2. Two systematic requirements for a theory of truth

Let us begin with the coherence theory of truth. If truth consists in the consistency of individual propositions and the coherence of a system of propositions, then the basic logical principles – the law of non-contradiction, the principle of identity, and the law of the excluded middle – are not only necessary conditions for truth, but also sufficient ones.Footnote ¹¹ Prima facie, this appears plausible: For something that is inconsistent certainly cannot be true, and something incoherent likely cannot be either. Accordingly, the negation of falsity seems to offer a reliable pathway to truth. Formally, we might define falsity as follows:

Given that truth is the opposite of falsity, one might attempt to arrive at a definition of truth by negating the definition of falsity:

Should we be happy with this definition? What guarantees that there is only one coherent system of propositions? Why not two, or twelve, or eight billion?Footnote ¹²

If each alternative in a contradictorily opposed pair of propositions (A or not-A) can be integrated without contradiction into a system of propositions already accepted as true, then it becomes either a wholly contingent matter which of the two is held to be true – for instance, because the subject happens to encounter one before the other – or an arbitrary one, in the sense that the subject chooses between them without reason. Both possibilities are incompatible with our intuitive conception of truth, since truth would thereby dissolve into a multiplicity of private, subjective truths. So, by this path, we arrive at a form of truth pluralism. The singular objectivity implicit in the very concept of truth, as that which transcends subjective arbitrariness, would be fragmented across a plurality of coherent systems of belief, with no possibility of privileging one over another based on objective reasons.

These considerations indicate that the concept of truth possesses an essentially objective–realist dimension, and that is the one that the coherence theory fails to account for. Following J. McDowell, what it lacks might be called ‘friction with the world’ (McDowell Reference McDowell1994: 11). So:

However, the correspondence theory also bears a difficulty, particularly when the abstract criterion ‘to correspond with an independently existing reality (the world)’ is taken as a final explanatory step. The truth-theoretical position which holds that things are as they are, irrespective of whether we can recognise them or not, is known as metaphysical realism (Putnam).Footnote ¹³ Why now is metaphysical realism troubling?

If the truth of a proposition consists in its correspondence, or agreement, with an entity that is, in principle, unrecognisable, then truth is a non-epistemic concept, one that means something that is not knowable in any possible way. The problem arises from the fact that such a notion is no longer applicable: an in-principle non-epistemic conception of truth, severed from any relation to knowledge, would render our entire practice of justification meaningless. No matter how well or poorly we justify a belief, each proposition would have an equal probability – 50 per cent – of being true or false, entirely independently of our epistemic efforts. Yet we would never be able to determine which of these alternatives is the case. So, a viable theory of truth must be embedded in an epistemological framework that explains how truth is in principle accessible to finite subjects. A conception of truth that is entirely detached from our epistemic capacities cannot play any role in supporting our knowledge claims. When correspondence is construed in a way that places the truth-makers beyond all possible knowledge, the result is not a deeper realism but a form of scepticism. The result of metaphysical realism is scepticism.Footnote ¹⁴

Since the scepticism resulting from metaphysical realism is just as detrimental to the concept of truth as the subjectivism associated with the coherence theory – in which the ‘world’ is no longer available as an intersubjectively shared, common objectivity – the following second desideratum (D2) must be posited:

Two key lessons concerning the concept of truth can be drawn from this. First, the consistency of a proposition and the coherence of a system of propositions are not sufficient conditions for truth, since objective reality must serve as the standard for distinguishing true from false propositions (cf. D1). Second, since a purely metaphysical and non-epistemic construal of correspondence makes the notion of truth unusable for finite knowers, a viable correspondence theory must integrate the correspondence criterion into an epistemological framework that explains how truth can be accessed (cf. D2).

Thus truth can be neither wholly dependent on subjective belief(s) nor entirely reliant on something that is, in principle, epistemically inaccessible to subjectivity. Put positively: objectivity (the world) must function as an epistemic corrective to our assertions. In section 2, rationalism – the tradition from which Kant decisively breaks in his critical philosophy – will be considered as a historical and systematic counterpoint, before we turn to Kant’s theory.

3. Rationalism and the concept-analytical model of truth

Early eighteenth-century German philosophy, shaped by the tradition of rationalism, identifies the conditions of thought with the conditions of being. The concept of truth underlying its epistemology and metaphysics reflects a synthesis of correspondence and coherence theories, yet in a form that displays both shortcomings outlined in section 1. The following passage from Gottfried Wilhelm Leibniz clearly articulates the praedicatum inest subjecto conception of truth, which is characteristic of rationalist epistemology and metaphysics:

According to this view, the truth of every affirmative proposition consists in the fact that all the characteristics of the predicate are contained within the subject: praedicatum inest subjecto.Footnote ¹⁶ I shall refer to this as concept-analytic truth. Leibniz thereby claims to have determined the nature of truth (natura veritatis), that is, its essence. According to him, the praedicatum inest subjecto principle is to be understood as a real definition of truth.

The epistemological consequence of this conception of truth is that all knowledge must consist in explicit or implicit identities. That is, all truths must be recognisable as analytic judgements – judgements whose truth or falsity can be determined by means of an analysis based on the principle of non-contradiction and the other basic formal principles of logic.Footnote ¹⁷ For example, the proposition The circle is square is analytically false because it is contradictory, while The circle is round is analytically true. Accordingly, concept-analytic truth is thought to have a generally sufficient epistemic criterion: the law of non-contradiction. However, the problem lies in the fact that most of the propositions we include in our body of knowledge are synthetic judgements – judgements in which the predicate is not contained in the subject. This is especially obvious in the case of empirical judgements, the so-called vérités de fait in Leibniz’s terminology. The negation of the proposition The circle is red, for instance, does not yield a contradiction, since red and circle do not stand in a purely conceptual relation to one another, but at most in a contingent factual one – one that is not accessible through conceptual analysis. The judgement is therefore synthetic.

According to this rationalist, concept-analytic position, synthetic propositions do not constitute a genuine class of judgements; rather, they are conceived as merely contingent and provisional judgements that require further clarification through progressive conceptual analysis, until their ultimately analytic form is revealed.

This understanding of truth follows René Descartes, who writes in his Meditationes de Prima Philosophia: ‘illud omne esse verum, quod valde clare & distincte percipio’ (Descartes Reference Descartes1897: vol. vii, 35); ‘Everything is true which I perceive very clearly and distinctly’ (my translation, SB)’.Footnote ¹⁸

According to this account, there are degrees of distinctness in cognition, and consequently degrees of truth. The more distinct a cognition becomes – and thus the truer it is – the more its constituent concepts are analysed and made explicit.Footnote ¹⁹ In most cases, for us as finite knowers, the complete truth of a proposition is either not yet recognised or, in principle, unknowable. Only the purely rational truths (vérités de raison) are considered fully recognisable, that is, either simple identities or metaphysical propositions accessible, if at all, only to philosophers, but only in a deficient mode (symbolic cognition). As a result, the supposedly epistemic truth criterion of the concept-analytic account, namely the law of non-contradiction, tends to exclude full truth from the reach of the human intellect, either in principle or indefinitely.

The ontological consequence of the concept-analytic conception of truth, and of the epistemology built upon it, is that the object to which cognition must correspond in order to be true is an entity that is purely intellectual in nature (ens rationis, thing in itself, noumenon). For rationalism, the sensible appearance of things is merely a deficient mode in which objects initially present themselves to the finite intellect. However, in principle, things are not objects of perception, but intelligible entities accessible through progressive conceptual analysis. The world thus grasped is the mundus intelligibilis.

Hence, we must conclude that concept-analytic truth fails to meet the requirements outlined in section 1. On the contrary, its only prima facie epistemic criterion – the principle of non-contradiction – leads, first, to the sceptical consequence that truth becomes a non-epistemic concept for the vast majority of propositions, namely for all synthetic judgements, either in principle or indefinitely over time.Footnote ²⁰ Moreover, it entails that the validity of logical principles cannot ground the full-fledged justification of knowledge claims, since rationalism’s gradational conception of truth allows such principles to function only as negative criteria: they can exclude falsity, but they cannot establish the positive truth of a judgement for finite knowers (contra D2).

Second, the world (mundus intelligibilis) is not available as an objective corrective for distinguishing between true and false propositions. In rationalist accounts, friction with the world is deferred into infinity (contra D1). This, in effect, is the sort of metaphysical realism Kant sets out to overcome.

4. Kant and the ‘logic of truth’ (CpR A62/B87)

Kant criticises rationalist metaphysics by challenging its underlying concept of truth, and thereby its entire epistemological and metaphysical framework. In the introduction to his Transcendental Logic, Kant employs a truth-theoretical argument against the use of formal logic as an instrument of metaphysics, as a metaphysical organon. He argues that rationalist metaphysics rests on a fundamental misunderstanding of the nature of truth. In doing so, he confronts the logicist metaphysics of rationalism with the aporia concerning the criterion of truth – a problem well known from sceptical philosophy:Footnote ²¹

The meaning of truth is here explained in terms of the correspondence theory – that is, in Kant’s words, as the agreement of a cognition with its object. This nominal definition, which enables us to distinguish the concept of truth from other concepts, is ‘granted and presupposed’ in the sceptical challenge (CpR A58/B82). What still requires clarification, however, is the ‘general and certain criterion of the truth of any cognition’. This is an epistemological problem: What criterion enables us to recognise the truth of any given cognition?

In section 2, I outlined how eighteenth-century rationalist philosophy takes up this challenge and, by appealing to concept-analytic truth, treats the law of non-contradiction, or more broadly, the formal-logical laws of finite reason, as positive truth conditions, that is, as both necessary and sufficient. Yet, this approach ultimately undermines itself. Kant takes a different route. Rather than attempting to answer the challenge directly, he emphasises that it is not merely the sceptic who is caught in difficulty here, but even more so the ‘logician’ who accepts the challenge and seeks to provide a general and certain criterion for the truth of any cognition.Footnote ²² The inconsistency inherent in the sceptical challenge can be brought to light by what I shall refer to as Kant’s criterion argument. It proceeds as follows:

We begin with the definition of truth:

1. (1) Truth consists in the correspondence of a cognition with its object (cf. CpR A58/B82).

For Kant, knowledge is attainable only in judgement.Footnote ²³ Since the object of a theoretical judgement exists independently of the act of judgement, and since truth and falsity are to be found ‘only in the relation of the object to our understanding’ (CpR A293/B350), what is at stake here is not an ontological, but a propositional conception of truth.Footnote ²⁴ The state of affairs asserted in a judgement, its factual content, may or may not exist independently of that judgement. Truth and its opposite, falsity, are therefore relational properties of judgements, grounded in the object-reference of the finite understanding.Footnote ²⁵

1. (2) A judgement is either true or false. (principle of bivalence)Footnote ²⁶

Taken together, (1) and (2) express a correspondence-theoretical conception of truth.

1. (3) Truth consists in the correspondence of a judgement with its object and falsity in their non-conformity.

Kant links this conception of truth to the claim that every judgement refers to a specific object. A judgement, by its nature, singles out something determinate, that is, one object distinct from others.

What is at issue here, and what the sceptical challenge ultimately attacks, is therefore material truth. This consists in the agreement of a cognition with the particular object to which it is related, since – as Kant notes – ‘a cognition is false if it does not agree with the object to which it is related even if it contains something that could well be valid of other objects’ (CpR A58/B83):Footnote ²⁷

1. (4) A judgement possesses a specific objective (semantic) content by means of which it either refers to its object (truth) or fails to do so (falsity).

So, every true judgement has a particular object in virtue of which it is true. If a judgement is true, it is true because it corresponds to its object, and not to any other.

1. With (4), two conditions of truth are established:

2. • the existence of a reference to an object (reference condition), and

3. • the correct determination through the predicative content (predication condition).

Kant formulates this duality of conditions explicitly when he states that a cognition is false if it ‘does not agree with the object to which it is related [reference] even if it contains something that could well be valid of other objects [predication]’ (CpR A58/B83, my emphasis SB). Conversely, a judgement is true if and only if it agrees with the object to which it refers (reference), because its content contains only determinations that apply to this very object (predication). The fact that judgements have content means, first, that there is a reference to an object, and second, that the subject in the judgement is determined by the predicate. The correspondence between a judgement and its object obtains if both conditions are fulfilled. In that case, the judgement is materially true. If the first condition (reference) is fulfilled but the object is incorrectly determined (i.e. the predicate does not apply to the subject), then the judgement is false.

The existence or non-existence of agreement between a cognition and its object – that is, truth or falsity – must be criterion-based within the framework of a real definition: one that defines not merely the word truth, but the thing itself. With regard to such a criterion, the following must hold:

1. (5) A sufficient criterion of truth holds universally for all knowledge.Footnote ²⁸

In order to achieve the required universality, one would have to abstract from all difference of objects and consequently from all ‘content of cognition (relation to its object)’ (CpR A58/B83):

1. (6) A general criterion of truth abstracts from all content of cognition.

A general and sufficient criterion of truth, by definition, would have to be indifferent to the specific contents of judgements, while at the same time being sufficient to distinguish true from false judgements in general. But this is impossible: The material truth of a judgement consists precisely in the specific content of the cognition (cf. 4). So, it follows that:

1. (7) A general, sufficient criterion of truth is impossible. (From 4, 5, 6).

This criterion argument has the form of a reductio ad absurdum and proves it to be generally impossible to explain the material truth of a judgement by stating a general and sufficient criterion: ‘no general sign of the truth of the matter of cognition can be demanded, because it is self-contradictory’ (CpR A59/B83).Footnote ²⁹ This establishes a systematic point against rationalism: the traditional account of what truth means, its nominal definition, does not amount to a real definition – pace Leibniz.Footnote ³⁰ Insofar as the argument demonstrates that the consistency of a proposition and the coherence of a system of propositions are not sufficient conditions for material truth, Kant’s criterion argument can also be read as a critique of the coherence theory of truth. And insofar as the criterion argument demonstrates that the traditional explanation of the concept ‘truth’, namely the agreement of a cognition with its object (cf. CpR A58/B82), does not amount to a real definition, it reveals that metaphysical realism rests on a truncated or incomplete conception of what ‘truth’ means.

However, the argument also contains a positive lesson: it shows that an adequate theory of truth must be interlinked with an epistemology that explains how – and thereby that – the abstract requirement of the correspondence of a cognition with its object is epistemically attainable, that is: in principle knowable. Therefore, we can expect that Kant develops a theory of truth that transforms the objectively realist feature of the concept of truth – that a cognition must correspond to its object – into epistemic conditions. How does Kant pursue this project in the first critique?

Recall that, in connection with proposition (4) of the criterion argument, it became clear that a materially true categorical judgement of the form ‘S is P’ presupposes two necessary conditions of truth:

1. (a) The subject term of the judgement must refer to something objective (reference condition).

   And:

2. (b) The object referred to must be correctly determined (predication condition).

The reference condition (a) is the more fundamental of these two truth conditions: it constitutes the condition for the truth valence – that is, the truth-value capability – of a judgement. For without the object reference of the subject term, the question does not even arise whether the predicate truly belongs to the subject or is rightly denied of it.Footnote ³¹ The Transcendental Analytic, Kant’s ‘logic of truth’ (CpR A62/B87), investigates the general and necessary conditions for the objective reference of our thinking; the conditions for the possibility of the object-reference of our judgements and the objective validity of our concepts. In Kant’s words, ‘the principles without which no object can be thought at all’ (ibid.).Footnote ³² This is why Kant’s Transcendental Analytic is the logic of the pure thinking of objects. Recall that Kant explicitly says that ‘no cognition can contradict it without at the same time losing all content, i.e., all relation to any object, hence all truth’ (ibid.).Footnote ³³

Analytic judgements concern semantic relations between concepts. The principle of non-contradiction functions as their transcendental principle, that is, as the epistemic criterion of truth for this class of judgements. However, reference to an object is made only in synthetic judgements, that is, in judgements whose truth or falsity cannot be determined by the principle of contradiction alone but requires another and different one.Footnote ³⁴ The task of the Transcendental Analytic then is to specify the conditions that all synthetic judgements must fulfil in order to lay claim to objective validity. Against this background, the central question of the Critique of Pure Reason ‘ How are synthetic judgements a priori possible? ’ (CpR B19) means: What is the general and necessary condition for the object-reference of our thinking? Or more pointedly: What is the a priori condition of material truth?

Tackling this question lies at the heart of Kant’s project in the Critique of Pure Reason, which he approaches as a correspondence theorist of truth, but on epistemological grounds. In a nutshell, the result is this: the supreme principle of synthetic judgements is the correspondence with the ‘form of an experience in general’ (CpR A222/B269, cf. A220f./B268). Objects that transcend possible experience – the classical objects of special metaphysics, such as the soul, the essence of the world, and God – cannot be determined in a truth-apt manner through theoretical judgements. In other words, they are, in principle, not objects of possible knowledge. For what counts as objectively real is determined by the transcendental truth of categorical judgement, that is, by the condition of objective reference, that is: ‘All our cognitions … lie in the entirety of all possible experience, and transcendental truth, which precedes all empirical truth and makes it possible, consists in the general relation to this’ (CpR A146/B185) The principles of transcendental cognition are themselves monovalently true – they are truths without an opposite – since they condition objective cognition as such. In the case of analytic judgements, these are the laws of formal logic: the principle of non-contradiction, the principle of identity, and the law of the excluded middle.

For synthetic judgements, in which the object- or world-reference of thought is expressed, the relevant principles are the synthetic principles of the understanding, that is, the categories, together with their transcendental schemata, which serve as conditions of their application in determining real objectivity. These principles are the conditions of the possibility of knowable objectivity.

Thus: What is truth? Kant does not approach this question primarily as a metaphysical project, but as an epistemological one. He is concerned with the question of how we recognise truth. In this context, truth like its opposite, falsity, proves to be a relational property of judgements about objects of experience.

The formal truth of cognition consists in its conformity with the form of the understanding – in its consistency and coherence. The coherence theory rightly captures this aspect of what any theory of truth must account for. However, the purely formal principles of the understanding neglect reference to the object. Since object-reference is essential to the very concept of truth (cf. D1) and equally indispensable for any epistemology that aims to explain the possibility of knowledge, the coherentist elements should not be regarded as features of the concept ‘truth’ itself, but as necessary components of a satisfactory theory of truth – one that must be embedded within a compelling epistemological account.

The material truth of a cognition, by contrast, consists in its correspondence – or agreement – with the object. In this respect, the correspondence theory also captures an essential feature of the concept of truth. In the Transcendental Analytic Kant shows, in opposition to metaphysical realism, that material truth, like formal truth, has a logical condition, more precisely a transcendental-logical one. The condition for the pure thinking of objects is their conformity with the form of experience in general.

Both conditions, those of formal and material truth, are logical and thus necessary conditions. This means: a judgement that does not satisfy them is either false or not truth-apt at all, which means: it is not even within the scope of truth or falsity, because it lacks object reference. In the Transcendental Analytic, Kant thus concretises the abstract criterion of correspondence into the requirement of correspondence with the form of experience in general. Through the categories and their temporal schemata as application conditions, the correspondence-theoretical concept of truth is rendered epistemically accessible in theory (e.g., substance is that which persists in time, etc.).Footnote ³⁵ Thus, the form of objectivity lies within the finite understanding.

If a predicate is attributed to a subject in a way that contradicts it – either conceptually or factually – the judgement is false (predication condition). However, if the judgement does not refer to any object because its subject expression fails to refer, it lacks truth on an even more fundamental level (cf. CpR A62/B87): it is not truth-apt (reference condition).

The predication condition allows for a precise determination of what falsity is. Falsity consists in a misrepresentation of being: the object is disclosed, but in a manner that does not correspond to its own nature (cf. Tugendhat Reference Tugendhat and Skirbekk1992: 438f.). Tugendhat’s formulation, drawing on Heidegger’s terminology, articulates elements that are central to Kant’s account, namely, first, that what exists is, in general, disclosed (or determined) only in the judgement; and second, that this determination (predication) can fail, since our relation to what exists is a distinctively mediated one ‘in such a way that it [what exists] is not given to us … itself, and yet we can still intend it, and therefore also intend it differently from how it is’ (440f., my translation, SB). Truth is not grasped intuitively by the finite human intellect, which, according to Kant, possesses an essentially discursive understanding. Instead, truth is mediated: the understanding determines the manifold of intuition – given by sensibility – as objective within the structure of categorical judgements. This is what constitutes the world as mundus sensibilis.

With respect to the correspondence theory of truth, Kant teaches us to see why it is misguided to infer from the correspondence relation an ontology of facts – understood as worldly truth-makers whose structure mirrors that of judgement. A paradigmatic example of such a fact-ontological position is Wittgenstein’s early claim that ‘the world is the totality of facts, not of things’.Footnote ³⁶ Kant shows that the logical form of judgement is contributed by the understanding and therefore cannot ground an ontology of facts or states of affairs as entities in the world. In Kant’s view, such a position would amount to hypostatising the forms of thinking. The discursive intellect does not relate to objectivity by matching propositional forms to independent entities; it relates to objectivity only mediately, through the spatiotemporal objects that are given in sensibility and conceived as objects in categorical judgement. While the form of cognition stems from the understanding, its matter is supplied by intuition, and only spatiotemporal appearances can serve as the objects of cognition and thus as the bearers of truth-making significance. There is therefore no need – and within the bounds of possible experience no room – for an additional ontological category of ‘facts’ as the correlates of true judgements.

With regard to the reference condition, the following applies: since human intuition is structured by the pure forms of space and time – forms which are, on the one hand, contingent in the abstract sense that alternative forms are conceivable (albeit only speculatively), but, on the other hand, necessary qua conditions of our sensible intuition – our reference to an object that exists independently of our thinking (i.e. material truth) is bound to these forms. Accordingly, no non-spatiotemporal object is recognisable.

At the same time, no spatiotemporal object is a thing in itself. A thing in itself, by definition, is either:

1. (1) a being grasped through pure intellectual intuition (a positive noumenon), or

2. (2) a thing only negatively conceived: as something that does not appear in space and time – a noumenon in the negative sense (cf. ‘On the ground of the distinction of all objects in general into phenomena and noumena’ CpR B294-315, cf. A235-60).

Since the Critique of Pure Reason demonstrates that the sensible is the interface at which mind and world meet, at least insofar as the world is knowable through theoretical reason, the world we determine in synthetic judgements, whether a priori according to pure form or materially enriched through experience, is the mundus sensibilis: the spatiotemporally appearing world of sensible objects. The traditional metaphysical claims to knowledge of the super-sensible are thereby exposed as mere ‘semblance of objective assertions’ (Blendwerk von objektiven Behauptungen, CpR A61/B85). Hence, Kant’s theory satisfies both desiderata:

• objectivity is epistemically accessible, since its form is grounded in the subject by the synthetic principles of the understanding (formal truth, D2);

• the object of our judgements is spatiotemporally appearing objectivity, which, although subjectively constituted in its form, is not subjectively conditioned in its material existence; it is not ‘constructed’ (material truth, D1).Footnote ³⁷

What general lessons can be drawn from this?

Truth, in the sense of adaequatio – a correspondence or agreement between something mental (a judgement) and something extramental (the world) – is more adequately grasped in Kant’s philosophy. Whereas Leibniz seeks to explain this correspondence by positing an ontology of intelligible objects, Kant avoids the need to hypostatise judgements as truth makers. He does so by distinguishing between sensible intuition, in which the object is given as a sensory (in our case: spatiotemporal) manifold, and the discursive concept, which synthesises this manifold through the categories into the concept of an object.Footnote ³⁸ In this way, Kant secures a correspondence-theoretical account of truth that is both epistemically grounded and metaphysically modest. It has thus become clear that both the coherence and the correspondence theories of truth each capture a legitimate aspect of the concept, and that Kant integrates both moments into his overall account.Footnote ³⁹

However, through his distinction between the logical conditions of formal truth and the transcendental-logical conditions of material truth, it becomes evident that the concept of truth resists a real definition. Neither the coherence theory nor the correspondence theory fully grasps the essence of truth; neither alternative can be regarded as offering a real definition of the concept. Nevertheless, there is a decisive reason why Kant’s theory of truth is ultimately to be understood as a correspondence theory, and why it may rightly be regarded as a form of moderate realism. Unlike metaphysical realism, however, the correspondence Kant envisions must not (per impossibile) be conceived as a relation between mental entities (cognitions) and something entirely independent of the mind (considered as things-in-themselves). Rather, the correspondence holds between cognition (more precisely: judgement) and appearance. This is possible because they share a common form: the form of experience in general. In this case, the problem of explaining correspondence disappears, since the shared form lies within the mind. This is Kant’s enlightened transformation of the Thomistic adaequatio intellectus et rei: the finite intellect is the lawgiver of natura formaliter spectata (cf. CpR B165). The mind-dependence of the objects of cognition is formal, not material. That means: our finite mind does not create the object but constitutes its form. For this reason, the coherence-related features that pertain to the materially enriched form of thinking concern the structure of knowledge rather than the concept of truth itself. They do not determine what it means for a judgement to be true, but rather how several judgements must be integrated into a unified system if that system is to count as knowledge.

This epistemological insight has an ontological consequence: the objects of cognition are appearances, not things entirely independent of the mind in their existence – not things in themselves. Although the conditions of formal truth are rightly captured by coherence theory – as consistency (principle of non-contradiction) and coherence (laws of logic), and thus as necessary conditions of truth – it must nonetheless be stated, in critical contrast to the coherence theory, that there exists no immanent criterion of material truth within consciousness. What coherence theory provides is a criterion of truth valence – a negative formal condition that excludes falsity – not a criterion of truth itself. The broader, epistemic sense of coherence, associated with systematic unity and the regulative ideas of reason, belongs for Kant to the conditions of knowledge, not to the concept of truth. Material truth requires object-reference, and object-reference is available only within the bounds of possible experience. This, however, presupposes an a priori condition: a cognition must accord with the form of experience in general. This is to say that the categories must be applied through their transcendental schemata, which serve as the a priori conditions of their objectively valid application. Only under these conditions can a cognition enter the relation of correspondence with an object which material truth requires.