1. A Verificationist Interpretation

Let us begin with the key passage in which Kant puts forward the principle of objective validity:

Kant considers the principle of objective validity to be applicable to all concepts, regardless of whether they are ordinary empirical concepts, mathematical concepts, pure categories, transcendental concepts or other a priori concepts. The concept of objective validity is a specifically Kantian notion, playing a crucial role in Kant’s distinction of the legitimate uses of concepts from illegitimate ones. Concepts having no objective validity, as in the case of many metaphysical concepts, are dismissed as ‘a mere play’. However, it is unclear how concepts, a priori concepts in particular, can be related to empirical intuitions and acquire objective validity.

It would be helpful to begin with an interpretation that reads Kant’s principle as a sort of verificationism. Such an interpretation was as noted put forward by Strawson, who refers to it as the principle of significance:

Strawson’s idea is that the bounds of sense determine not merely the bounds of knowledge or true judgements, but even that of intelligibility. Concepts without objective validity would simply be meaningless. When we use concepts without objective validity, we could not utter any meaningful statements nor even understand what we are saying. Furthermore, Strawson interprets the required relation of concepts to empirical intuitions in a verificationist fashion. If there is no empirical observation or situation that would count as evidence for or against the certain employment of a concept in a judgement, then the judgement would be unintelligible and the employment of that concept illegitimate. Strawson’s reading places Kant very close to British empiricism and logical positivism, as this principle of significance sets similar criteria for cognitive significance as the verification principle (1966: 18). Another influential Kant scholar in the same period, Bennett, offers a more explicit verificationist interpretation of Kant, ascribing concept- and meaning-empiricism to him (1974: 27).Footnote ²

A verificationist interpretation of Kant may appear odd to many, but Kant’s commitment to the empirical dependence of concepts makes this reading plausible, at least prima facie. Even such sympathetic Kant interpreters as Henry Allison admit that:

The dependence of concepts on empirical intuitions is a result of Kant’s distinction between sensibility and understanding as two irreducible faculties of cognition. In order to express any knowledge, we have to use concepts to form judgements, but judgements cannot be true unless they are capable of describing objects. Such employments of concepts must be subject to conditions that allow the judgements to be related to the objective world. Thus the possibility of cognition depends on a more fundamental possibility of relating representations to objects. The latter possibility, as Kant wrote in a letter to Marcus Herz, ‘constitutes the key to the whole secret of metaphysics’ (Kant Reference Kant1999: 133; 10: 130). Kant’s distinction of sensibility from understanding implies that the function of relating to objects neither belongs nor is reducible to the function of judging or the use of concepts, but must rely, directly or indirectly, on intuition.Footnote ³

If the function of relating to objects is performed by intuitions, there is a question of how concepts can be related to objects and acquire objective validity. Kant’s notion of objective validity, which is often but not always used synonymously with the notion of objective reality,Footnote ⁴ can be applied to all kinds of representations including intuitions, concepts and judgements, expressing their respective way of being related to objects. In the case of concepts, they are related to objects by virtue of being applicable to them. It is to be noted that Kant distinguishes between two different senses of object: between a real, thick sense of an object which can properly be said to exist in the objective world, and a logical, thin sense of an object which includes anything of which something can be predicated in a judgement:

Every logically consistent concept has its ‘object’ in the logical, thin sense, but this does not mean that every concept ‘designates’ an object in the real, thick sense. Only when there can possibly be real objects that fall under a particular concept does the concept have objective validity.

In order to ensure the applicability to objects, any application of concepts must be subject to the conditions under which objects are given and the content of the concepts must thus be consistent with the spatio-temporal forms of intuitions. As empirical concepts are formed a posteriori through empirical intuitions, the sensible forms have already been included in their formation. However, a ‘pure concept is one that is not abstracted from experience but arises rather from the understanding even as to content’ (Kant Reference Kant1992: 590; Jäsche Logic, 9: 92), and its content is not automatically compatible with the sensible forms. There are pure concepts, such as pure geometrical concepts, whose content is derived from and is thus automatically compatible with the forms of intuition, but there are other pure concepts, including pure categories and transcendental concepts, whose objective validity is in need of justification. Kant’s crucial idea is that, although pure concepts do not have empirical origins, they must still be mediated by the sensible conditions of intuitions in order to ensure objective validity. The pure categories of the understanding in particular have to gain their empirical applicability through transcendental time determination, being transformed into temporal schemata that are homogeneous to empirical intuitions (A138–9/B177–8).

If the application of concepts must be subject to empirical conditions, the possibility of metaphysics is in danger, since it is quite obvious that metaphysical concepts are, by their very nature, unrelated to empirical intuitions. The principle of objective validity certainly plays an important role in Kant’s Dialectic.Footnote ⁵ According to Strawson and Bennett, much of Kant’s ground-breaking ideas and his critique of metaphysics therein follow logically from the principle of objective validity. However, their verificationist reading does not do justice to Kant’s subtle position. If all employment of metaphysical concepts is, in principle, devoid of objective validity, why does Kant have to trouble himself with such a detailed critique of metaphysics in the Dialectic? He could simply have dismissed all metaphysical debate, just as the logical positivists did, and the Dialectic could have been much shorter, even if Kant still had other problems to deal with in the Dialectic.

More problematic is the fact that the verificationist interpretation would affect the very theoretical foundation on which Kant develops his epistemology, and this is the main problem that I address in this article. How can those transcendental concepts such as sensibility, understanding and transcendental apperception acquire objective validity? They are supposed to be conditions that make experience possible, but are themselves neither part of the empirical world nor experienceable through sensible intuitions. How can a theory that is built around these transcendental concepts be objectively valid and true? The verificationist interpretation, if correct, would not only eliminate the metaphysical theory of transcendental idealism, but also undermine the very foundation on which Kant’s epistemology, including the principle of objective validity itself, is based.Footnote ⁶

2. Logical/Analytic versus Real/Objective Significance

Despite his rationalist commitment to the existence of pure concepts, Kant is aware of the risk that the content of pure concepts may be a mere construction:

In claiming that a concept without the possibility of being given an object ‘has no sense, and is entirely empty of content’, the above passage seems to provide a stronger support for the verificationist interpretation. However, lacking objective validity and having no sense do not mean the same thing; concepts without objective validity are not literally empty of content. A more precise differentiation can show where the verificationist interpretation went wrong.Footnote ⁷ To begin, Kant distinguishes between concepts of understanding and concepts of reason. The latter are Ideas, which would straightforwardly be empty of content according to the verificationist interpretation. But if all Ideas were literally empty, we would be unable not only to know anything about their objects, but even to make meaningful statements about them. Moreover, the pure categories would also be empty of content until they were schematized. Kant has indeed suggested that, when abstracted from their sensible conditions, the pure categories would ‘lose all meaning’ and become ‘empty titles for concepts without any content’ (A679/B707),Footnote ⁸ but how could the categories be distinguished from each other if they were literally empty?

A distinction between different senses of ‘content’ has to be made. The categories of substance and causality, for example, would be left with ‘the logical representation of the subject’ (A242/B300) and the representation of ‘something that allows an inference to the existence of something else’ (A243/B301), respectively, which would specify the logical content of the unschematized categories, i.e. content analytically contained in the concepts. In order to become applicable to the empirical world, the categories need to be further determined in a way that makes their content homogeneous to what can be given in sensibility. In other words, they need to have a content that objects given in intuition could possibly satisfy so as to fall under them. The schematization thus enriches the pure categories with temporal determinations, making them appropriate for empirical employment.

For Kant, schematization does not just add further determinations to the pure categories, simply making them more specific, but rather transforms the pure logical content into appropriate temporal relations. It may appear that the unschematized category of cause, for example, is applicable to every empirical object to which the schematized category of cause is applicable, since the latter seems to pick out a subset of things that are picked out by the former, just as the concept of animal is applicable to everything to which the concept of mammal is applicable. However, schemata do not just represent a further specification of pure categories. Instead, schematization gives a definite temporal interpretation to the pure categories, which would otherwise remain indeterminate as to how they are to be applied to temporal appearances. Without schematization, it is indeterminate whether it is, for instance, the pure concept of cause or that of effect that is applicable in an empirical situation. As Kant explains:

Pure categories do not have content that is appropriate for empirical application; yet they do have ‘the logical form of a concept’. Since all concepts are connected with each other in a complicated logical relationship, the logical form of a concept is its specific logical connection with other concepts, which determines the intension of the concept.Footnote ⁹ This can be called the analytic or logical significance of the concept in contrast to its objective or real significance in the sense of empirical applicability.Footnote ¹⁰ The logical significance of a concept amounts to the content after abstraction from all sensible content.Footnote ¹¹

Theoretically, it is possible to arbitrarily invent or construct any concept independently of all sensible conditions. An arbitrary concept has its specific logical significance and can be defined precisely (Jäsche Logic, 9: 141–2; Blomberg Logic, 24: 268–9), but this intensional content alone does not guarantee empirical applicability. Surely, pure categories are not just arbitrarily constructed concepts, but their object-relatedness has to be provided by sensible intuitions. Now ‘if one removes this [sensible] condition, all significance, i.e., relation to the object [my italics], disappears’ (A241/B300). What is absent in a concept lacking objective validity is the relation to objects. Any arbitrarily constructed, logically meaningful concept has its objects in the logical, thin sense, but whether it can possibly be applied to an object in the real, thick sense is what the principle of objective validity is about.

Kant’s principle does not deprive empirically unrelated concepts of logical or intensional content, but only of their real significance in the sense of object-relatedness, leaving them extensionally empty. Empirical concepts can happen to have empty extension, as in the case of a unicorn, but concepts without objective validity are extensionally empty on principle. Put in metaphysical terms, there exists nothing that could possibly fall under any concept lacking objective validity. This may sound a rather strong metaphysical thesis, but as I have argued elsewhere (Lau Reference Lau2010: 125–33) it follows logically from Kant’s theory of categories and the synthetic principles of pure understanding. According to the Second Postulate of Empirical Thinking, the category of existence or actuality is only applicable to something ‘which is connected with the material conditions of experience (of sensation)’ (A218/B266). Thus only things that are subject to the sensible, spatio-temporal conditions of experience can be said to exist, and this rules out the existence of non-spatio-temporal objects such as abstract entities. All objects in the real, thick sense exist in the spatio-temporal realm.

Based on the above distinctions, we are in a position to spell out the principle of objective validity more precisely. Since there is no other use of concepts than in judgements, the principle can be explained in terms of properties that apply to judgements. Judgements can be either analytic or synthetic. For Kant, the truth of analytic judgements depends solely on the conceptual relationship between subject and predicate (A6–7/B10–11). Since concepts can be constructed artificially, it is possible to make analytically true judgements about the constructed conceptual relationships without relating them to the objective world. In other words, if the judgements only determine the logical relations between concepts in respect to their analytic or logical significance, it is possible to form analytically true judgements with concepts lacking objective validity.

However, if concepts are to form synthetically true judgements, they cannot simply be arbitrarily constructed. The truth of synthetic judgements depends no longer merely on conceptual relationships, but also on external states of affairs. If the concepts employed in a judgement have no objective validity, the judgement as a whole would fail to be related to any objects in the real, thick sense. Since Kant adopts the traditional correspondence conception of truth (A58/B82), a synthetic judgement without objective validity can never turn out to be true because no correspondence could ever hold if a judgement is not related to an object. Synthetic judgements with objective validity can be true or false; without objective validity, they could never be true. Therefore, objective validity in respect to synthetic judgements means truth-aptness, although I shall leave it open whether judgements without objective validity should be called false or rather lacking in truth value. Kant’s principle of objective validity can thus be specified as follows: A synthetic judgement can be true only if all the concepts in it have objective validity.

Applying the above distinction to pure concepts such as categories seems to imply that pure categories are left with their logical significance until they are enriched with sensible content and transformed into schemata. Kant also warned against the tempting misuse of pure categories, particularly in making metaphysical claims:

What happens when this claim is applied to transcendental concepts? Indeed, what is the nature of this claim itself? The question is not about how the claim can be justified, but how it should be understood or whether it is intelligible. Kant’s principle of objective validity raises the threat that the concepts involved in the above claim may have no objective validity and thus that the claim itself cannot be synthetically true. Or is the claim a merely analytic description of the concept of pure categories? Whether or not the claim is analytic depends on a set of concepts including categories, objects, sensibility and understanding. Obviously, Kant cannot just define these concepts at will in order to make his theory analytic. For Kant in fact philosophy, unlike mathematics, should not start with definitions (A730/B759). Philosophy is essentially different from mathematics, which has the privilege of being able to guarantee the objective validity of concepts that it constructs arbitrarily. Philosophical concepts, by contrast, are susceptible to a lack of objective validity. The failure to understand the difference between mathematical and philosophical cognitions accounts for many of the mistakes traditional metaphysics has made. If Kant wants to avoid the charge he has brought against traditional metaphysics, his theory has to guarantee the objective validity of its own transcendental concepts.

3. Empirical versus Transcendental Truth

Kant’s concept of objective validity is subtly connected with his concept of truth, and the connection offers a way to account for the objective validity of transcendental concepts. Although Kant did not distinguish between different senses or orders of objective validity, he did distinguish between empirical and transcendental truth, and, along with it, between empirical and transcendental cognition. According to Kant’s correspondence theory, the truth of an empirical cognition consists in ‘the agreement of [the] cognition with its object’ (A58/B82). The agreement with objects is a specific kind of relation to objects, and empirical truths depend on the object-relatedness of concepts involved in the cognition. This object-relation is something that Kant has to account for in his theory of cognition. If his theory is to be successful, it must contain a great deal of true descriptions about the conditions of cognition. This kind of truth, if any, cannot again be empirical, but must be of another kind, to which Kant refers as transcendental truth:

While empirical truths consist in particular correspondences of judgements to their objects, transcendental truths are about the general subject–object relation that makes particular correspondences and thus empirical truths possible (Hanna Reference Hanna1993: 9). It is, however, unclear how transcendental truths can be compatible with Kant’s correspondence conception and what transcendental truths are true of. The nature of transcendental truths certainly hinges on Kant’s notion of transcendentality. Although the notion has been used by Kant in a variety of contexts, and sometimes in slightly different senses, it is primarily predicated of a particular kind of a priori cognition.

‘Transcendental’ and ‘empirical’ are not contradictory notions, although the former implies the negation of the latter. There is non-empirical cognition which is not qualified as transcendental, including analytic judgements and pure geometry. Transcendental cognition is a subset of synthetic a priori cognition, which deals reflexively with the very conditions of the possibility of cognition (Bubner Reference Bubner1975). Transcendental cognition and transcendental truth are both about the general relation of cognition to objects. They do not directly describe any object that exists in spatio-temporal reality, but rather the conditions under which true descriptions of spatio-temporal reality become possible. If ordinary empirical cognition is a first-order cognition of objects, then transcendental cognition is a second-order cognition that accounts for the conditions of first-order cognition. The same structure applies to the relation between empirical and transcendental truths. However, it is unclear in what sense transcendental truth ‘precedes all empirical truth and makes it possible’ (A146/B185). The relation is certainly not a causal one, but something of a more abstract nature. I shall come back to this problem at the end of the article.

According to Kant’s theory, the conditions of the possibility of experience consist of a complex system of cognitive faculties and their formal structures, including the spatio-temporal forms of sensibility and the categories of understanding. Everything in possible experience must conform to these subjective forms since they determine the basic structures that define what can possibly exist as an object. Kant’s theory has to show that the descriptions of sensibility, understanding and their formal structures are largely true. Since these descriptions of the faculty of cognition, if true, are transcendental and not empirical truths, they cannot be empirical descriptions of the factual features of the human cognitive system. Accordingly, transcendental concepts such as those of sensibility and understanding do not, at least not directly, pick out any cognitive module or mechanism of the human mind.

Now if the transcendental concepts do not describe any empirical objects, they would not have objective validity according to the principle of objective validity discussed above, and this would imply that no synthetically true judgement could be formed with them. However, these transcendental concepts are indispensable constituents of transcendental truths, which are synthetic. There must be another sense of objective validity and significance that transcendental concepts can legitimately lay claim to. It turns out that Kant identifies the objective validity or reality of these concepts with their transcendental truth:

An alternative way for concepts to acquire objective validity is to demonstrate a relation, not to a particular experience or empirical objects, but to ‘the form of an experience in general’. Although Kant was thinking mainly of the categories, this sense of objective validity also applies to such non-empirical concepts as those of sensibility and understanding, which in turn determine what categories mean. These transcendental concepts are not related to any particular object, but they are related to all experience, though indirectly by being ‘strictly a priori conditions for a possible experience, as that alone on which its [sic; i.e. their] objective reality can rest’ (A95).

If objective validity means applicability to objects or object-relatedness, there turn out to be two different kinds: the ordinary empirical one ‘consists of elements of a possible experience’, while the transcendental one ‘belongs itself within the concept of possible experience’ (A95). The ‘concept of possible experience’ or ‘the form of an experience in general’ (A222/B269; cf. A125) specifies the necessary structure, including the functions of the faculty of cognition, for the possibility of experience. It is thus not any particular experience but rather the form of possible experience as a whole that provides the ground for transcendental concepts to gain objective validity and form transcendental truth. The latter kind of validity is of second order, in comparison to the first-order objective validity of empirical concepts because the objective validity of transcendental concepts does not, at least not directly, consist in their applicability to empirical objects, but rather in their validity to the structure by virtue of which empirical concepts can be related to objects and acquire first-order objective validity. In contrast to the empirical significance of ordinary concepts, transcendental concepts can be said to have transcendental significance (Westphal Reference Westphal2004: 46–50).Footnote ¹²

Hanna makes a similar distinction between these two levels of objective validity: a ‘distinction between “primary objective validity” (POV) and “secondary objective validity” (SOV)’ (2001: 91–2). Having offered a very detailed specification of them (2001: 92–5), Hanna does not provide any argument for the distinction nor an explanation of why certain non-empirical concepts can have SOV at all. I shall attempt to offer an account of the relation between first-order and second-order objective validity in the next section. However, an important hint can be given by comparing another difference between Hanna’s distinction and mine. Hanna draws the wrong line between the two levels of objective validity. He is mistaken in claiming that ‘all the transcendental principles including the Axioms of Intuition, the Anticipations of Perception, the Analogies of Experience, and the Postulates of Empirical Thought, have SOV but not POV’ (2001: 94). It is true that pure categories, prior to their schematization, are not related to empirical intuitions and thus lack first-order objective validity (or POV). They obtain SOV through their respective schemata, which have incorporated the form of time and are applicable in empirical reality. This shows that the temporal schemata themselves must have POV. When we describe the causal relations of natural phenomena, we are directly applying a causal schema to objects of experience based on the Second Analogy. Hanna is thus wrong in denying the POV of the schemata and principles.Footnote ¹³

Now the relation between unschematized categories and temporal schemata offers an important clue for understanding in what sense transcendental concepts can lay claim to second-order objective validity. As explained above, Kant’s faculty of cognition cannot be equated with the human cognitive system, which is, in a sense, just a contingent product of the long process of evolution. By contrast, cognitive faculties such as sensibility and understanding represent the necessary functional requirements that determine the structure of cognition and even the structure of the objects of cognition. If a pure category can become applicable to objects through temporal schematization, then, in a similar way, transcendental concepts can acquire objective validity through a transformation comparable to the schematization of pure categories. It thus remains to be explained in what sense transcendental concepts can be ‘schematized’ and become related to the psychological mechanisms of empirical cognizers such as humans.

4. Transcendental Concepts and Empirical Realizations

In order to account for the conditions of possibility of objective cognition, Kant has to engage in a kind of theoretical reflection on the faculty of cognition and its relation to objects. While focusing on the conditions of first-order cognition of empirical objects, Kant has only made occasional remarks on the nature of second-order transcendental cognition. I shall now try to infer the characteristics of transcendental concepts and truths based on the framework developed above.

According to Kant, the subjective forms of cognition can be validly applied to all objective cognition because objects of cognition are nothing but appearances whose reality depends, in a sense, on our faculty of cognition. What can become an object of cognition must be subject to the spatio-temporal forms of sensibility and the categories of understanding, unified under transcendental apperception. However, since this object-relatedness finally rests on intuitions, it is the spatio-temporal framework, instead of the categories, that determines the bounds of empirical objects. As space is only the form of outer sense and thus its form does not apply to all appearances, the bounds of all empirical reality are determined by and are identical to the bounds of time. But while all appearances are in time, the conditions that ground the temporality of all appearances are not. Thus Kant could not have explained why appearances must be arranged in a temporal order by describing mental processes that take place in time, since this would have assumed the very thing that has yet to be accounted for. In a sense, it is the subject’s cognitive conditions that first ‘produce’ time and space, and so the conditions of temporality cannot be anything temporal (B422).

Since transcendental cognition is about the grounds or conditions of empirical cognition, its ‘objects’ cannot be in space and time. Transcendental cognition certainly includes descriptions about the necessary forms of space and time in empirical cognition, but the descriptions are merely about the concepts of space and time and not about anything spatio-temporal. If Kant’s accounting for the conditions of empirical cognition and reality is based on a theory of the faculty of cognition, the cognitive faculties such as sensibility and understanding do not represent any cognitive modules of a human brain or any psychological process that takes place in time. In analysing the cognitive functions that are necessary for empirical cognition, Kant often gives the impression of describing hidden psychological mechanisms, but this impression is false and incompatible with his transcendental idealism.Footnote ¹⁴ Because temporality is a necessary condition of the schematized category of causality, the cognitive functions described in the Critique, such as intuition, synthesis and apperception, cannot be equated with any proper causal mechanisms either. The whole transcendental theory of the faculty of cognition does not appeal to any spatio-temporal properties, which implies the absence of all schematized categories including causality.

The absence of spatio-temporal and causal relations in transcendental cognition is a logical consequence of Kant’s distinction between sensibility and understanding. The spatio-temporal form of intuition has no role to play in a discourse in which no reference to any empirical object will be made. Second-order transcendental cognition includes an analysis of the concept of objects in general without amounting to first-order cognition of objects. Kant repeatedly emphasizes that cognition requires both sensibility and understanding. If the above analysis is right, then this requirement applies only to first-order cognition of empirical objects, not to second-order transcendental cognition. Transcendental cognition does not rely on sensibility and its spatio-temporal form, but only on pure concepts, which, as explained above, have logical or analytic significance independent of empirical intuitions. Kant’s theory does not rule out the possibility of using concepts independently of intuitions,Footnote ¹⁵ but only denies that such use of concepts can lead to ‘a greater sphere of objects’ (A254/B309). The possibility of using concepts independently of intuitions does not violate Kant’s famous dictum: ‘[t]houghts without content are empty, intuitions without concepts are blind’ (A51/B75). This is because such use of concepts is indeed empty in the sense of lacking empirical significance or first-order objective validity. Transcendental cognition does not lead to any cognition of objects in the real, thick sense. There are no objects in the proper sense to which concepts such as sensibility, understanding and transcendental apperception can apply, at least not directly.

The cognitive faculties are objects of transcendental cognition only in the logical, thin sense, defined by unschematized concepts. Just as unschematized categories abstract from the sensible form of time, the cognitive faculties of sensibility and understanding are not conceived in spatio-temporal or causal terms either. For example, while sensibility is the capacity to ‘relate to objects’ (A19/B33), occupying what is nowadays known as the function of reference, understanding provides the categorial unities for the organization of concepts and transcendental apperception provides the ultimate unity to which all the representations of a cognitive subject must be ascribable. All these functions are said to belong to the faculty of cognition, which as an object in the logical, thin sense is a merely theoretical construct that specifies the necessary functional constraints for all possible cognizers. By contrast, the human mind is a concrete cognitive system that operates in spatio-temporal reality. If human beings are in fact capable of cognition, the implication of Kant’s theory has it that the human brain must somehow have evolved the cognitive capacities and operations that appropriately execute the functions specified by sensibility, understanding and transcendental apperception. In this sense, the human cognitive system can be seen as a particular biological instantiation of Kant’s faculty of cognition. As the transcendental concepts express specific functional structures, it is natural to appeal to the functionalist terminology to call this instantiation an ‘empirical realization’.

Although the transcendental concepts that describe the faculty of cognition stipulate abstract functional requirements using unschematized categories, their empirical counterparts realize the functional constraints in spatio-temporal reality by appropriate causal mechanisms. This transcendental-empirical relation can best be illustrated by Kant’s distinction between transcendental and empirical apperception. Although transcendental apperception is, for Kant, the most fundamental cognitive function that provides the ultimate logical unity for all representations that can possibly be ascribed to a cognizer (B131–2), it is not anything experienceable in inner sense, in which nothing continuously identical is to be encountered.

Empirical apperception, which is the consciousness of one’s own existence in time or identity over time, is the empirical counterpart of transcendental apperception. This is no longer a transcendental concept, but depends on the empirical consciousness of external persisting objects, as Kant argued in the Refutation of Idealism (B274–9). Kant also distinguished between transcendental and empirical aspects of other cognitive functions, suggesting in the following passage that each of the three basic cognitive powers can be considered empirically on the one hand and transcendentally on the other:

I have in another paper developed a detailed functionalist account of the distinction and relation between transcendental cognitive functions and their empirical counterparts (Lau Reference Lau2014); here I shall confine my discussion to the problem of objective validity and the relation between transcendental and empirical truths. The transcendental–empirical distinction is one of the most important ideas in Kant’s Critique, but rarely has it been consistently maintained by commentators, and even Kant himself is not very consistent either. The failure to distinguish transcendental cognitive functions from their empirical realizations has led to the accusation of psychologism.Footnote ¹⁶ The empirical realizers are temporal, causal and psychological, but the cognitive functions that belong to Kant’s account of the possibility of experience and objects of experience are not. Nevertheless, in order for Kant’s account to be successful, these transcendental concepts have to be, in principle, realizable by causal-psychological mechanisms that fulfil the functional requirements.

5. Objective Validity and Transcendental Truth

Since, as explained above, transcendental concepts are a specific type of pure concepts, their objective validity is of the same second-order kind as that of pure categories. If the pure categories have to be schematized in order to become empirically applicable, the same is true of transcendental concepts. It is the possibility of an empirical realization that confers a second-order objective validity on transcendental concepts, just as temporal schematism makes pure categories applicable to empirical objects. Put in terms of the principle of objective validity, Kant can formulate synthetically true judgements with transcendental concepts such as those of sensibility and understanding only if there can possibly be causal-psychological mechanisms that fulfil the functional requirements defined by them. Although transcendental concepts are non-empirical, their validity is still in a sense subject to the constitution of the empirical world. If there is no possible world in which the functions of sensibility and understanding could ever be actualized by appropriate causal-psychological mechanisms, then the faculty of cognition would be a mere invention, without any objective validity. Transcendental concepts such as those of sensibility and understanding are related to the empirical world indirectly through their empirical realizers, just as the pure categories become applicable to the empirical world by the mediation of their corresponding temporal schemata.

The distinction between the two orders of objective validity is very important for Kant’s project, but it has rarely been discussed in Kantian literature.Footnote ¹⁷ Concepts with second-order objective validity provide the conceptual constituents for the transcendental truths that Kant’s theory aims to discover,Footnote ¹⁸ and the structure of empirical realization developed above helps us to better understand the nature of transcendental truths. Although transcendental truths are supposed to make empirical truths possible, the former do in a certain sense depend on the latter. The second-order objective validity of pure categories and transcendental concepts consists in their indirect relation to empirical objects through the mediation of temporal schemata and concepts of appropriate causal-psychological mechanisms, respectively.

If ex hypothesi an indirect relation always depends on the direct relations that mediate between two indirect relata, then the second-order kind of objective validity depends on the first order in the same respect. However, this kind of dependence does not make empirical concepts or empirical truths more fundamental than transcendental ones. Consider the possibility that the course of evolution had been different and the world had never evolved Homo sapiens or any organisms that are capable of cognition. There would have been nothing in our empirical world that would count as an appropriate realization of the functional requirements defined by the transcendental concepts. If such an imaginary, but not unlikely, scenario had been the case, would it mean that Kant’s theory of the faculty of cognition is false? Not at all. Kant’s transcendental theory could be refuted by showing that it failed to identify the right set of necessary conditions of the possibility of cognition, but neither by the eventual extinction of human beings nor by the factual non-existence of all empirical cognizers. If the world had never produced any appropriately capable cognizers, such as humans, then the conditions proposed by Kant would not have been met, but this would not mean that the conditions are wrong.

Transcendental truths are not analytic, nor are they truths about a more fundamental, presumably noumenal reality that would exist behind or beyond the empirical world. If Kant’s theory is successful, transcendental truths are true of the general structure of all those possible worlds in which objective cognition or experience is possible.Footnote ¹⁹ In this sense, transcendental truths are more fundamental than empirical truths, although transcendental concepts have to be mediated by their empirical realizers to become related to empirical objects. In order for any particular experience or any empirical truth to obtain, the formal structure of the empirical world has to conform to the conditions expressed by transcendental truths. Any particular experience could have been different from how it is, but if Kant’s theory is largely correct, the way any experience could possibly happen varies within the framework defined by the faculty of cognition. Transcendental truths pick out a set of possible worlds whose structure allows empirical truths to obtain. It is in this sense that we must understand Kant’s claim that transcendental truth ‘precedes all empirical truth and makes it possible’ (A146/B185).Footnote ²⁰