The significance of Kant's mere thoughts

ABSTRACT

Kant distinguishes cognition and thought. Mere thoughts do not conform to the conditions that Kant places on cognition and hence do not represent objects of experience. They are, nevertheless, intelligible, and play a vital role in our mental and moral lives. I offer the beginnings of an account of mere thought using Kant's resources. I consider four key cases of intelligible representations that lack objective validity: unschematized categories; transcendental ideas; philosophical concepts; thoughts that violate principles of the understanding.

KEYWORDS:

• Cognition
• Kant
• objective validity
• thought
• transcendental ideas
• unschematized categories

1. Introduction

Kant makes an interesting and important distinction between cognizing and thinking. Cognition is objective; cognitions represent objects of experience (even if they don't always correctly represent them).^1,2 Mere thought is not objective in this sense; mere thoughts do not conform to the conditions that Kant places on cognition and hence do not represent objects of experience.³ Nevertheless, we can think and understand mere thoughts.

This distinction is hugely important for understanding Kant: throughout his philosophy, he writes about matters that, by his own lights, we cannot cognize. There are concepts we need to understand his philosophy, such as thing in itself. Moreover, thoughts involving the transcendental ideas, such as God, have an important role to play in our search for knowledge (and, if those same ideas feature in the practical postulates, a role in morality and action). Kant himself stresses that just because these ideas cannot represent objects of experience, that does not render them ‘superfluous and nugatory’.

For even if no object can be determined through them, they can still … serve the understanding as a canon for its extended and self-consistent use, through which it cognizes no more objects than it would cognize through its concepts, yet in this cognition it will be guided better and further. (A239/B385)⁴

We need the transcendental ideas to guide the understanding in seeking knowledge. Kant limits knowledge and cognition to the realm of possible experience, in part to leave room for morality and faith beyond the domain of cognition (Bxxx). But, as Van Cleve puts it, ‘there is hardly room for faith in what is demonstrably lacking in sense’ (1999, 69). In short, the heart of Kant's philosophy rests on our ability to understand mere thoughts.

As such, it is now broadly agreed that mere thoughts are not nonsense: they can be thought and understood by creatures with minds like ours, i.e. the kind of mind that Kant describes in the Critique of Pure Reason. But it remains to be explained how this can be so. Arguably, one of Kant's main interests in the Critique is aboutness or intentionality. He has more to say about when representations are or are not ‘objectively valid’, that is, represent objects of possible experience. He has less to say about thinkability or intelligibility independent of that. Nevertheless, it's an important question how it is that we can think and understand thoughts that go beyond the bounds of cognition. It's important for understanding Kant's philosophy. It's also interesting as an example of an account of something like non-intentional thought (although I do not have space to explore this beyond the Kantian context here).

My aim in this paper is thus to contribute to a systematic understanding of mere thought in Kant. The topic is vast, and so I will not be able to address it from all angles, nor answer all of the questions that may arise in due course. To make my task here more tractable, I intend to focus on the following aspect of mere thought. I aim to show how, in a few key cases, focussing on representative examples, one can account for our capacity to think and understand mere thoughts by drawing on objective representations and principles for how to combine or transform those objective representations into (constituents of) mere thoughts. The general picture that emerges from this is one according to which one can begin with (resources for) objectively valid representations, apply plausible principles for how to combine or otherwise transform those representations (and resources), and thereby derive representations that we can think and understand, but which are not objectively valid. Such a picture, it seems to me, is well within the spirit of Kant's critical philosophy: we should be wary of anything which purports to be a representation or knowledge of that which lies beyond the realm of possible experience, but that does not mean that such representations are to be summarily rejected. On the contrary, they have a systematic connection to objective representation. Kant emphasises this in one direction: mere thoughts play a crucial role in helping to increase and systematise our cognition. One might take the moral of this paper to highlight a connection in the other direction: we are able think and understand those mere thoughts in virtue of their relation to cognition.

To further clarify, my aim is to develop the beginnings of an account of mere thought using resources from Kant's philosophy; an account that Kant could have given. Whether this is the view Kant had precisely in mind is a more vexed issue. The (or at least one major) purpose of the Critique of Pure Reason is to investigate what it is possible for creatures with our cognitive capacities to objectively represent and to know, in order to curb the pretensions of metaphysics, and so to redirect metaphysics towards ‘the secure course of a science.’⁵ Kant's focus is thus on cognition and knowledge (or a lack thereof) rather than thinkability. However, this brings along a background presupposition that those thoughts that don't live up to the standards of cognition or knowledge at least make sense: we are not guarding against mistaking nonsense for knowledge (which seems to be more straightforward), but against mistaking something that is at least thinkable for knowledge. In sum: it is interesting and important to give an account of mere thought in Kant, but it is far from straightforward to say that this is Kant's account of mere thought.

My plan is as follows. First, I outline in more detail the notions of cognition and mere thought, and isolate the main cases for attention. I consider four key cases: unschematized categories; transcendental ideas; philosophical concepts; and thoughts that violate principles of the understanding. For each case, I show how Kant can account for their intelligibility, and highlight the key principles that lie behind this.

For reasons of space, I focus only on Kant's theoretical philosophy, and set aside consideration of cognition and mere thought in his practical philosophy.⁶ Again, for reasons of space, I will not here tackle the question whether mere thoughts have a truth value. I agree with Vanzo (2012) that there is good evidence that Kant took mere thoughts to be truth-apt, i.e. to have a truth value.⁷ As such, I will not take truth-aptness to be distinctive of cognition or of objective validity, as I discuss in the next section.

2. Thought, cognition, possibility, and objective validity

The distinction between thought and cognition appears prominently in the Critique of Pure Reason. At the core of Kant's critical philosophy is the claim that we can only cognize appearances and not things in themselves. There are many different interpretations of Kant's distinction between appearances and things in themselves, but they all agree more-or-less on the same core claim:⁸ Kant does not allow that we can have objective representations of things in themselves, of the kind that we can have of appearances.⁹ However, it is clear that he wants to be able to make claims that concern things in themselves.¹⁰ How? We can have thoughts of things in themselves, even if we can't cognize them.

[E]ven if we cannot cognize these same objects [of experience] as things in themselves, we at least must be able to think them as things in themselves. (Bxxvi)

The present aim is to make progress in understanding mere thought. To that end, we need an understanding of cognition. (I focus on the theoretical side of this distinction; by ‘cognition’ I henceforth mean ‘theoretical cognition’.) To understand cognition, I also need to unravel some associated notions, in particular real possibility and objective validity.

Kant seems to have two slightly different conceptions of cognition. In the well-known Stufenleiter passage, concepts and intuitions are species of cognition.

An objective perception is a cognition (cognitio). The latter is either an intuition or a concept. (A320/B376-7)

However, earlier in the Critique, cognition is defined as requiring both concepts and intuitions.

Intuition and concepts therefore constitute the elements of all our cognition, so that neither concepts without intuition corresponding to them in some way nor intuition without concepts can yield a cognition. (A50/B74)

Both conceptions share the crucial element that cognitions are objective. I here reserve the title ‘cognition’ for the latter notion, to contrast with mere thoughts, and capture the former notion in terms of objective validity (of thought constituents).

Henceforth, by ‘cognition’ I mean that representation which requires both concepts and intuition, or, more precisely, possible intuition of an object. On this latter point, I am in broad agreement with Grüne and Stang.¹¹

A Kantian cognition … only requires a relation to really possible objects; that is, a relation to objects whose existence is really possible. It does not require a relation to actually existing objects. (Grüne 2017, 114)

Kant is not claiming that for a concept to be [a cognition] we must be given an actual instance of the concept in intuition. … [Kant] often makes clear that he means the concept relates to an object possibly given in intuition. [E.g., Bxxvi, A3/B6, A4/B8, A63/B88, A239/B298, A245, A247/B304, B383, B391, and B479]. (Stang 2016, 173)¹²

One could take the view outlined here in one of two ways: roughly, cognition does require intuition, but the intuition can be of a possible object, or, cognition requires the possibility of being given an intuition, where an intuition would present an actual object. I prefer the latter option, and will assume that throughout. But the core idea is shared: cognition can occur without an intuition of an actual object, so long as there is some possibility condition fulfilled (possibly an intuition, or possibly an object).

There is much textual evidence to be adduced here. But consider:

To cognize an object, it is required that I be able to prove its possibility. (Bxxvin)

Kant here links cognition not with actual intuition, but with possibility. If, for a representation to be a cognition, it must be possible for its object to be given in intuition and to be thought, then the cognition must conform to the conditions under which objects can be given and thought. These conditions are precisely the conditions of experience in terms of which Kant defines real possibility (A218/B265). Vice versa, if a cognition conforms to the conditions under which it is possible for objects to be given and thought, then it is possible for the object of the cognition to be given in intuition. Cognition involves two capacities – we need to be (able to be) given objects of cognition, and to apply concepts to them in order to represent them as anything. The conditions of cognition involve both the conditions under which we can be given objects – pure forms of sensibility, space and time – and the conditions under which we can think about and apply concepts to objects – the categories, such as cause and substance. So to be a cognition – to be objective – a representation must be of the kind of thing that could be given in intuition, and it must conform to principles arising from the categories.

I focus on thought and cognition in this paper, but note that, for Kant, experience is empirical cognition; cognition involving empirical intuition (B147). And judgment is ‘the mediate cognition of an object’ (A68/B93): insofar as judgment-constituents relate to objects, so the judgment does indirectly through them. So judgment and experience are also prima facie species of cognition.

Next, let me introduce ‘objective validity’ into this picture. A representation is objectively valid when it does or can relate to an object of experience. Kant glosses objective validity as real possibility.

To cognize an object, it is required that I be able to prove its possibility … . But I can think whatever I like, as long as I do not contradict myself, i.e., as long as my concept is a possible thought, even if I cannot give any assurance whether or not there is a corresponding object somewhere within the sum total of all possibilities. But in order to ascribe objective validity to such a concept (real possibility, for the first sort of possibility was merely logical) something more is required. (Bxxvin)

Both concepts and thoughts can be objectively valid.¹³ A concept is objectively valid if and only if it is really possible, i.e. it is possible for it to be instantiated by objects of experience.¹⁴ (In general, when I write that a concept is ‘really possible’, that is shorthand for ‘it is possible for the concept to be instantiated by objects of experience’.) For that to be so, it must be possible for the concept to be given objects that fall under it (in contrast to the mere logical possibility (consistency) of a concept). Kant also writes explicitly that the objective validity of a concept rests only on the conformity of the concept to possible intuitions (A289/B345).¹⁵

Kant connects his distinction between thought and cognition to the distinction between real and logical possibility. In the Bxxvi footnote, the objective validity of a concept is connected to its real possibility, which in turn is connected to cognition as contrasted with thinking. Constraints on thinking are merely logical; thoughts should not be contradictory.¹⁶ But the consistency of a thought is not sufficient to guarantee it a genuine representational relation to objects (of experience). Cognition requires more: real possibility. A thought is really possible just when it conforms to the conditions under which objects can be given to us, and the conditions under which they can be thought.¹⁷ A limiting case of conformity to these conditions is where the representation under consideration itself forms such a condition, for example, it is a principle of the understanding.

One might object: the beginning of the Bxxvi passage suggests that cognition requires something stronger: a proof of real possibility. However, in the passage Kant continues that if we want to ascribe objective validity to a concept, we need to prove its real possibility. This may seem right precisely because, if a concept is objectively valid just when it is really possible, in order to show that the concept is objectively valid – in the service of ascribing objective validity to it – I would need to show that it is really possible. I thus take cognition to be a species of thought, objectively valid thought, where a thought is objectively valid if and only if it is really possible.^18,19

I am tempted to think of the difference between cognition and mere thought as one between being about objects and not being about objects at all. More carefully, cognitions are about objects of experience, mere thoughts are not. One might argue that mere thoughts are nevertheless about some other kind of object, say, noumena. Alternatively, one might take Kant to be rethinking our very notion of an object, broadly understood, such that the notion of an object that we cannot experience or know is defective in some sense, and such that mere thoughts are not about any kind of object at all.²⁰ What follows here should be compatible with either kind of interpretation: for all that I attempt to account for mere thoughts drawing on the resources of cognition, that doesn't on the face of it rule out those thoughts being about a special kind of object or property. Moreover, given that we cannot cognize, experience or know anything other than objects of experience, it is unclear what role such otherwise inaccessible noumenal objects could play in an account of our thinking and understanding of mere thoughts. As such, it might be better to account for mere thoughts without essential reference to the noumenal realm, regardless of what one makes of such a realm.

We can now delineate the kinds of mere thought on which I focus. There are several different varieties of mere thought, corresponding to different ways in which a thought may lack objective validity.

First, some thought constituents lack objective validity. So at least some thoughts containing them are not objectively valid either.²¹ I consider three important cases of objectively invalid thought constituents: (1) Unschematized categories. (2) Transcendental ideas: concepts such as God, soul, and world, and certain predicates applied to them, such as simplicity (of the soul). These apply beyond the bounds of, and are not applicable to, possible experience.²² (3) Kantian philosophical concepts: to understand Kant's philosophy we need certain concepts, such as noumenon, which pertain to that which lies beyond the bounds of possible experience.²³

Second, a thought may be composed of objectively valid constituents, but fail to agree with conditions of cognition in their particular combination. For example, take the principle: ‘All alterations occur in accordance with the law of the connection of cause and effect’ (B232). For Kant, this is a condition under which we can have cognition of objects. A thought that was incompatible with this principle would fail to be objectively valid. For example: the tomato ripened without any cause. The constituents – tomato, ripening, cause – are individually objectively valid. We can prove that the empirical concepts are by demonstrating actual instances – e.g. tomatoes; and that the pure concept, causation, is, via the Transcendental Deduction in general, and the Second Analogy in particular. However, in the combination proposed, the thought as a whole is not objectively valid, and so is not a cognition; an uncaused alteration is not really possible.²⁴

There are further putative cases of objectively invalid representations that I won't consider here, such as invented concepts (A222/B269), or merely subjectively valid judgments.²⁵ As noted earlier, the topic is vast. I have chosen these cases to focus on because they play an important role in Kant's philosophy and, as I hope we shall see, they highlight some interesting lessons about mere thought.

3. Unschematized categories and the form of a concept

Even after abstraction from every sensible condition, significance, but only a logical significance … is left to the pure concepts of the understanding. (B186)

Although there are systematic reasons to deny that mere thoughts are nonsensical, Bennett and Strawson disagreed. They took Kant to be committed to a kind of verificationism, according to which objective validity is a necessary condition for intelligible thought. By briefly reviewing why they were led to think this, and how one might respond – especially by reference to Kant's remarks about unschematized categories – we will uncover our first principle of mere thought: we can derive certain concepts from form as well as content.

Towards the end of the Transcendental Analytic, Kant connects the objective validity of a concept to whether it ‘signifies anything’ or ‘has sense’.

For every concept there is requisite, first, the logical form of a concept (of thinking) in general, and then, second, the possibility of giving it an object to which it is to be related. Without this latter it has no sense [Sinn], and is entirely empty of content [Inhalt], even though it may still contain the logical function for making a concept out of whatever sort of data there are. (A239/B298, my emphasis)

In this passage, we can read ‘content’ as referring to the matter – as opposed to the form – of a representation. Kant contrasts the form of a concept with its content. Compare: in his introduction to the table of judgments, Kant also contrasts form with content.

If we abstract from all content [Inhalte] of a judgment in general, and attend only to the mere form of the understanding in it … (A70/B95)

Kant appears to claim in (A239/B298) that a concept without any possible relation to an object (of experience) has no content and no sense. This seems to imply that a concept has sense – whatever that means – insofar as it is objectively valid. As well as putting the point in terms of sense [Sinn] and content [Inhalt], Kant frequently makes a similar claim in terms of ‘Bedeutung’, usually translated as ‘significance’. For example,

[T]he issue is … whether it relates to an object and therefore signifies [bedeute] anything. (B302-4, note)

One can understand why, in light of such passages, Strawson and Bennett concluded that, for Kant, a lack of objective validity constitutes a lack of intelligibility.

Every sentence containing “noumenon” is unintelligible … to know what a sentence means I must know something of what it would be like to have evidence of its truth. (Bennett 1966, 24)

If we wish to use a concept in a certain way, but are unable to specify the kind of experience-situation to which the concept, used in that way, would apply, then we are not really envisaging any legitimate use of that concept at all. In so using it, we shall not merely be saying what we do not know; we shall not really know what we are saying. (Strawson 1966, 16, emphasis added)

Strawson calls this the ‘Principle of Significance’. According to this principle, inapplicability to experience does not merely indicate illegitimate use of a concept, but unintelligibility.

The short repost here is to appeal to a distinction between two different things: something like the meaningfulness or intelligibility of a representation versus its relation to an object. Watkins (2002, 203), for example, distinguishes between two kinds of meaning: ‘meaning_ref’ – ‘reference to a determinate object’ – and ‘meaning_prop’ – ‘meaning in its more standard sense of representing a property’. This distinction allows for a representation to have meaning_prop without meaning­_ref. Similarly, Bird (1982, 75) distinguishes between representations that have sense and reference, and those that have sense but lack reference. This is an important distinction however one presents it. But it doesn't yet tell us anything positive about how and why representations can be intelligible absent objective validity, nor how the two sides of the distinction relate. My aim here is to show that, in at least some central cases, one can account for mere thought in terms of the resources of objectively valid representations.

An important first step comes from considering some of Kant's remarks in the Schematism. Kant takes his Transcendental Deduction to have shown that the categories apply to appearances (B161); in the Schematism Kant turns to the question how and when they so apply. A schema provides a restriction of the application of the categories to objects given in sensible intuition.²⁶ Since time is the a priori form of all intuitions, this amounts to a temporal condition of the application of the categories.²⁷ For example, the schema of the category of substance is ‘the persistence of the real in time’ (A144/B183). Kant does not use the terms ‘schematized category’ and ‘unschematized category’, but they have become well-used in the secondary literature to refer to categories plus their schema for application to (sensibly given) objects of experience, and categories minus their schema respectively. Kant discusses what the significance of an unschematized category, with no application to sensible intuition, would be.

Even after abstraction from every sensible condition, significance, but only a logical significance [Bedeutung] of the mere unity of representations, is left to the pure concepts of the understanding, but no object and thus no significance [Bedeutung] is given to them that could yield a concept of the object. Thus, e.g., if one leaves out the sensible determination of persistence, substance would signify [bedeuten] nothing more than a something that can be thought as a subject (without being a predicate of something else). Now out of this representation I can make nothing, as it shows me nothing at all about what determinations the thing that is to count as such a first subject is to have. Without schemata, therefore, the categories are only functions of the understanding for concepts, but do not represent any object. (B186-7)²⁸

Despite denying unschematized categories objective validity, in the same breath Kant specifies for these concepts a significance, albeit a merely logical significance.²⁹ Kant takes at least some concepts to be significant even though they are not objectively valid.³⁰ Whether ‘significance’ means something like ‘meaningful’, ‘intelligible’, or ‘important’, that certainly seems to imply that these concepts are at least not nonsensical or unintelligible.

He also here explains why unschematized categories lack objective validity. They do not specify how they would apply to objects given to us in intuition, and hence they are not – as they stand – applicable to objects. It may seem strange to say that the concept of something that can be thought of only as a subject doesn't apply to objects. One might think that unschematized categories are simply more general versions of the categories such that, if anything falls under the concept substance, it also falls under the more general concept. Compare: if something is a tiger, it is a mammal. However, this is the wrong way to think about the difference that sensible conditions make to the categories.

If we leave aside a restricting condition [the schema], it may seem as if we amplify the previously limited concept; thus the categories in their pure significance, without any conditions of sensibility, should hold for things in general … In fact, even after abstraction from every sensible condition … only a logical significance … is left … but no object. (A146-7/B186)

Sensible conditions do not merely restrict the extension of a concept to a smaller sub-extension; they add content that allows the concept to be sufficiently determinate to apply to objects of experience at all, and hence confer objective validity.³¹

Schematization does not just add further determinations to the pure categories, simply making them more specific, but rather transforms the pure logical content … 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. (Lau 2015, 451)

The following picture thus emerges. An objectively valid concept has two elements: (1) ‘relation to an object’, i.e. determinate application conditions to objects of experience, and (2) ‘the logical form of a concept … the logical function for making a concept out of whatever sort of data there are’ (A239/B298). Something about unschematized categories seems to allow that (2) is sufficient for intelligibility, despite Kant's further remarks that, ordinarily, a lack of (1) makes for a lack of sense.

In the case of empirical concepts, relation to an object plays an essential role, for, according to Kant, such concepts ‘arise from the senses through comparison of objects of experience and attain through the understanding merely the form of universality’ (9:92; Kant 1992). So, for example, the concept tree has a content abstracted from experience of trees (9:94-5; Kant 1992) and has generality as its form. If all empirical concepts have this same form – generality or universality – and nothing further to distinguish them than their empirical content, then it does seem that very little is left over once that content is removed. Perhaps, after all, Bennett and Strawson are right about empirical concepts.

However, pure concepts are different. Their content is by definition not dependent on empirical experience (A20/B34). One can plausibly understand the transcendental content of the categories in terms of an application of the logical functions of judgment to the pure forms of sensibility.

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 understanding. The same understanding, therefore, and indeed by means of the very same actions through which it brings the logical form of a judgment into concepts by means of the analytical unity, also brings a transcendental content into its representations. (A79/B104-5)

The logical functions of judgment are functions of unity – ways of combining representations into thoughts or judgments with various associated logical forms. For example, the logical form of a categorical judgment is S is P (subject-predicate). These functions of unity, when applied to synthesise intuitions in the form of time, gain additional content and are thereby transformed into the categories. This content is transcendental, rather than empirical, because it arises from conditions of possible experience – the forms of sensibility – and not from empirical experience. For example, the categorical logical function is transformed into the category of substance: subject and predicate are transformed into substance and accident (A80/B106). One can think of the unschematized categories as these concepts abstracted from that added temporal content: for example, the concept of substance becomes that of ‘a something that can be thought as a subject’. The unschematized categories are therefore extremely close to the logical forms of judgment: where the latter provides a form of judgment, we might think of the former as the concept of a constituent of that form, e.g. the concept of a subject.^32,33

So, unlike empirical concepts, different pure concepts can remain distinct even when determinate application conditions to objects of experience are taken away, because the ‘form’ element of them is more than mere generality: their distinctive meanings are in part determined by different logical forms. The schematized categories are objectively valid because they are enriched with conditions of application to objects in (the form of) time.³⁴ The unschematized categories lack this additional ‘transcendental content’, but still have a distinctive ‘logical’ meaning, deriving from form not content.³⁵

In light of this account of the unschematized categories, we can state our first distinctive Kantian principle pertaining to mere thought. In some cases (pure concepts), conceptual form can distinguish intelligible concepts in the absence of any content, empirical or transcendental.

Table

[F]	Pure concepts are distinguishable by and intelligible in light of form without content.

4. Transcendental ideas

A concept made up of notions [pure concepts], which goes beyond the possibility of experience, is an idea. (A320/B377).

There are standardly thought to be three transcendental ideas: soul, world, and God. However, Willaschek (2018) argues that there are nine, four of which characterise the soul (the soul as substance, simple, unity, spiritual); four of which characterise the world (the world as containing complete composition, complete division, complete origin(s), complete dependence); and a single idea of God as ens realissimum (Willaschek 2018, 169). I do not have space to properly assess his arguments here, but in any case, even if soul and world are not Kant's transcendental ideas, these concepts do appear as constituents of (at least some of) the concepts that Willaschek claims are Kant's transcendental ideas, e.g. the simplicity of the soul (2018, 193), the complete series of spatial regions of the world (2018, 205). If we are to account for the intelligibility of Willaschek's transcendental ideas, we need to account for that of soul and world as well. Regardless of how we count transcendental ideas, there is clearly a class of intelligible concepts that are not objectively valid – including soul and world – to be accounted for. In what follows, then, I take it to be crucial to give an account of the standard three – soul, world, God – even if this is only part of the story. I base my account on these three core ideas of the unconditioned, then extend it to Willaschek's nine ideas.³⁶

Kant takes the origin of transcendental ideas to lie in relational functions of judgment, and the different forms of syllogism associated with each such function.

The form of judgments (transformed into a concept of the synthesis of intuitions) brought forth categories that direct all use of the understanding in experience. In the same way, we can expect that the form of syllogisms, if applied to the synthetic unity of intuitions under the authority of the categories, will contain the origin of special concepts a priori that we may call pure concepts of reason or transcendental ideas. (A321/B378)

In the Transcendental Analytic, we learn that the functions of judgment, when applied to intuitions, yield categories (A79/B104-5). Similarly, the form of a syllogism applied to cognitions – ‘the synthetic unity of intuitions under the authority of the categories’ – yields transcendental ideas.

These transcendental ideas are ideas of the ultimate unconditioned source of an ascending chain of syllogistic reasoning (prosyllogism). For Kant, reason is the faculty of logical reasoning. In its descending function it derives conclusions from premises; in its ascending function it seeks ultimate explanations, i.e. it seeks the premises from which our knowledge could follow as conclusions.

The very same action of reason leads to a ratiocinatio prosyllogistica, which is a series of inferences, that can be continued to an indeterminate extent either on the side of the conditions … or on the side of the conditioned. (A331/B387-8).³⁷

Corresponding to the three relations in a judgment, there are three forms of syllogism, each with a different relation in the major premise, corresponding in turn to three (kinds of) concepts of reason – ideas pertaining to the unconditioned sources of these prosyllogisms.

Kant leads us carefully from how a syllogism works, to the unconditioned. First, ‘in the conclusion of a syllogism we restrict a predicate to a certain object, after we have thought it in the major premise in its whole domain under a certain condition.’ (A322/B378-9) For example, we conclude that Caius is mortal, having thought the predicate, mortal, under the condition human, in addition to the premise that Caius is human. Kant then continues:

This complete magnitude of the domain, in relation to such a condition, is called universality (universalitas). In the synthesis of intuition this corresponds to allness (universitas), or the totality of conditions. So the transcendental concept of reason is none other than that of the totality of conditions to a given conditioned thing. Now since the unconditioned alone makes possible the totality of conditions, and conversely the totality of conditions is always itself unconditioned, a pure concept of reason in general can be explained through the concept of the unconditioned, insofar as it contains a ground of synthesis for what is conditioned. (A321-322/B378-379)

In the ascending function of reason, one seeks conditions for conditions. We can then take the totality of these conditions for some conditioned. But the totality of conditions cannot itself be conditioned, otherwise there would be some further condition X for the totality T. Since the conditioned (C) is conditional upon T, if T is in turn conditional on X, then C would also be partially conditional upon X, meaning that T was not the totality of conditions for C after all, as it omits X. The totality itself is unconditioned.

Kant also writes that the unconditioned ‘makes possible’ the totality of conditions. Here is it helpful to first consider the prosyllogisms for each relation of judgment.

There will be as many [kinds of] concepts of reason as there are species of relation represented by the understanding by means of the categories; and so we must seek an unconditioned, first, for the categorical synthesis in a subject, second, for the hypothetical synthesis of the members of a series, and third, for the disjunctive synthesis of the parts in a system. (A323/B379)³⁸

An idea (or ideas) of the unconditioned arises for each of the three kinds of relation in a judgment: categorical, hypothetical, and disjunctive.

In brief, take the relation of subject to predicate: A is B. And take a categorical syllogism: A is B, B is C, therefore A is C. Note: the middle term, B, occurs in both subject and predicate place. Such syllogisms can be chained together. Going downwards, we can link to A is C, C is D, therefore A is D. Upwards, we would look for syllogisms ending with A is B or B is C. The idea of the unconditioned here is the idea of something at the very top of such a chain, a subject that cannot occur as a predicate (unlike B). Similarly, take the relation of ground to consequence, and a hypothetical syllogism: If P then Q, if Q then R, therefore if P then R. Again, we can chain such syllogisms together. The idea of the unconditioned in this case is the idea of something at the very top of such a chain, a ground that is not also a consequence of something else (unlike Q).

Finally, take the relation of disjunction to be an exclusive and exhaustive division of some class (A73-4/B99). The idea of God as the most real being is supposed to arise from this (see Longuenesse 1998, 155). Kant begins with the principle of thoroughgoing determination.

Every thing, … stands under the principle of thoroughgoing determination; according to which, among all possible predicates of things, insofar as they are compared with their opposites, one must apply to it. (A571-2/B599-600)

For every pair of contradictorily opposed predicates, any individual must fall under one or other predicate; individuals must be determinate, one way or the other, with respect to all possible predicates. So long as everything is determinate in this way, we can think of any predicate or concept as drawing a line between the things falling under the predicate or concept and everything that doesn't. This kind of division is the function of the disjunctive form of judgment, which in turn grounds the principle of thoroughgoing determination (Longuenesse 2005, 218). We can think of any determinate individual in terms of the determination of a long disjunction of all possible properties: it is F or not-F, G or not-G, and so on. Kant argues that our concepts of positive properties are fundamental, and that concepts of negative properties are derived from the positive (A575/B603), so our concept of any individual presupposes the idea of all the positive properties. Hence the unconditioned, ultimate ground of our concepts of individuals is the idea of all the properties with respect to which that individual must be determinate. This idea of the sum total of all possible predicates goes beyond the bounds of possible experience.³⁹ Finally, a mere aggregate of all possible properties isn't truly unconditioned, for it depends upon each element of the aggregate. Hence, the unconditioned is an individual ground for all those possible properties, not the aggregate of properties themselves (A579/B607).

Altogether, we have ‘a subject that is no longer predicate, … a presupposition that presupposes nothing further, and … an aggregate of members of a division such that nothing further is required for it to complete the division of a concept’ (A323/B379-380). Consider these unconditioned termini of prosyllogisms. All the conditions in the prosyllogistic chain depend upon this unconditioned: they are conditional upon it. Hence, we can see why Kant says that ‘the unconditioned alone makes possible the totality of conditions’, as well as that the totality of conditions itself is unconditioned.⁴⁰

Let us return to our crucial question: how does such an account guarantee the intelligibility of ideas derived in this way? We saw that ‘a pure concept of reason in general can be explained through the concept of the unconditioned’ (A322/B379). We have an account of how transcendental ideas are derived – at least to some extent – from relational forms of judgment. We have already seen how in general intelligible and distinctive concepts may arise from mere form ([F]). We now require a further principle:

Table

[U]	The idea of an unconditioned derived from a relational form of judgment is intelligible.

The thought here is: if we can understand a chain of judgments of a relation, then we can understand the idea of the unconditioned of such a chain. The antecedent is not at issue: it is assumed that we can understand judgments instantiating the different forms of relation, and that we can understand syllogisms of associated kinds. But does our understanding of parts of such a chain allow for understanding of its terminus? For example, one might conjecture that our understanding of the concept event is tied up with an understanding of events as causal relata – as being both causes and caused – in which case, although we could perfectly well understand both causal statements and the idea of a causal chain of events, the idea of an ‘unconditioned’ event that was a cause but not an effect would be unintelligible.

To address this, let us return to the totality of conditions. It seems reasonable that if I can grasp the concept of a condition, and I can grasp the concept of totality (as I must, for totality is a category), then I should also be able to grasp the concept of a totality of conditions. (Note: just because I might understand the idea of such a totality, it does not follow that I can thereby cognize such totalities: we might indeed need to be able to understand the idea of a totality of conditions in order to learn that such totalities are not cognizable.) But if I truly grasp the concept totality of conditions, then I will be able to understand that this is unconditioned (as per the argument earlier). We can apply this to each of the three different kinds of prosyllogism, differentiated by different kinds of condition (e.g. subject to predicate), and thereby secure the intelligibility of the idea of an unconditioned in each case.

This introduces something like a principle of composition: If two concepts are each graspable and hence intelligible, then a concept composed from them is graspable and hence intelligible.

Table

[C]	If concepts F and G are intelligible, then a concept H composed of F and G is also intelligible.

I will have more to say about compositionality below.

This line of thought draws crucially on the concept of totality. If we also want to account for Willaschek's list of nine ideas, then we need to draw on the resources of further categorial concepts. Willaschek (2018, 172) highlights that, for Kant, ‘reason “free[s]” a concept of the understanding (a category) from its restriction to possible experience (A409/B435)’ and that ‘transcendental ideas are thus categories that are “extended to the unconditioned” (A409/B436)’. This coheres with Kant's statement that ‘a concept made up of [pure concepts], which goes beyond the possibility of experience, is an idea’ (A320/B377). How are categorial concepts thus transformed into concepts of the unconditioned? I have no space for a detailed account, but offer a promissory sketch.

Consider first the psychological ideas: the soul as substance/simple/unity/spiritual. At the beginning of the Paralogisms, Kant presents ‘the topics of the rational doctrine of the soul, from which everything else that it may contain has to be derived’ (A344/B402):

1. The soul is substance

2. In its quality, simple.

3. In the different times in which it exists, numerically identical i.e. unity (not plurality).

4. In relation to possible objects in space.

These source materials are then supposed to generate the psychological ideas.

From these elements, at least through composition, spring all the concepts of the pure doctrine of the soul … This substance, merely as an object of inner sense, gives us the concept of immateriality; as simple substance, it gives us that of incorruptibility; its identity, as an intellectual substance, gives us personality; all these points together give us spirituality … (A345/B403, emphasis added).

Three of the key terms correspond straightforwardly to categories: substance (category of relation), unity (quantity), possibility (modality). One would then expect a category of quality as a fourth, however, the categories of quality are reality, negation, and limitation: they don't include simplicity. However, the categories of quality relate, in their application to intuition, to intensive magnitude: ‘that magnitude which can only be apprehended as a unity’ (A168/B210). What can only be apprehended as a unity does not, to that extent, have parts: ‘the real in appearance always has a magnitude [which] does not proceed from the parts to the whole’ (A168/B210). That which does not have parts is simple. Hence, Kant appears to take the categories of quality to involve a representation of simplicity.

We can take the psychological ideas to be a ‘composition’ of the idea of the soul – the unconditioned of the categorical prosyllogism – and each of these categorial concepts: the concept of the soul as substance, soul as simple, and so on. The intelligibility of these ideas derives from a combination of other intelligible representations. We know the categories are intelligible. I have argued that (and how) concepts of the unconditioned are intelligible. Combinations of intelligible concepts are themselves intelligible (assuming [C]). Therefore, the psychological ideas are intelligible. They are not, however, objectively valid, for they purport to represent the unconditioned: all objects of experience are conditioned so, by definition, a concept of the unconditioned cannot apply to an object of experience. What we have are ‘concept[s] made up of [pure concepts], which [go] beyond the possibility of experience’ (A320/B377).⁴¹

We can similarly understand the cosmological ideas in terms of different categories fleshing out the hypothetical relation up to the unconditioned. (1) The world as containing complete composition draws on the categories of quantity, which concern part-whole relations (extensive magnitudes, A162-6/B202-7). (2) One might expect that The world as containing complete division should also draw on mereological concepts of part and whole. However, as above, we can understand the categories of quality to concern simplicity. Indeed, the second antinomy, which concerns this idea, is stated in terms of ‘simple parts’ (A434-5/B462-3).⁴² (3) The world as containing complete origin(s) draws on the category of causation. (4) The world as containing complete dependence draws on a concept of conditional necessity, the modal category of necessity.⁴³

Again, we can take the four cosmological ideas to be composed from the idea of the world – the unconditioned of the hypothetical prosyllogism – and categorial concepts. The ideas are intelligible because they are composed from intelligible representations ([C]). But they are not objectively valid, because they purport to represent the unconditioned.

Finally, Willaschek (2018, 219) argues that the theological idea of God is not just the ens realissimum, the concept of a ground of all possibilities, which I derived from the disjunctive prosyllogism, but the concept of the ens realissimum as absolutely necessary. This case is trickier than the others, as this can't be understood straightforwardly as a combination of the idea of the ens realissimum with the category of necessity, for that category is quite clearly the concept of conditional, not absolute necessity.⁴⁴ However, it is plausible to understand Kant as taking the concept of a ground of all possibility just to be the concept of absolute necessity. If something is a ground of all possibility, then if it ceased to be, all possibility would be cancelled.⁴⁵ Hence, a ground of all possibility must be absolutely necessary. In short, once we derive the idea of an ens realissimum as a ground of all possibility, this is immediately the idea of an absolutely necessary being. But as Kant makes clear in his discussion of necessity in the Postulates, concepts of absolute modality cannot be cognized (A232/B285).

Willaschek (2018) gives an alternative derivation of the transcendental ideas, but our differences are perhaps not too deep, once one takes account of our differing purposes. Willaschek argues that the transcendental ideas are to be derived from ‘necessary inferences of reason’, not prosyllogisms. However, one can understand Willaschek's account as more concerned with why cognitive beings like us end up acquiring these ideas at all, and what we (should) do with them. Prima facie, there is no particular reason to think that we will engage in the right kinds of prosyllogisms and composition with categories that I have described. By contrast, Willaschek gives an account of why we are led into dialectical inferences, and how these inferences lead us to acquire the transcendental ideas. This may be an enlightening account of how we acquire and use transcendental ideas, but it does not seem to me to rule out my account of their very intelligibility.

5. Philosophical concepts

No one can think a negation determinately without grounding it on the opposed affirmation. (A575/B603)

The concepts thing in itself and noumenon cannot by definition apply to objects of experience. But we can derive them from concepts that can and do.

Kant defines two concepts of a noumenon: one positive, one negative.

If by a noumenon we understand a thing insofar as it is not an object of our sensible intuition, because we abstract from the manner of our intuition of it, then this is a noumenon in the negative sense. But if we understand by that an object of a non-sensible intuition, then we assume a special kind of intuition, namely intellectual intuition, which, however, is not our own, and the possibility of which we cannot understand, and this would be the noumenon in a positive sense. (B307)

We can understand both concepts in terms of negation of the concept of an object of sensible intuition – i.e. an object that can be given to us in experience. For the negative concept, we negate the whole, object of sensible intuition, to form the concept not an object of sensible intuition. In the positive case, we negate sensible intuition to form the concept object of non-sensible intuition. In both cases, the concept derives from the concept object of sensible intuition and familiar operations of negation, in the same way as we might understand the concept of darkness to be derived from that of light (see A575/B603).⁴⁶

This suggests another principle.

Table

[N]	If concept F is intelligible, then the negation of F is intelligible.

Kant comes close to endorsing this principle when he writes:

[N]o one can think a negation determinately without grounding it on the opposed affirmation. The person blind from birth cannot form the least representation of darkness, because he has no representation of light … All concepts of negations are thus derivative, and the realities contain the data, the material, so to speak, or the transcendental content, for the possibility and the thoroughgoing determination of all things. (A575/B603, emphasis added)

Kant endorses the principle: all concepts of negations are derived from representations of positive realities. This implies that the positive representation itself is intelligible, and that the negative representation derives what content it has from the positive one. From this we might extract the principle: if the negation of F is intelligible, then F is intelligible. This is the opposite direction to [N]. However, if one takes all negations to be derivative, then it does not seem unreasonable to also endorse the additional principle, that one can derive an intelligible concept via negation from any intelligible (positive) concept.

One might worry that there are some universally applicable concepts the negation of which should not count as intelligible. For example, the concept of self-identity is intelligible, but one might argue that the concept self-difference is not only empty, but logically incoherent, hence unintelligible. However, it seems clear to me that such concepts are intelligible; that explains how we can recognise that they couldn't be instantiated. In Leech (2017, 2015) I argue that contradictions are meaningful, and that Kant is committed to contradictions and contradictory concepts being meaningful. Moreover, if U is some universally applicable objectively valid concept, then it is intelligible. The concept not-U is derivable from U, and by the proposed principle, is thereby intelligible. It is no objection to this that not-U is not objectively valid, for we have already accepted that objectively invalid concepts may be intelligible. It remains to be shown that there is a special case of such a concept that is unintelligible, the argument for which does not rest either on the lack of objective validity or on the contradictoriness of the concept.

Bird has a different account, whereby the concept noumenon derives from that of appearance: if there is an appearance, there must be something that appears. I agree that this may give us reason to commit ourselves to noumena. However, in the passage Bird points us towards, Kant writes

the word “appearance” must already indicate a relation to something the immediate representation of which is, to be sure, sensible, but which in itself … must be something, i.e. an object independent of sensibility.

Now from this arises the concept of a noumenon. (A252).

What immediately precedes the introduction of the concept noumenon is not ‘the thing that appears’, but ‘an object independent of sensibility’. We can understand the concept noumenon as deriving from some negation of sensibility, as I propose, and not as the concept of that which appears.

The concept of a thing in itself can be understood in a similar way. In the Transcendental Aesthetic, to move from the idea of an object of our senses to that of a thing in general, Kant invites us to abstract ‘from the sensibility of our intuition, thus from that kind of representation that is peculiar to us’ (A35). He claims that ‘what may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us’ (A42, emphasis added). Hence, Bird writes that ‘the concept of [things in themselves] is necessarily implied as a correlate of a philosophical conception of a pure sensibility’ (Bird 2006, 553). Again, we can take the concept of an object of sensible intuition – of a receptive faculty of sensibility – and negate it. So the concept of a thing in itself is the concept of not being such an object: not an object of sensible intuition.

This account has the consequence of taking negative noumena and things in themselves to mean the same. Some passages indicate that this is correct, e.g. ‘the concept of a noumenon, i.e., of a thing that is not to be thought of as an object of the senses but rather as a thing in itself … ’ (A254/B310). One may prefer a finer-grained account, according to which one set of concepts (things in themselves/appearances) is defined with respect to object of sensible intuition, and the other (positive noumena/negative noumena/phenomena) with respect to object of experience, where the latter takes account of both sensible and conceptual conditions of experience. Either way, the present proposal can be applied: the objectively invalid concepts are derived via negation.

Finally, note that nothing I've said about the derivation of these concepts adjudicates on an interpretation of the distinction between appearances and things in themselves. Even if, for example, one has a two-object interpretation, taking there to be a distinct realm of noumenal objects, one still cannot give an account of the meaning of our concept noumenon in terms of experience of them. Hence, it would still be necessary to understand the content of such a concept in some other way; I suggest, in terms of negation.

6. Thoughts and compositionality

All judgments are … functions of unity among our representations, since instead of an immediate representation a higher one, which comprehends this and other representations under itself, is used for the cognition of the object. (A69/B94)

Thus far, I have focused on objectively invalid thought constituents, which in many cases render the thoughts in which they appear objectively invalid as well. I now turn to the thinkability of thoughts that contain only objectively valid constituents, but which fail to be objectively valid as a whole. Take, for example:

Table

(Tom)

The tomato ripened without being caused to do so.

This is incompatible with Kant's causal principle: ‘All alterations occur in accordance with the law of the connection of cause and effect’ (B232). This is a principle of the possibility of experience, hence, the thought as a whole cannot apply to objects of possible experience. Nevertheless, this is surely an intelligible thought.

One constituent of (Tom) is the category causation. We have already seen that, when not applied within the bounds of possible experience, a(n unschematized) category can retain a ‘logical’ significance. However, we should not account for the intelligibility of (Tom) in terms of this. The problem with (Tom) is supposed to be that as a whole it makes a causal claim that is incompatible with the causal principle. But if it were understood according to the merely logical significance of the unschematized category, then it would lack objective validity due to containing an objectively invalid constituent, not for contradicting the principle. What is required is a way to understand such thoughts that allows for retaining the objectively valid meaning of their constituents.

A natural option is to appeal to a principle of compositionality.

Table

[C*]	The meaning of a thought depends upon the meanings of its constituents.

Compositionality is usually discussed in relation to language, but the same principle seems to carry over to thoughts as well. Compositionality allows us to explain our ability to produce and understand a potentially infinite variety of novel thoughts (and sentences). This is not to say that those constituents must be able to acquire meaning, or remain meaningful, outside the context of a thought or sentence.⁴⁷ It is merely to claim that, once a constituent does have meaning, that meaning contributes in a systematic way to its use in new contexts. Applied to our present concern, we can take the content of a thought to be determined by its constituents and its mode of composition. In some cases those thought constituents are objectively valid, e.g. tomato and causation in (Tom). These constituents are then put together in a well-formed combination. Such a combination of thought constituents is intelligible only if thoughts with that general form can be intelligible. Compare, for example, the pupil cleaned the board without being asked to do so. The combination will also be objectively valid if as a whole it conforms to the conditions of cognition. (Tom) does not, so it is an intelligible thought, but not a cognition.

We can encompass the various claims made here in a general principle for thought.

Table

[T]	A thought T is intelligible if and only if (i) the constituents of T are intelligible, and (ii) thoughts of the form of T can be intelligible.

In the case of thoughts with objectively valid constituents, (i) involves a relation (empirical or transcendental) to possible experience, (ii) concerns the intelligibility of thoughts conforming to the forms of judgment, as Kant takes these to be exhaustive of the possible forms of judgment (A70/B95). I take it as given that all forms of judgment can have intelligible instances.

This proposal is reminiscent of a defence of verificationism that allows for whole sentences that are meaningful yet unverifiable, so long as they are composed from constituents and modes of composition that are appropriately sensitive to empirical evidence. For example, McDowell's weak verificationist holds that mastery of a language must ‘essentially involve speakers’ sensitivity to evidence’ (1998, 24). The strong verificationist, by contrast, holds that mastery of a language must be understood ‘as consisting solely in sensitivity to evidence’ (1998, 25). For weak verificationism, it is sufficient if each sentence-constituent and each mode of combination has an appropriate relation to evidence. For example, the word ‘tall’ is meaningful in virtue of possible evidence of tallness, and a combination of names and predicates into sentences of the form ‘N is F’ is meaningful in virtue of possible evidence for cases such as ‘Jane is tall’ (see McDowell 1998, 24–5).

Similarly, we might think that a capacity for thought is essentially rooted in experience. A huge part of our cognitive lives involves representations that are objectively valid: we live in, navigate, learn about, and think about the world, for which we need representations of the world. Nevertheless, just as the verificationist can allow that from a mastery of language based in sensitivity to evidence can grow meaningful yet unverifiable sentences, so the Kantian can allow that from a secure base of cognition based in objectively valid representations can grow intelligible yet objectively invalid thoughts.

McDowell claims that in giving a weak verificationist account of sentence-constituents and combinations, we can give an account of the meaning of even those sentences which are unverifiable.

The systematic nature of the theory would involve its consequently representing the understanding of other sentences … as consisting — as with all sentences — in knowledge of truth-conditions, even though there might be no possibility, with those other sentences, of such direct consideration of evidential prompting. (McDowell 1998, 25)

Support for this comes from the idea that mastery of a language should include the ability to understand novel sentences. If I have learned some vocabulary and grammar, that should allow me to understand new sentences conforming to the grammar, containing the vocabulary.

Opposition to this, it seems, would have to involve the idea that mastery of one sentence is a state independent of mastery of the next, as if sentences were always learned as disconnected units. But that idea, which leaves no room for the fact that a competent speaker can understand new sentences, is totally unacceptable. (McDowell 1998, 25)

Analogously, one might argue that we should be able to think and understand new thoughts, not completely anew each time, but based on prior understood constituents and combinations. Paraphrasing: opposition to this would have to involve the idea that understanding of one thought is a state independent of understanding of the next, as if thoughts were always grasped as disconnected units. But that idea, which leaves no room for the fact that a competent thinker can grasp new thoughts, is totally unacceptable.

This proposal might seem to stray too far from Kant. Indeed, ‘compositionality’ is a philosophical term more familiar from the twentieth century. However, I shall briefly sketch why I think something like this proposal is at least in the spirit of Kant's thinking about judgment and thought.

At the beginning of the Transcendental Logic, Kant sets out his view of judgment.

All judgments are … functions of unity among our representations, since instead of an immediate representation a higher one, which comprehends this and other representations under itself, is used for the cognition of the object, and many possible cognitions are thereby drawn together into one. (A69/B94)

Kant takes judgments to be ‘higher order’ representations, which represent objects mediately by unifying (‘drawing together’) other representations, some of which immediately relate to objects. Kant also calls judgment ‘the mediate cognition of an object’ (A68/B93): a judgment relates to objects mediately, in part by virtue of the relations of its constituents to objects. Now, this is far from a clear statement of compositionality. And of course Kant is here concerned with relation to an object, rather than mere intelligibility. Nevertheless, it is important that judgments unify other representations together, and that what the judgment is about depends at least in part on those other representations that are thus unified. I thus take my proposal in this section to be amenable to, if not directly extracted from, Kant's view.

7. Conclusion

In the preceding sections, I’ve isolated some key principles that allow us to make sense of how and why mere thoughts can be intelligible without being objectively valid, that is, without applying to objects of experience. The first principle, [F], highlights a general and distinctive, perhaps surprising, feature of Kant's view, namely, that form can give rise to intelligible and distinctive representations, independently of (transcendental or empirical) content. This is also evident in the following principle, [U]. The remaining principles – [C], [N], [C*], [T] – tell us how intelligible thoughts and representations can arise via various functions, such as negation and composition. In all cases, I have drawn on the resources already implicated in objectively valid cognition – categories, forms of judgment, and objectively valid concepts – and shown how they can be plausibly transformed into objectively invalid representations. We thus have the skeleton of an account of Kant's mere thoughts, i.e. an account of an important range of objectively invalid representations, and the mere thoughts that contain them.⁴⁸

Disclosure statement

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Notes

1 Unless specified otherwise, by ‘cognition’ I mean ‘theoretical cognition’ not ‘practical cognition’.

2 Mathematical cognition is objectively valid but does not straightforwardly represent objects of experience. Rather, mathematical ‘objects’ are constructed from the pure form of intuition. Nevertheless, mathematics is, for Kant, applicable to objects of experience. For example, geometrical truths discovered by inspection of a triangle constructed in pure intuition are applicable to triangular things in the world.

3 Here I state Kant's ultimate view, that objective theoretical cognitions represent objects of experience. If we say that a representation is objective insofar as it represents objects, then we can frame Kant as arguing that only our representations of objects of experience are objective. However, my focus here is on the consequences of Kant's view, rather than his route there. Thank you to an anonymous referee for raising this.

4 All references to the Critique of Pure Reason, Kant (1998), are given using A/B numbers. See bibliography for details of translation and edition.

5 This phrase appears throughout the B-Preface.

6 Some passages suggest that the very same transcendental ideas of the Critique of Pure Reason reappear in the practical postulates of the Critique of Practical Reason, e.g., ‘In order to extend a pure cognition practically there must be a purpose given a priori … and in this case that is the highest good. This, however, is not possible without presupposing three theoretical concepts (for which, because they are only pure rational concepts, no corresponding intuition can be found and consequently, by the theoretical path, no objective reality): namely, freedom, immortality, and God’ (5:134; Kant 1997a). Kant also claims that whilst freedom is not theoretically cognizable, it is amenable to practical cognition (see, e.g., 5:105; Kant 1997a). This all raises questions concerning the nature of practical cognition and its relations to theoretical cognition and thought. See e.g. Kain (2010).

7 For example, Kant takes the opposing statements of the Antinomies to be mere thoughts but either both false (for the Mathematical Antinomies, A503-4/B531-2) or both true (for the Dynamical Antinomies, A535-7/B563-5, A560/B588). As an anonymous referee also notes, this raises pressing questions about how mere thoughts can be true, given that they lack an object, in light of Kant's nominal definition of truth as agreement of a cognition with its object (A58/B82). This is a question that I cannot properly address here. Although, note that the nominal definition is given only for cognitions, potentially leaving scope for a different definition of truth for mere thoughts. See also Vanzo (2010) for a discussion of what a nominal definition of truth gives us.

8 See Allais (2015); Allison (2004); Bird (2006); Stang (2014) for recent interpretations.

9 ‘We can have cognition of no object as a thing in itself, but only insofar as it is an object of sensible intuition, i.e. as an appearance’ (Bxxvi); ‘how things in themselves may be … is entirely beyond our cognitive sphere’ (A190/B235).

10 E.g., ‘Space represents no property at all of any things in themselves nor any relation of them to each other’ (A26/B42). See also the examples in the previous note.

11 See Gomes and Stephenson (2016), Watkins and Willaschek (2017), for interpretations according to which actual intuition is required.

12 Stang distinguishes semantic and modal characterizations of cognition. I omit these details here.

13 Kant predicates objective validity of many kinds of representation, including intuitions (e.g. A40/B57), concepts (e.g. A111, A128, A255/B311, A289/B345, A361), cognitions (e.g. B137, A694/B722) and judgments (or the relation or synthesis in a judgment, e.g. B168, A157-8/B196-7, A202/B247). I focus here on concepts and cognitions, i.e., thoughts that are objectively valid. As an anonymous referee notes, there is a question whether ‘objective validity’ means exactly the same in each of these applications, which I will not be able to fully answer here. I propose an account of objective validity for each in terms of real possibility, but note that the conditions of real possibility for concepts and thoughts are slightly different.

14 See, e.g., Lau (2015, 449): ‘Only when there can possibly be real objects that fall under a particular concept does the concept have objective validity’ and Hanna (2001, 92–5). Hanna and Lau distinguish between objective validity for empirical and pure concepts.

15 See A34/B51, A35/B52, A57/B81, A89/B121-2, A93/B126, A125, B142.

16 Kant takes laws of logic to be normative (in some sense), hence, we should understand this to say that I ought not think contradictions, not that I cannot. See Leech (2015, 2017) and, contra, Tolley (2006).

17 See 29:821–2; Kant (1997b).

18 Kant sometimes seems to suggest that thinking is a kind of cognition: ‘Thinking is cognition through concepts’ (A69/B94); ‘Thinking is the action of relating given intuitions to an object’ (A247/B304). One way to account for these passages is that they emphasise points other than a contrast with cognizing. First, the connection to concepts is emphasised. Second, this seems to be a prelude to introducing mere thought, in cases where there is no intuition.

19 An anonymous referee notes that some scholars, such as Allison (2015), have characterised objective validity in terms of truth-aptness, i.e. ‘a capacity to be either true or false’ (Allison 2015, 366). See also Longuenesse (1998, 82). I agree that objectively valid thoughts are truth-apt, but, as noted earlier, it is plausible to read Kant as allowing objectively invalid thoughts to have a truth value. If this is so, then one cannot take truth-aptness to be distinctive of objective validity (see Vanzo 2012, 114). I do not have space to fully defend this here: at least, understanding objective validity in terms of real possibility rather than truth-aptness avoids having to resolve this matter for the time being.

20 See Gardner (1999, 37–39).

21 I say ‘at least some’, to allow for cases such as Obama is not God, where we use an objectively invalid concept (God) to make what appears to be a true, objective judgment.

22 See A642/B670ff.; 5:3–4; Kant (1997a).

23 See, e.g., A235-260/B294-315.

24 Hanna (2001) disagrees: ‘Not only true a priori propositions but also false a priori propositions have [“secondary objective validity”]—for example, the denial of the Second Analogy of Experience, “Some events do not have causes”.’ (95). However, I do not see how this can be so, given the link that Kant draws between objective validity and real possibility. It is clear that, for Kant, an event without a cause is not really possible, and could not be given in experience, hence a denial of the Second Analogy is not objectively valid.

25 See e.g. B142; 4:299 Kant (2004); Beck (1998); Longuenesse (1998); Sassen (2008); Vanzo (2012).

26 All concepts – empirical and pure – have schemata, but I focus here on pure concepts.

27 Space is the form of outer sense; time is the form of inner sense, in which all representations of outer sense are also represented. Hence time is the universal form of sensibility. See A34/B50, A138/B177.

28 Note the similarity between the points made here in this passage, using ‘Bedeutung’ and cognates, and (A239/B298) quoted earlier, using ‘Sinn’ and ‘Inhalt’. It seems to me that the points made are so similar as to show that the difference in terminology here is not deep. I do not have space in this paper for a detailed philological analysis of these terms in Kant, but I see no significant terminological problem in these key passages.

29 See Bird (1982, 76).

30 Lau (2015) argues that unschematized categories are indirectly objectively valid. But it seems clear to me that the passages just quoted support the view that Kant took unschematized categories to lack objective validity.

31 Watkins (2002) argues that schemata ‘add to rather than replace the meaning the categories had previously’ (201). I agree, but contend that adding content can transform the content, as described, from something not sufficiently determinate to apply to objects of experience, into something sufficiently determinate.

32 Thank you to Nick Currie for helpful discussion on this point.

33 Note: on this view, the table of categories (A80/B106) presents us with schematized categories. This may seem in tension with Kant's suggestion in the Schematism that schemata are distinct from categories: they are introduced as a ‘third thing’ in addition to appearances on the one hand, and categories on the other (A138/B177). Nevertheless, Kant takes the categories when stripped of their schemata to be objectively invalid, and distinct from those categories listed in the table of categories, e.g., the unschematized category is no longer substance but subject. I cannot resolve all of these issues here: I merely present what I take to be one plausible and well-supported way to interpret these thorny passages. Thank you to an anonymous referee for raising this issue.

34 Space is also important. At the end of the Analytic of Principles, Kant concludes that ‘in order to understand the possibility of things in accordance with the categories … we do not merely need intuitions, but always outer intuitions’ (B291). However, space is not given a role in the Schematism, so this remark may refer more to the conditions under which we’re able to apply categories objectively – cognizers must have outer intuitions – rather than to their transcendental content. Thank you to an anonymous referee for raising this issue.

35 Longuenesse (1998) discusses in detail Kant's understanding and use of matter and form. This is a relative distinction, depending on the level of comparison: ‘Objects are the matter for concepts, universality their form. Concepts are the matter for judgment, the combination of concepts by means of the copula “is” or the connective “if … then” or “either … or” their form. Judgments …  are the matter for syllogisms, the mode of inferring (consequentia) their form. Finally, combined and connected cognitions are the matter for the whole of cognition, system its form’ (149–150). In that sense, of course pure concepts can be considered as form, insofar as they contribute form to the matter of experience. However, my point here is that what is striking in the case of unschematized categories is that they seem to be abstracted away from any matter at all – whether empirical or transcendental content – and owe their meaning only to logical form.

36 An advantage of Willaschek's classification is that recognising more transcendental ideas helps us to make sense of Kant's apparent claims to be drawing on the same theoretical concepts of speculative reason in his practical philosophy. Those concepts include freedom and immortality, which are not the same concepts as world and soul. (5:3-4, 5:134-5).

37 See also Gardner (1999, 216–7).

38 Willaschek (2018, 182) alters the translation to ‘There will be as many kinds of pure concepts of reason [so vielerei reine Vernunftbegriffe] … ’ (emphasis added). This change turns on the meaning of ‘vielerei’. Willaschek remarks (183n23) that ‘“Vielerei” in German means “various, of many kinds”’. My consultation with native German speakers and various dictionaries suggests that it can mean either ‘many’ or ‘many kinds’. I tentatively include the change in square brackets.

39 ‘Thoroughgoing determination is … a concept that we can never exhibit in concreto in its totality.’ (A573/B601)

40 But see Willaschek (2018, 178–82).

41 I do not have space to explore how Kant transforms these concepts further into concepts of immateriality, incorruptibility, and so on. But I have at least laid some foundations.

42 ‘Every composite substance in the world consists of simple parts, and nothing exists anywhere except the simple or what is composed of simples’ vs. ‘No composite thing in the world consists of simple parts, and nowhere in it does there exist anything simple’ (A434-5/B462-3).

43 See A227-30/B279-82, e.g., ‘the proposition “No necessity in nature is blind, but is rather conditioned … necessity” … belongs to the principles of modality’ (A228/B280-1). See also Leech (forthcoming).

44 See (A232/B285).

45 See Stang (2016, 124).

46 See also Kant's ‘Table of Nothing’ (A290-2/B346-9), where Kant discusses various applications of negation. The ‘nothing’ to which a logically possible yet really possible concept applies is called a ‘thought-entity’, which lines up with my categorisation of such concepts as appearing in mere thoughts.

47 Compositionality is compatible with a version of Frege's context principle, and an interpretation of Kant as taking concepts to acquire meaning in the context of a judgment. See Szabó (2013).

48 My thanks go to John Callanan, Sacha Golob, Joe Saunders, Bob Stern, Mark Textor, an anonymous referee, and audiences in Oxford and Luxembourg for helpful discussion and feedback on various versions of this paper.