that it is only by representing two states of affairs as successive states of a single changing thing that one can distinguish the perception of an objective change from a mere change in what is perceived or attended to.Footnote ¹⁸ But the only point I wish to make here is that on either of the arguments Kant suggests, and however that argument is supposed to work, it is clear that Kant’s argument proceeds from a feature of the structure of time itself or of the way in which states of affairs fill time to a principle that in turn requires the use of one of the categories of relation, and not the other way around.

(2) In the second “Analogy,” Kant argues that recognition of a rule according to which one state of affairs must succeed another, and thus the use of the category of causation, is also a necessary condition for the perception of an objective change. In this case at least, it thus becomes clear that Kant does not argue merely that the categories of substance and causation must each have some use, but in fact that both must apply to each perception of a change. Briefly, Kant’s argument is something like this: the categorization of two states of affairs as successive states in the alteration of a single substance is a necessary condition of the determination that an objective change has taken place, but not a sufficient condition, because this requirement by itself leaves it open in what order the two states have occurred and thus what change – the change of s from F to G or from G to F – has taken place. We might think that order is immediately given, but it is not, because, of course, we are not immediately given states F and G, but only representations of them (call them ƒ and g). But I can always imagine that I have been given two representations in the opposite order from which I suppose I have been given them (B 233), so I can no more read the objective order of states of affairs directly from the order of my representations of them than I can be directly given that order. Instead, to determine what event has occurred I must derive both the determinate order of the objective states of affairs as well as that of my perception of them from “a rule in accordance with which the appearances in their sequence, i.e., as they occur, are determined through the preceding state, and only under that presupposition alone is the experience of something that happens even possible” (A 195/B 240).Footnote ¹⁹ And given Kant’s schematism of the concept of causation, this principle necessitates the use of that category. Kant’s claim is thus that to see time as determinately filled by a sequence of events, we must be able to conceive of each of those events as a change in the state of a substance that is dictated by a rule stating that given the occurrence of the relevant cause such a change must take place.Footnote ²⁰

In the third “Analogy,” Kant argues that interaction between substances in different positions in space is the condition of the possibility of the perception of their simultaneity: “All substances, insofar as they can be perceived in space as simultaneous, are in thoroughgoing interaction” (B 256). Again, Kant’s claim is not that the logical availability of the category of interaction (supposed to be associated with the disjunctive form of judgment) necessitates its use, but rather that a fact about time, or about our ability to make judgments about the states of affairs that fill time, necessitates the use of this category. Here Kant’s argument is that since it would take a succession of perceptions in time to perceive objects existing at two different points in space, there cannot be an immediate perception of the simultaneity of the states of such objects (A 212/B 259); instead, it is only if the state of one object existing at a moment depends on the state of another existing at the same moment and vice versa that both states can be judged to exist simultaneously at different positions in space: “Thus each substance … must simultaneously contain the causality of certain determinations in the other and the effects of the causality of the other, i.e., they must stand in dynamical community (immediately or mediately) if their simultaneity is to be cognized in any possible experience” (A 212–13/B 259).

I will make only two observations about this argument.Footnote ²¹ First, although Kant presents it as an argument based on a determination of time, it is clear that it actually appeals to the spatial as well as the temporal character of our experience: it assumes that we can make judgments about the simultaneity of states of objects, in other words, a temporal judgment, but also assumes that we cannot have simultaneous perception of objects in different regions in space, and therefore must base our judgment of their simultaneity not on direct perception but on knowledge of their interaction. This presumes the fundamental spatiality of our experience and addresses the condition of the possibility for making the temporal determination of simultaneity in light of that spatiality.

Second, this argument might appear to suggest that either the category of causation or that of interaction must be applied to any given appearance, but not both. But this conclusion would be hasty, for while any given state of affairs succeeds some states of affairs, it is also simultaneous with others, and thus the categories of both causation and interaction (as well as of course substance) apply to each empirical intuition. Indeed, perhaps this could be argued by appeal to the use of the concept of causation itself: while the cause of a change is what determines that its effect follows rather than precedes an antecedent state of affairs, in many if not in most cases the cause is not the antecedent state of affairs but is rather simultaneous with its effect. But I will not attempt to make this argument in detail.Footnote ²²

(3) I conclude this section with a brief comment on the “Postulates of Empirical Thinking in General.” Here Kant demonstrates that each of the modal categories – possibility, actuality, and necessity – has an application by appealing to aspects of the analysis of the conditions of the possibility of human experience that have been analyzed throughout the preceding argument from the “Transcendental Aesthetic” to the “Analogies of Experience.” First, Kant claims that “The postulate of the possibility of things … requires that their concept agree with the formal conditions of an experience in general” (A 220/B 267), or that “Whatever agrees with the formal conditions of experience (in accordance with intuition and concepts) is possible” (A 218/B 265). This is to claim that in order to show that a concept is the concept of a possible object, it is not enough to show that it satisfies the requirements of general logic, that is, is free of internal contradiction; it must also be shown that it satisfies the requirements of transcendental aesthetic and transcendental logic, that is, that it could be given to us in an intuition we are capable of having and conceived by means of the categories already demonstrated to be necessary. “The postulate for cognizing the actuality of things requires perception, thus sensation of which one is conscious” (A 225/ B 272; cf. A 218/B 226): this means that for a concept to be that of something actual, it must be not only consistent with the structure of pure intuition, but also evidenced by empirical intuition.Footnote ²³ Finally, Kant claims that only “That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily” (A 218/B 265), because “there is no existence that could be cognized as necessary under the condition of other given appearances except the existence of effects from given causes in accordance with laws of causality” (A 227/B 279–80) (although it would seem that Kant should also extend this to include the effects of interaction as well as unidirectional causality). In other words, we cannot use the concept of necessity to transport us to the existence of a necessary being outside the sphere of empirical intuition and its causes; we can use it only to express the application of the law of causation (and interaction) to empirical intuition.

By means of these arguments, then, Kant has pretty clearly attempted to supply the completeness proof for his list of categories that is so obviously missing in the “Metaphysical Deduction,” at least to the extent of arguing that each of the categories enumerated there has an indispensable application within human experience, an application dictated not by the logic that makes those categories available but by the structure of the intuitions, ultimately the empirical intuitions, to which they must be applied. This is the vital addition that the “Analytic of Principles” makes to the “Analytic of Concepts,” which could only prove that the categories must apply to empirical intuition en bloc. It would be an interesting task to see how far we could go in arguing that each of the categories must apply to each intuition. There is room only for a few observations on this subject, however. First, Kant should think that the categories of both unity and plurality could apply to any intuition – any intuition can be thought of as part of a larger whole, but also as a whole of smaller parts – but the category of totality might have to be reserved for the whole extent of objects in space or the whole sequence of events in time, neither of which could ever be given completely in perception.Footnote ²⁴ Second, while every empirical intuition could be categorized as both a reality yet also as a particular degree or limitation of the relevant reality – every visual intuition, for example, has some color, but also some degree of that color – it might seem as if the category of reality is always used in contrast to that of negation; however, one might also argue that every reality is also the negation of another – what is red is not blue – so wherever the category of reality applies, there the category of negation also applies. Third, it is clear that Kant thinks that the categories of causation and interaction are always applied in tandem with the concept of substance, but it might seem natural to suppose that the categories of causation and interaction are always applied in exclusion of each other; however, as already suggested, whatever is successive to one thing may also be simultaneous with something else, so perhaps both of these categories, thus all three of the relational categories, apply to every state of affairs presented in empirical intuition. Finally, Kant clearly believes that the concept of necessity applies only to the actual: what is necessary is just what is actual insofar as it is seen as subject to causal law. Kant even goes so far as to argue that the sphere of the possible is no greater than the sphere of the actual, on the ground that the only thing that could be added to the possible if something additional were needed to make it actual is the impossible (A 231/B 284) – a dubious argument if ever there were one. So perhaps Kant would have been better off to have stopped before reaching this point, and to have contented himself with the conclusion that each of the categories under the two headings of quality and relation applies to each empirical intuition, but that in the case of the categories of quantity we must reserve the category of totality for an ideal of completeness that is never actually attained and that in the use of the categories of modality we must certainly distinguish between a merely possible and an actual object (to which the laws of causality also apply).

1.5 Empirical and A Priori in Kant’s Method

I will now step back from the details of my argument and conclude with two more general observations. I have argued for an intimate connection between Kant’s conception of the forms of intuition and his argument for the objective reality of the categories. This has certainly not been meant to undermine the distinction between intuition and concept, one of Kant’s most fundamental contributions to philosophy. But it is meant to show the equal importance of Kant’s characterization of the structure of human intuition and his analysis of the resources of logic in his method of argumentation, and to show that what we call his transcendental method depends on the appeal to both of these resources. If there is in turn something irreducibly empirical in Kant’s characterization of the forms of intuition, then this means that there is also an irremovable empirical core in Kant’s transcendental arguments.Footnote ²⁵ This is explicit in Kant’s argument in the “Anticipations of Perception,” where he directly invokes a feature of empirical intuition that cannot be derived from pure intuition. But it could be argued to be implicit in other phases of Kant’s argument as well. Thus, it is at least arguable that it is an empirical fact, though in some sense a deep one, that we are capable of making judgments about succession and simultaneity, or that we cannot make such judgments by the direct perception of the position of events in absolute time but only by inference from dynamical laws. And the claim that we cannot perceive the state of objects at two different positions in space simultaneously but must also infer this from dynamical laws also seems empirical. Thus, while if we were to attempt to reconstruct Kant’s completeness proof for the categories on the basis of logic alone we should surely fail, when we avail ourselves of the full range of considerations on which this proof actually depends we must also recognize an irremovable empirical core in this argument.

The second suggestion I want to make is that the dependence of Kant’s proof of the necessity of the use of all the categories on the forms of intuition might well compromise his own insistence that we can at least conceive of non-empirically accessible objects by means of the categories, an assumption that underlies Kant’s use of the categories in practical philosophy. Since Kant typically maintains that without the forms of intuition the categories can be used only to think objects, never to cognize them, perhaps he would not be guilty of any outright self-contradiction here. But he certainly is committed to the use of the full range of particular categories, especially the categories of relation, in practical reasoning – in thinking of ourselves as moral agents, we certainly think of ourselves as substances who can be causally efficacious in initiating actions but must also interact with others in forming a moral world. But apart from the demands of intuition, we may have not only no clear meaning to attach to these concepts, but no obvious justification for their use. The dependence of Kant’s categories on the structure of human intuition at least raises the question of whether those categories could be used in moral thinking without equal dependence on the structure of human intuition. If not, then Kant’s theory of moral agency might have to be reconceived as a theory with phenomenal and therefore empirical rather than noumenal content. Of course, this would hardly be an unwelcome result for the present author.

[2025]: The three chapters in Part I of this volume, to which we now turn, reflect further on Kant’s method in philosophy. Chapter 2 examines Kant’s explicit contrast between his own “transcendental” method and the “physiological” method of his great predecessor, John Locke, in some ways an even more important target on the purely empiricist side than David Hume.Footnote ²⁶ Chapter 3 contrasts Kant’s own conception of his transcendental method to the interpretation of it from a perspective rooted in the philosophy of language offered by Peter Strawson in his path-breaking 1966 book The Bounds of Sense, while Chapter 4 offers a defense of Kant’s “transcendental psychology” from Strawson’s criticism of that as an “imaginary subject,” and by implication attempts to defuse the charge of “psychologism” brought against Kant by many since the nineteenth century – or to reinterpret the character of Kant’s own supposed “anti-psychologism.” The three chapters in Part II take up issues about our representations of space and time that have been touched on in the present chapter, while clarifying the argument against Kant’s transcendental idealism that I have been making since Kant and the Claims of Knowledge. The first two parts of this book may thus be read as a qualified defense of Kant’s transcendental method without his transcendental idealism. Finally, the three chapters of Part III go beyond ground covered in this chapter: Chapters 9 and 10 concern Kant’s revision of a traditional conception of teleological judgment, thus a qualified defense of it from the modern rejection by such philosophers as Descartes and Spinoza, while Chapter 8 begins this part with an account of the regulatively teleological character of Kant’s approach to philosophy in general.