1 Introduction

At the heart of Kant’s Critique of Pure Reason are the categories: twelve a priori concepts the possession and applicability of which are necessary conditions of possible experience. One of the categories is a concept of necessity. Amongst the abundant work that Kant’s philosophy has generated, there has been little satisfactory explanation of the role that the concept of necessity, as Kant defines it, plays in possible experience. My aim here is to offer a reading of Kant that fills this lacuna: the category of necessity is required to make necessity as it features in the world of experience understandable: a concept that the understanding—our capacity for conceptual thought—can grasp and employ in cognition—experience and thought of an objective world.

My account here is intended to contribute to our understanding of Kant, but there is a further potential application. In giving an account of the role of a certain concept of necessity in Kant’s account of cognition, we thereby uncover more generally an account of the role that judgments of necessity—judgments employing this concept of necessity—might play. There is increasing interest in questions concerning the function of modal judgment. I thus conclude by briefly canvassing the potential for Kant’s view to make an original contribution to this debate.

I proceed as follows. First, I provide an outline of Kant’s modal categories, then articulate more clearly the key questions that his view raises. Then I move on to my account of the role of the category of necessity in Kant’s theory of experience, followed by an account of why Kant calls the principle of necessity a postulate. As a coda, I offer some remarks on the potential wider significance of Kant’s view for accounts of the function of necessity judgments.

2 Kant’s Modal Categories

In the Critique of Pure Reason (= CPR), Kant presents a table of twelve categories, the pure concepts of the understanding (A80/B106).¹ They are pure, meaning they are not derived from sense experience; they are concepts that we require, according to Kant, as a prerequisite for experience in the first place.

The categories belong to what Kant calls the understanding, our capacity for conceptual thought and judgment. He distinguishes this from sensibility, our capacity to be presented with or ‘given’ objects via our senses (to ‘intuit’ objects). In order to have genuinely objective conscious representations of objects we require both sensibility and understanding. We need to be able to be given objects, but we also need to be able to apply concepts to them in order to experience them as objects of a particular kind. As Kant famously put it, “Thoughts without content are empty, intuitions without concepts are blind” (CPR A51/B75). Kant argues that these two capacities each have prior representations that must be presupposed as conditions of the possibility of experience: objects must be presented to us in the forms of space and time, and objects must fall under (some of) the categories, such as substance and causation. The result is our familiar experience of objects with a size and shape, bearing properties, standing in causal and reciprocal relations.

Cognition, for Kant, is objective conscious representation, and requires input from both sensibility and understanding. We might say that cognition is the subsuming of intuitions under concepts. But that leaves open a number of options. The intuition subsumed may be empirical—as in empirical experience of an object given to us—or pure—as in mathematical cognition of an object constructed in pure intuition (e.g. a triangle).² The intuition may be actual or possible: the object of a cognition must at least be possibly given in intuition.³ An empirical concept might apply directly to an intuited object, because the concept has been acquired via experiences of objects of that kind, e.g. the concept tree. Other concepts—pure concepts—apply to intuitions insofar as they are required to combine intuitions in cognition. So, for example, causal connections are not given to us in experience, but they are present in the world we experience, insofar as the mind introduces this kind of connection into experience as a precondition of the possibility of cognition at all.

So far so familiar. Kant argues that the possession and applicability of the categories is a necessary condition of the possibility of a subject having objective experience. This is a general claim, applying to all categories, and so in particular to the three modal categories, possibility, actuality and necessity.⁴ However, this is difficult to understand when we look closer at Kant’s definition and discussion of the modal categories in The Postulates of Empirical Thinking in General.

The first nine categories—of quantity, quality, and relation—concern features that objects of experience must have, such as standing in causal relations. However, the Postulates are different. Kant claims of the modal categories that “as a determination of the object they do not augment the concept to which they are ascribed in the least, but rather express only the relation to the faculty of cognition” (CPR A219/B266). For Kant, in claiming that something is possible, actual or necessary, we are not “augment[ing] the concept” of that thing, we are not saying more about what that thing is like, or its relations to other objects, as we would, say, by claiming that something is red, or square, or that it was caused to be square by being squashed. Rather, we are making a different kind of claim, about how (the concept of) that object relates to our capacity for cognition. In each postulate, a relation to conditions of experience (formal, material, general) is referenced:

1. Whatever agrees with the formal conditions of experience (in accordance with intuition and concepts) is possible.

2. That which is connected with the material conditions of experience (of sensation) is actual.

3. That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.

CPR A218/B265–266; emphasis in original

The postulates make explicit reference not just to experience, but to the conditions under which experience is possible for beings like us.

Kant is not simply presenting an account of when something is possible, actual, and necessary. He is claiming that modal concepts with this content are categories; that the possession and applicability of concepts with this content are a necessary condition for the possibility of experience. But why should that be? Why should we need to have concepts that are sophisticated enough to make reference to our capacities for cognition in order to have any objective experience at all? In short, if this is the content of modal concepts, then why are the modal concepts categories? Elsewhere I answer this question for the principle of possibility (Leech forthcoming). In this paper, I explore an answer for the principle of necessity.

Such questions are pressing, but surprisingly underexplored. Many commentaries on the Critique barely discuss the Postulates at all. To give a few examples: In his detailed treatment of the Critique, Allison (2004) follows a chapter on the Analogies of Experience with a chapter on the Refutation of Idealism, entirely skipping over the (other) Postulates. His only interest in them here seems to be what they have to say about actuality (40, 286). Bennett has a little more to say, but is scathing, taking the Postulates to be a catalogue of errors (1966, 164–167). In Longuenesse the principles of quantity, quality and relation each get a chapter (1998, chs. 9, 10, 11), the Postulates do not. Similarly, in Guyer we see chapters spanning these principles, as well as the Refutation, but no significant treatment of the Postulates. His brief discussion of them (1987, 275–276) tellingly begins ‘The “Refutation of Idealism” is the only argument of major significance contained in the final section of the “Principles”, the “Postulates of Empirical Thought”’ (275).

More promisingly, there has been a recent surge of interest in Kant on modality. However, much of this work has largely focused on other aspects—such as Kant’s pre-critical thought about modality (e.g. Chignell 2009, 2012, 2014; Stang 2016; Watkins & Fisher 1998; Yong 2014), the development of Kant’s thought about modality from pre-critical to critical (Abaci 2019, Stang 2016), and Kant’s modal forms of judgment (e.g. Leech 2012). Work that does focus on the Postulates tends not to seek a transcendental argument for them, but explores other aspects, such as the range of different notions of modality (Stang 2011), and Kant’s remarks concerning the co-extension of possibility, actuality and necessity (Abaci 2016). There is one recent source that comes closest to my present aims—Kannisto (2017)—but I shall explain in due course how my view compares.

3 Questions

Why should we expect Kant to have an account of the role of a concept of necessity in the conditions of possible experience? Our primary evidence is circumstantial, but weighty.

First, and obviously, the concept appears in the table of categories (A80/B106). So it is a category. Kant’s conclusion to the Transcendental Deduction is that

all synthesis, through which even perception itself becomes possible, stands under the categories, and since experience is cognition through connected perceptions, the categories are conditions of the possibility of experience, and are thus also valid a priori of all objects of experience.

CPR B161

The category of necessity, like the others, must then have some role to play in synthesis and the possibility of experience. But what?

In the Analytic of Principles section of the Critique, Kant expands upon the conditions under which the categories apply to objects and defends synthetic a priori principles arising from those categories. For example, in the Second Analogy Kant argues that our concept of causation is implicated in the possibility of objective relations of temporal succession. There is a section where Kant discusses the modal categories—The Postulates of Empirical Thinking in General—and a part of that where Kant discusses the principle of necessity. So we might expect—given the general structure of the text—to find a fuller account of the application and role of the category of necessity there. Again, the presence of this section is circumstantial evidence, but evidence nonetheless, of there being an account of the role of necessity to be found in the Critique. In the following, I shall draw out the argument that I believe one can find there, exactly where one should expect to find it.⁵

Let us then clarify more keenly our questions. We have our first and basic question:

(Q1) Why is the concept of necessity a category?

The intent of this question is to uncover the role that the concept of necessity plays in the possibility of experience, as a category. This kind of question is plausibly answered throughout the Principles for each of the categories, for example, in the account of the role of the categories of relation in objective temporal relations (see, e.g. CPR, A177/B219). My intent is not to ask why we have the categories that we do in fact have rather than others. This would be to ask a question that Kant explicitly rejects.⁶ In the B-Deduction, Kant writes:

for the peculiarity of our understanding, that it is able to bring about the unity of apperception a priori only by means of the categories and only through precisely this kind and number of them, a further ground may be offered just as little as one can be offered for why we have precisely these and no other functions for judgment […].

CPR B145–146

Indeed, he makes a similar point in the Postulates, where he takes questions such as whether we could have other forms of understanding to “[belong] solely to reason, which goes beyond all possible empirical use of the understanding” (CPR A232/B285).⁷

We may then clarify our question to be:

(Q1*) What is the role of the principle of necessity in the possibility of experience?

In the Postulates, Kant introduces the principle of necessity.

That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.

CPR A218/B265–266; emphasis in original

Elsewhere in the Principles, Kant offers transcendental arguments for the synthetic a priori principles, which explain their role in the possibility of experience. So we can expand our question to another:

(Q2) What (if any) is Kant’s transcendental argument for the principle of necessity?

Finally, Kant takes pains to distinguish the modal categories, including necessity, from the others. The principles of modality are ‘subjectively synthetic’ not ‘objective-synthetic’ (A233–234/B286), which is connected to their being called ‘postulates’. So we have a third question:

(Q3) Why is the principle of necessity called a ‘postulate’?

In brief, I will argue that: (A1) The category of necessity is required to make necessity as it features in the world of experience understandable. (A2) There is an argument for the principle of necessity to the effect that in order for the concept of necessity inherent in the (other) principles to be understandable, that concept of necessity must be as defined in the principle of necessity. (A3) The principle of necessity is a postulate because the understandability of necessity is a condition of possible experience at one remove: it is a condition on conditions of experience.

4 First Step: An Understandable Kind of Necessity

The postulates concern real modality, whether there could be, are, or must be certain things, rather than logical modality, which concerns only the logical consistency or contradictoriness of the representations of things.⁸ The modal categories are each defined in terms of a relation to some conditions of experience; roughly, the concept of something must bear a certain relation (e.g. agreement) to certain conditions of experience (e.g. formal conditions) for it to have a real modal status (e.g. there could have been things of that kind).

According to the principle of possibility, something is possible just when (the concept of) it is compatible with the formal conditions of experience (the forms of sensibility and the principles arising from the categories). Let us call this kind of possibility ‘formal possibility’ (Stang 2011, 2016). One might expect necessity to be similarly defined, such that something is necessary just when it follows from the formal conditions of experience. Put in terms of compatibility:

It is formally necessary that p just in case it is incompatible with our forms of experience that not-p.

Stang 2011, 448

The principles that state the formal conditions of experience are formally necessary: insofar as they state what our forms of experience are, they are incompatible with their own negations.⁹ Furthermore, they are a priori: “we can cognize of things a priori only what we ourselves have put into them” (CPR Bxviii). Kant explains synthetic a priori knowledge in terms of the formal contribution our minds make to experience.

So, Kant has a concept of formal necessity, which is plausibly co-extensive with the a priori (Stang 2011, 448–451). However, in the principle of necessity Kant gives us something different:

That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.

CPR A218/B266; emphasis in original

There are three distinctive features of this principle. First, necessity is defined in terms of a connection with the actual. Necessity is not simply what is determined by conditions of experience, but what is determined by those conditions given what is actual. Second, the relevant conditions of experience are general rather than formal. The formal conditions of experience are also general; they do not concern particular things, but how things must in general be as regards their form. But in addition to conforming to formal conditions of experience, we can also only have experience if we are given objects. This condition is general—the claim is just that some objects or other must be given to us—but it is not formal. So in addition to formal conditions, the general conditions of experience include being given some matter of experience. Third, the principle allows for things to exist necessarily, not just for the necessity of a principle or proposition.

Why does Kant make these additions, instead of presenting a definition of formal necessity? Kant argues that we cannot cognize existence a priori, hence we cannot cognize necessary existence. So the only concept of necessity that allows for necessary existence, that could be used in cognition, is one of material necessity: a kind of conditional necessity.

As far as the third postulate is concerned, it pertains to material necessity in existence […] Now since no existence of objects of the senses can be cognized fully a priori, but always only comparatively a priori relative to another already given existence, but since nevertheless even then we can only arrive at an existence that must be contained somewhere in the nexus of experience of which the given perception is a part, the necessity of existence can thus never be cognized from concepts but rather always only from the connection with that which is perceived, in accordance with general laws of experience.

CPR A226–227/B279

For Kant, cognition is either analytic or synthetic. Existence is not a determining predicate, hence it cannot be analytically contained in the concept of something (CPR A598/B626). So we couldn’t cognize the existence of something a priori via conceptual analysis. Synthetic a priori cognition arises only from our knowledge of conditions of possible experience (CPR A156/B195). But these conditions are general, and do not pertain to particular things, or to particular kinds of things. So we could not cognize synthetically a priori the existence of a particular individual, or the existence of a particular kind of individual. Hence, we cannot cognize existence a priori. For Kant, all cognition of necessity is a priori (CPR B3). Hence, we cannot have any cognition of necessary existence. Recall, formal necessities are a priori, so this conclusion holds for formal necessity: we cannot cognize formally necessary existence. This should come as no surprise: the formal conditions of experience concern only the form of experience, not the matter, but cognition of things requires them to be given in the matter of experience. So there’s no way for the existence of something to be formally necessary.

What kind of cognition of necessary existence could we have? We might be able to cognize what must happen next, given what is actually the case and our knowledge of actual laws of nature. This could be comparatively a priori, because once you know the actual state of things, and the laws for how states change, then one can infer a priori what will happen next.¹⁰ This kind of cognition relies upon how things actually are, and actual laws of nature, accounting for Kant’s reference to “the actual” in the postulate (CPR A218/B266), as well as why he refers to general, not merely formal, conditions. This material kind of necessity is tied up with material conditions of experience as well as formal conditions, insofar as it involves what objects have actually been given to us, and their actual behaviour (according to empirical laws of nature).

Kant thus claims that necessary existence can only be cognized “from the connection with that which is perceived”, i.e. with actual experience, “in accordance with general laws of experience” CPR A227/B279. He then argues that the only things we could cognize as necessary in this sense would be (the existence of) states of objects as caused by prior states.

[T]here is no existence that could be cognized as necessary under the condition of other given appearances except the existence of effects from given causes in accordance with laws of causality. Thus it is not the existence of things (substances) but of their state of which alone we can cognize the necessity, and moreover only from other states, which are given in perception, in accordance with empirical laws of causality.

CPR A227/B279

Stang accordingly calls the necessity defined in the third postulate ‘empirical-causal necessity’:

It is empirically-causally necessary that p if and only if it is incompatible with actual natural laws, and the past history of the empirical world up until time t, that ¬p.

Stang 2016, 216; emphasis in original

If it is formally necessary that p then it is also empirically-causally necessary that p, but not vice versa.¹¹ Moreover, given that every event has a cause, every actual event is relatively necessary in this sense. Actuality and material (empirical-causal) necessity, to this extent, coincide.

At this point in Kant’s argument, then, we have isolated a concept of material necessity which can be cognised, namely, that defined by the principle of necessity.

5 Second Step: Laws and the Unity of Nature

Having explained why the principle of necessity concerns material necessity in connections between states, Kant introduces four “a priori laws of nature”.

Everything that happens is hypothetically necessary; that is a principle that subjects alteration in the world to a law, i.e., a rule of necessary existence, without which not even nature itself would obtain. Hence the proposition “Nothing happens through a mere accident” (in mundo non datur casus) is an a priori law of nature;[…].

CPR A228/B280

[…] likewise the proposition “No necessity in nature is blind, but is rather conditioned, consequently comprehensible [verständliche] necessity” (non datur fatum).

CPR A228/B280

The principle of continuity forbade any leap in the series of appearances (alterations) (in mundo non datur saltus) […].

CPR A228/B281

[…] but also any gap or cleft between two appearances in the sum of all empirical intuitions in space (non datur hiatus).

CPR A229/B281

Kant claims that these laws play a crucial role for the possibility of the unity of experience.

They are all united simply in this, that they do not permit anything in empirical synthesis that could violate or infringe the understanding and the continuous connection of all appearances, i.e., the unity of its concepts. For it is in this alone that the unity of experience, in which all perceptions must have their place, is possible.

CPR A229–230/B282

One way to begin to understand what Kant means here is to note a parallel between these laws and the principles (i.e., all the principles from the Analytic of Principles). We know that the principles taken together, arising as they do from the categories, constitute necessary conditions for possible experience. Is that all Kant means here: to reiterate the role of all of the principles? Watkins (2001) has noted that in the development of Kant’s thought, these four laws of nature correspond loosely to the principles. For example, in the Metaphysics Mrongovius lectures (1782–1783),

Kant also explicitly orders the four cosmological principles according to the headings of his table of judgments/categories. The principle of no leap is related to quality, no gap to quantity, no chance to relation, and no fate to modality.

Watkins 2001, 75

It is customary to understand the first two principles—the Axioms of Intuition and Anticipations of Perception—as concerning the synthesis of intuitions into determinate objects, and then to take the remaining principles—the Analogies and Postulates—to concern the relations of those objects. One can see how the laws of ‘no leap’ and ‘no gap’ might therefore line up approximately with the Axioms and Anticipations, and the other laws with the Analogies and Postulates.

Indeed, in the following key passage, Kant is quite explicit in linking the first two laws (in mundo non datur casus and non datur fatum) to the dynamical principles, i.e., the Analogies and Postulates.

Both are laws of the sort through which the play of alterations is subjected to a nature of things (as appearances), or, what is the same thing, to the unity of the understanding, in which alone they can belong to an experience, as the synthetic unity of appearances. Both of these belong to the dynamical principles. The first is properly a consequence of the principle of causality (under the analogies of experience). The second belongs to the principles of modality, which adds to the causal determination the concept of necessity, which, however, stands under a rule of understanding.

CPR, A228/B281; emphasis in original

There are several further important points to be gleaned here. First, we are told that these two laws play a role in subjecting ‘the play of alterations’ to the unity of the understanding. Recall: the concept of material necessity that Kant has just introduced was shown to concern states of things conditional upon other states, i.e., alterations of things. Second, this ‘subjection’ plays a transcendental role: these alterations must be subjected to the unity of the understanding in order to belong to experience. Third, Kant links the unity of the understanding to nature: ‘a nature of things’. It is worth noting that he also introduces the first law as, “without which not even nature itself would obtain” (CPR A228/B280) (more on which below.) Fourth, Kant indicates that the first law should be linked to the Analogies, in particular the principle of causality, and the second to the principle of necessity.

So, even if Kant does here reiterate to some extent the role of all the principles, he does seem to be carving out a particular role for the principle of necessity as well. It is the second law, non datur fatum, which is singled out as a principle of modality. What does this law decree? That necessity in nature is conditioned and therefore comprehensible. Or rather: in the German, Kant writes, “[…] bedingte, mithin verständliche Notwendigkeit” (CPR A228/B280). Guyer and Wood translate ‘verständliche’ as ‘comprehensible’, Kemp Smith as ‘intelligible’. But a more literal and, given the context, in my view, more perspicuous translation is ‘understandable’. This captures in English the obvious link between ‘verständliche’ and ‘Verstand’ that is present in German. If we read the law as saying that necessity in nature is conditioned and therefore understandable this emphasises that Kant is not here arguing that necessity in nature simply makes sense, but that it is amenable to the understanding, i.e., the understanding has a concept of this necessity that it is able to apply in cognition.

Kant contrasts a conditioned and therefore understandable necessity with ‘blind’ necessity. Thielke (2006) draws our attention to Kant’s discussions of blind necessity (“fate”, “destiny”), and blind accident (“chance”, “fortune”), in Kant’s work. Particularly helpful is Kant’s remark, from his Lectures on Metaphysics, Metaphysik L₁, that

Blind means when one oneself cannot see; but also that through which one cannot see. Blind necessity is thus that by means of which we can see nothing with the understanding.

Lectures on Metaphysics 28:199, trans. Ameriks & Naragon

By ‘blind’ Kant does not mean that blind necessity cannot itself see, but rather that it is something through which one cannot see, just as we might say that you can’t see round a blind bend, or over a blind summit, or down a blind alley. Kant’s comment that we cannot see anything by means of a concept of blind necessity thus fits nicely with the view I have extracted from the Postulates so far. It is a concept of a conditional, material, necessity that the understanding can use in cognition. A concept of unconditioned or absolute necessity is unsuitable for use by the understanding in cognition; metaphorically speaking, the understanding can ‘see’ no objects using such a concept. Hence, a concept of unconditioned necessity is ‘blind’. A concept of conditioned necessity, as defined in the Postulates, is ‘understandable’. It is worth briefly noting that Thielke (2006) draws a different conclusion regarding the precise account of what makes a concept ‘blind’, although he agrees that, for Kant, blind necessity “fails to be comprehensible by the understanding” (Thielke 2006, 451).¹²

The second law, then, states that all necessity in nature is conditioned and therefore the kind of necessity that can be cognised. We have already seen that the kind of necessity imputed in the principle of necessity is a kind of conditional necessity, and we have also seen Kant’s line of reasoning for why this is the kind of necessity that would be cognisable. In discussing these laws of nature, and in particular the second law, Kant has introduced the claim that this concept of necessity—and the law in which it is implicated—play a crucial role in the unity, and hence the possibility, of experience.

To clarify: formal necessity can be cognized insofar as we can have a priori cognition, e.g., mathematical cognition. But one couldn’t apply this concept of necessity to an object of experience, i.e. the occurrence of a state or event. Of course, necessary mathematical truths are applicable to possible experience because they are grounded in the formal conditions of experience, e.g., geometry is grounded in our pure intuition of space (A48/B65). To that extent, one could judge that given that there is a triangle, there must be something with internal angles which sum to 180°. But note: this is not simply the formal necessity of the latter existence, but the existence of it in connection with the actual, i.e., given the actual existence of a triangle. Formal necessity applies to the whole proposition or principle, but in application to an object of experience, it is conditional on what is actual.

6 Digression: Unity in the Transcendental Deduction

What, then, is the role of the concept of material necessity, and the law in which it is implicated? As already noted, all the categories and principles have some role to play in the unity of experience. The role of the categories in general in the unity of experience, which is also a necessary unity, is presented in more detail in the Transcendental Deduction. The connections between representations that form a whole cognition are not, argues Kant, something that is given in experience. So they must be an a priori contribution of the subject. Kant’s suggestion is that the ultimate source of the unity or combination in cognition is the unity of self-consciousness. This allows us to combine representations by applying higher-order representations, such as the forms of judgment or the categories. The source of unity is “in us”, as part of our capacity for judgment and experience. (See in particular A108; B130–131.)

One act of unity described in the Deduction is the unification of the manifold of intuition in the concept of an object: “An object, however, is that in the concept of which the manifold of a given intuition is united” (CPR B137; emphasis in original).¹³ Manifold appearances are unified in the concept of an object, in which they are necessarily connected. As well as unity in an object, there is also unity of experience as a whole. In the A-Deduction, Kant writes

There is only one experience, in which all perceptions are represented as in thoroughgoing and lawlike connection, just as there is only one space and time, in which all forms of appearance and all relation of being or non-being take place. If one speaks of different experiences, they are only so many perceptions insofar as they belong to one and the same universal experience. The thoroughgoing and synthetic unity of perceptions is precisely what constitutes the form of experience, and it is nothing other than the synthetic unity of the appearances in accordance with concepts.

CPR A110; emphasis in the original

In the B-Deduction he writes about nature:

Categories are concepts that prescribe laws a priori to appearances, thus to nature as the sum total of all appearances (natura materialiter spectata), and, since they are not derived from nature and do not follow it as their pattern (for otherwise they would be merely empirical), the question now arises how it is to be conceived that nature must follow them, i.e., how they can determine a priori the combination of the manifold of nature without deriving from the latter.

CPR B163

[…] everything that can ever reach empirical consciousness, i.e., all the appearances of nature, as far as their combination is concerned, stand under the categories, on which nature (considered merely as nature in general) depends, as the original ground of its necessary lawfulness (as natura formaliter spectata).

CPR B164–165

For Kant, the unity of an orderly whole of experience according to rules is what he means by ‘nature’:

without understanding there would not be any nature at all, i.e., synthetic unity of the manifold of appearances in accordance with rules.

CPR A126–127¹⁴

Nature understood materially is the sum total of appearances (what is given to us in intuition), and nature understood formally is the sum total of the rules that connect these appearances into one experience (cf. Prolegomena to Any Future Metaphysics 4:295, 4:318). Both aspects of nature constitute the unity of experience as a whole; a sum total of appearances connected in a law like way.

A crucial feature of cognition, experience and judgment, then, is unity, in an object, and of experience as a whole.¹⁵ What are the transcendental conditions of the unity of experience? What must be the case for it to be possible? Kant’s answer is that the unity of experience has its source in the transcendental unity of apperception, which functions via a priori rules of synthesis, i.e. the categories (CPR B143, A114). The same point is made time and time again, that “the order and regularity in the appearances, which we entitle nature, we ourselves introduce” (CPR A125). Objective unity is necessary in an important sense. It is for this reason, Kant argues, that unity must have an a priori source (A114). For if we were presented with the unity of nature in empirical experience, it could only be contingent unity. As already noted, Kant does not allow that we can gain knowledge of necessities via empirical experience.

Accordingly, Kant entitles the understanding the “legislation for nature”.¹⁶ We introduce a priori laws into the world of experience. As a priori laws, they have the special status of being conferred upon the world by the understanding, and not merely ‘borrowed from experience’ as a result of empirical methods.

Rules, so far as they are objective (and thus necessarily pertain to the cognition of objects) are called laws. Although we learn many laws through experience, these are only particular determinations of yet higher laws, the highest of which (under which all others stand) come from the understanding itself a priori, and are not borrowed from experience, but rather must provide the appearances with their lawfulness and by that very means make experience possible. The understanding is thus not merely a faculty for making rules through the comparison of the appearances; it is itself the legislation for nature, i.e., without understanding there would not be any nature at all, i.e., synthetic unity of the manifold of appearances in accordance with rules.

CPR A126–127

This interconnection according to a priori laws between different parts of experience is described in the postulate of necessity.

That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.

CPR B266; emphasis in original

The determination of actual things in connection with others in accordance with general conditions of experience is precisely the idea that has emerged in the preceding steps—a unified whole of experience where different parts are interconnected according to rules which have their source in a priori conditions of the possibility of experience. The very possibility of nature rests upon necessary connections amongst everything which happens in experience. Nature, the unity of experience as a whole, is an essential feature of our experience. So the postulate of necessity is a transcendental condition of experience.

It would seem, then, that we have an answer to our first two questions. Necessity plays a crucial role in the necessary unity of experience, and there is an argument for this that can be extracted from the Transcendental Deduction. However, such answers are premature. The necessary unity introduced in the Deduction has its source in the unity of self-consciousness. The passage quoted from A126–127 continues:

[…] the synthetic unity of the manifold of appearances in accordance with rules […] is possible only in the unity of apperception. The unity of apperception, however, is the transcendental ground of the necessary lawfulness of all appearances in an experience.

CPR A127

It is the unity of apperception, not the principle of necessity, that grounds the unity of experience. Moreover, our circumstantial evidence adduced earlier suggested that we should find an account of and argument for the principle of necessity in the Postulates, not 100 pages earlier in the Deduction.

So, our work is not yet done, although there is an important lesson to be learned from the Deduction, namely, that the categories—in service of the unity of apperception—introduce in general an interconnection and necessary unity according to a priori laws between different parts of experience, which resembles the kind of necessity described by the postulate of necessity. Our question thus now becomes: what does the principle of necessity add to the work already done in the Deduction?

7 Third Step: Understanding Necessity

The Deduction establishes a certain kind of necessary unity of experience, introduced by the application of the categories by the transcendental unity of apperception (or a story similar to that). One can think of the principles, explicated in the Analytic of Principles, as laying out in more detail what each category contributes to the structure of experience, and in what circumstances in a spatiotemporal world the category applies. E.g. causation contributes objective temporal direction, and applies in cases where one state determines another, say. In the passage where Kant introduces and discusses the four a priori laws of nature, it looks as though Kant is reprising this. But why? Why does he do this in the context of discussing the principle of necessity? What might he be adding here?

The particular claim made concerning the law that Kant tells us belongs to the principles of modality is that necessity in nature is conditioned and therefore understandable. Kant is adding here, not the necessity in the necessary unity of experience, but the understandability of that necessity. If we are to cognise this necessity, we need a concept for it, and that concept is provided as the category of necessity, as defined by the principle of necessity. Kant has already argued that this concept of necessity—material necessity—is the only relevant cognisable notion of necessity that applies to (the existence of) things. There is material necessity in experience, and to the extent that the understanding is able to grasp this necessity, it must be that kind of necessity that Kant has argued is the only cognisable kind. Why do we need to be able to grasp this kind of necessity? Well, it may be that the source of the necessary unity of experience is a pure necessity imputed by the transcendental unity of apperception, but this is transformed, in application to a spatiotemporal world, into the (material) necessity of laws of nature. Such a material necessity is not given in experience, but it is nevertheless present, so it must be the contribution of the mind. Hence, we must be in possession of such an a priori concept. We need a concept of necessity that can capture necessity in the world of experience, that is suitable for application in cognition (‘understandable’), and which, given that the relevant necessity is a condition of the possibility of experience, is pure. Without such a concept, there would be no way to account for the necessary unity of nature: a concept of the pure necessity of the transcendental unity of apperception would not be determinately applicable to the world of experience, and any empirical concept would be inadequate.

Hence, we need a category of necessity, as presented in the principle of necessity. One might put things thus: it is the transcendental unity of apperception that brings necessary unity to experience, but that is a pure kind of necessary unity that will take a different form when applied to our particular forms of intuition, space and time; it is then the principle of necessity that articulates the cognisable, understandable, concept of necessity that is to be found in experience. This is a concept of a necessary connection between actual things, and also thereby of the necessary existence or occurrence of one actual thing conditional on the existence or occurrence of another. Such a necessity thus concerns not only the formal conditions of experience (that there should be such connections), but also the material conditions of experience (that some actual things are given). The applicability of this concept of necessity does not imply that we are given necessary connections in experience, but rather that such necessary connections, and conditional necessary existence, become part of the world of experience in virtue of the contribution of the understanding to experience.

We can now make good sense of Kant’s discussion of the principle of necessity in the Postulates, stretching from A226/B279 to A232/B285. First, Kant lays out an argument for what a cognisable, ‘understandable’, concept of necessity must be like. It can’t be unconditioned, and it must be a priori. So we end up with material necessity as defined in the postulate (CPR A226–227/B279–280). Then, Kant applies this in the case of the four a priori laws of nature. These laws are conditions of experience, but in order to be so their necessity must be cognisable. They need to be necessary—and understandably so—in order to bring objective unity to ‘nature’. Hence, we need this concept of necessity as a condition of these laws, which themselves are conditions of experience (CPR A227–230/B280–282).

Kant then immediately moves on to discuss modal questions that are not understandable, that is, questions that ‘belong to reason’, thereby introducing a clear contrast with the modal concepts that can be cognized by the understanding, and those modal questions that are beyond possible experience and knowledge and hence belong to reason (CPR A230–232/B282–286). He begins the long passage by introducing some modal questions, stating quite clearly that they belong to the province of reason.

Whether the field of possibility is greater than the field that contains everything actual, and whether the latter is in turn greater than the set of that which is necessary, are proper questions, […] though they also fall under the jurisdiction of reason alone.

CPR A230/B282

Kant explains that this is because the questions concern, roughly, whether there could have been different appearances given to us, and whether they could have been combined differently. But the understanding is only qualified to synthesise what is actually given to us under its actual rules, not to speculate on the possibility of alternatives to what is given and to those rules.

Whether other perceptions than those which in general belong to our entire possible experience and therefore an entirely different field of matter can obtain cannot be decided by the understanding, which has to do only with the synthesis of that which is given.

CPR A231/B283

Having explained our limitations thus, Kant then reiterates that the modal concepts inherent in these kinds of modal questions are not concepts of the understanding, but belong “solely to reason”: “Hence we have had to satisfy ourselves here with a merely critical remark, but otherwise left the matter in obscurity pending further treatment later on” (CPR A232/B285). And indeed, 500 or so pages later, in the Ideal of Reason, Kant reprises his discussion of modality (see CPR A581–583/B609–611 and Leech 2017 for discussion).

Kannisto (2017) offers an alternative account of the argument and role of the postulate of necessity. He argues that the argument of the Second Analogy supports only the weak causal principle (necessarily, every event has some cause), and that in the Postulates Kant seeks to argue for the strong causal principle (the same cause will necessarily produce the same effect). Insofar as Kannisto makes a different claim concerning the aims and argument of the Postulates to mine, we disagree, although it is not clear that the disagreement is deep. I do not have space to engage in detail with all of his arguments, especially those concerning the aims and achievements of the Second Analogy, but let me note some key differences, and why one might think that my view at least has something to add to Kannisto’s.

First, Kannisto and I appear to be led by different remarks from the main necessity passage (CPR A226–230/B279–282): I have focused on the claim that necessity in nature is “conditioned, consequently understandable”; Kannisto has focused on the claim that the non datur fatum law is claimed to “[add] to the causal determination the concept of necessity” (CPR A228/B281). My approach to understanding the principle of necessity allows one to explain why Kant reviews all four a priori laws of nature, and by association all of the principles; they all concern necessary unity of some kind, and the principle provides a cognisable concept of necessity for us to grasp this. It also allows one to make sense of the contrast with non-cognisable modal questions that belong to reason. In comparison, Kannisto is able to make good sense only of one aspect of Kant’s discussion—the remarks he makes about one of those a priori laws, but not of these aspects of Kant’s wider discussion.

For all I have said, it may be that our views are perfectly compatible: one could perhaps take Kannisto’s view to be a detailed account of necessity in one of the four a priori laws of nature, where I then set this into a wider context. My one remaining reservation is the problem I posed earlier, which is that necessary unity is supposed to have been accounted for in the Transcendental Deduction, so that a plausible criterion for making sense of the Postulates is that we shouldn’t try to claim that they are doing the same work. If Kannisto is right that Kant intends the principle of necessity to add necessity to the causal connection—turning merely contingent causal connections between alterations into genuinely necessary ones—then this risks doing that double duty. This is why I prefer an interpretation according to which the principle of necessity allows us to understand this necessity, but does not strictly speaking add necessary unity to (this aspect of) experience. At least some of the evidence adduced by Kannisto for his interpretation can also be taken to support my alternative. For example, where Kant remarks that

Necessity therefore concerns only the relations of appearances in accordance with the dynamical law of causality, and the possibility grounded upon it of inferring a priori from some given existence (a cause) to another existence (the effect).

CPR A227–228/B280; my emphasis

Kannisto takes the ground of the possibility of our thus inferring that is mentioned to be the strong causal principle; the thought being that a necessary condition of inferring a priori B from A is that A necessitates B. This may be the case, but another necessary condition of our being able to carry out such an inference is simply possessing the requisite concepts, namely, that of the necessary connection between A and B. We need to be able to recognise, even if only implicitly, in the relevant sense, that B must follow A.

8 Necessity as a Postulate

Let us now consider our final question: Why is the principle of necessity called a ‘postulate’? Recall, Kant claims that “as a determination of the object [the modal categories] do not augment the concept to which they are ascribed in the least, but rather express only the relation to the faculty of cognition.” (CPR A219/B266). Kant reprises this point when he explains why his modal principles are called ‘postulates’. He connects this feature of the principles of modality to their being subjectively, rather than objectively, synthetic.

The principles of modality are not, however, objective-synthetic, since the predicates of possibility, actuality, and necessity do not in the least augment the concept of which they are asserted in such a way as to add something to the representation of the object. But since they are nevertheless always synthetic, they are so only subjectively, i.e., they add to the concept of a thing (the real), about which they do not otherwise say anything, the cognitive power whence it arises and has its seat.

CPR A233–234/B286

To be objectively synthetic, the modal concepts would have to “add something to the representation of the object” (A233/B286), which we have seen they do not. They do, however, relate the concept of the object to conditions of possible experience. More particularly, the concept of necessity relates the concept of the object to general conditions of experience.

Kant then relates this to his understanding of a postulate. There are postulates elsewhere in Kant’s work,¹⁷ but he chooses a mathematical example in this context. In mathematics, postulates are claims that cannot be proven in the usual way; rather, they provide the basis upon which proof might begin. For example, we can’t prove anything about circles without having the concept of a circle, which is generated via a procedure for constructing circles.

Now in mathematics a postulate is the practical proposition that contains nothing except the synthesis through which we first give ourselves an object and generate its concept, e.g., to describe a circle with a given line from a given point on a place; and a proposition of this sort cannot be proved, since the procedure that it demands is precisely that through which we first generate the concept of such a figure.

CPR A234/B287

Similarly, explains Kant, the principles of modality are not regular claims—even amongst the synthetic a priori—which are amenable to regular forms of justification. On the contrary, there must be something about the principles of modality that provides a basis for regular justification (if Kant’s analogy with the mathematical case is to be illuminating). He continues

Accordingly we can postulate the principles of modality with the very same right, since they do not augment* their concept of things in general, but rather only indicate the way in which in general it is combined with the cognitive power.

CPR A234–235/B287

How is this indication of combination with our cognitive powers comparable to the construction of a circle? In general: the principles of modality are postulates because they draw out conditions on the conditions of possible experience. They don’t directly concern conditions on objects of experience, but rather concern how those conditions must be to be conditions on objects. This is why they are ‘subjectively’ synthetic: they do not directly concern objects, but rather concern the conditions of our representation of objects. But they are nevertheless, by this token, still conditions of possible experience at one remove. (Hence, the Deduction wasn’t wrong in trying to show that all of the categories are conditions of possible experience). Abaci makes a similar point in terms of our construction of a system of empirical cognition:

The assignment of each modal status to an object, rather than contributing to the representation of the object itself, contributes to our overall construction of a system of empirical cognition against the background of the structure and conditions of experience.

Abaci 2019, 206

How, more particularly, do the modal principles thereby relate to the other, direct, conditions of possible experience? Elsewhere, I have argued that the principle of possibility is implicated in the possibility of having concepts with empirical content—especially a priori concepts (Leech forthcoming). My argument here has been that the role of the category of necessity—as explicated in the principle of necessity—is to capture an ‘understandable’, cognisable, notion of necessity, one which is implicated in the (other) principles which are all otherwise conditions of the possibility of experience. Put this way, it is clear that the principle of necessity itself provides a condition on conditions of possible experience; it is needed for those principles themselves, in their application to objects of experience, to be understandable—by virtue of the necessity they impute. One might think of the principles as a priori laws of nature (where nature is the unity of experience). The principle of necessity ensures that the conditional necessity in the things that are governed by these laws is understandable. At bottom, a pure necessary unity in experience is attributed to the activity of the transcendental unity of apperception (in the Deduction), but we need a further concept of necessity to capture necessary unity as it applies to objects given in space and time, which, Kant argues, is a lawlike necessary connection between states of things.

Kant describes a postulate in mathematics as a practical proposition. Should we also take the modal principles to be practical propositions?¹⁸ I cannot fully settle this issue here. However, a crucial disanalogy is that, whilst all concepts have both form (generality) and matter, mathematical concepts have a “made” matter, whereas the categories have a “given” matter, albeit one that is given independently of experience.¹⁹ As Kant outlines in (CPR A234/B287), the object of a mathematical concept must be produced in order to generate the concept—the matter of the concept must be constructed. Since the construction of the circle contributes to the very generation of the concept, one cannot justify the construction procedure by appeal to the concept of a circle. The modal concepts are not mathematical concepts, and so we cannot carry over this precise line of reasoning. We can however carry over the general idea, which is that because the modal categories concern conditions on conditions of possible experience, they cannot receive the same treatment as straightforward conditions on experience.

Does this mean that they should receive no justification or explanation at all? After all, Kant offers “proofs” of the other principles (CPR A162/B202, A165/B207, A176/B218, A182/B224, A189/B232, A211/B256), but only an “elucidation” of the modal principles (CPR A219/B266). No. Just because something cannot be “proved”, it does not follow that one cannot give a different kind of explanation of it. We can allow that Kant does give an argument for the principle of necessity; we must just take it to be a different kind of argument. And indeed, rather than arguing that the principle of necessity is (straightforwardly) a condition of some aspect of possible experience, Kant argues—or so I say—that it is a condition on conditions of possible experience; a condition on the necessity in the a priori laws of nature.

9 CODA: The Function of Necessity Judgments

At the beginning of this paper, I asked: What is the role of the principle of necessity in the possibility of experience? What (if any) is Kant’s transcendental argument for the principle of necessity? Why is the principle of necessity called a ‘postulate’? To these I have answered that, for Kant, a concept of material necessity is required to make necessity as it features in the world of experience understandable, and that there is an argument to that effect to be found in the Postulates. The principle of necessity is a postulate because the understandability of necessity is a condition of possible experience at one remove: it is a condition on conditions of experience. These are questions and answers within the context of understanding Kant’s philosophy, but do they, or could they, have wider significance?

Kant’s views on modality naturally lend themselves to questions that have only relatively recently received serious attention from analytic metaphysicians, but which, arguably, are of signal importance: What is the function of modal judgment? What, if any, is the function of making judgments of possibility and necessity for us? Are such judgments in principle eliminable from our cognitive repertoire? Is their function merely instrumental or practical, or do they play a more integral role in our cognitive lives? If, ultimately, the function of modal judgment turns out to be limited or dispensable, should our metaphysical theories of modality be similarly curtailed?²⁰

Existing approaches to answering such questions have tended to draw on the role of modality in counterfactual or suppositional reasoning (Divers & Elstein 2012; Divers & González-Varela 2013; Kroedel 2017 and Williamson 2007). To develop such approaches, one must explain both where modality arises in that form of reasoning, and the function and importance of that form of reasoning. For example, Williamson (2007) takes thinking about metaphysical necessity to be a limiting case of counterfactual thinking: what is metaphysically necessary is whatever would have been the case, no matter what was the case (159). He in turn takes counterfactual thinking to play various roles: in our use of evidence, learning from the past, planning for the future, and thinking about causation (137–141).

Whatever the merits or pitfalls of this approach, Kant is ideally placed to offer alternative insights. He is continually asking what cognitive role key concepts play: Are they conditions of the very possibility of thought? Of cognition? Do they guide our epistemological endeavours in a particular way that is needed for some purposes, but threatens to be misleading? Kant gives detailed accounts of the content and role of certain modal concepts when he includes them as categories, and thereby gives them a role as necessary conditions of possible experience. The very set up of Kant’s discussion of modal concepts is designed to provide us with potential answers to questions about the cognitive function of judgments of possibility and necessity. Not only that, but such a set up will provide us with a particular kind of answer: modal concepts, if Kant is right, are not of mere instrumental value, but play a necessary role in our very ability to represent and experience the world at all. (See Leech 2014, 2018).

What might we say about Kant’s account of the function of the concept of material necessity? This is not the place for a detailed discussion, but let me offer a sketch of how things might go. On the face of it, the role of the category of necessity is to make understandable the necessity in conditions of possible experience. If you don’t buy this latter, very Kantian, idea, one might assume that one also won’t have much use for an account of the function of necessity judgments based upon it. However, setting aside issues of whether one should agree with Kant on the need for conditions of possible experience involving the categories, at its heart the issue here is one of the relation between necessity and objectivity. A core Kantian idea is that the distinction between the objective and the subjective, roughly speaking, lines up with a distinction between necessity and contingency (see Leech 2018). There is something distinctive about objective unity that involves necessity. At a pure level, that involves a kind of necessary unity of self-consciousness, but this necessity, in wider application to the unity of the world that we experience in space and time, develops into a more familiar kind of law-governed necessary connection between states. Hence, there is scope for a different kind of answer to the function question, which strikes to the heart of our understanding of our capacity for objective representation: insofar as the objective/subjective distinction implicates any kind of modal distinction, the function of modal judgment in general, and judgments of necessity in particular, may be to contribute to the conceptual framework required by objectivity.