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1. Jessica Leech
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A Transcendental Argument for the Principle of Possibility
To appear in The Sensible and Intelligible Worlds: New Essays on Kant's Metaphysics and
Epistemology, eds N. Stang and K. Schafer.
1. Introduction
In the Critique of Pure Reason, Kant famously offers a 'transcendental deduction' of the
pure concepts of the understanding (categories), an argument intended to show that the
categories are applicable to objects of possible empirical experience, in spite of their a
priori origins. Following the Deduction, in the Analytic of Principles, Kant then offers more
specific arguments for each of the categories: transcendental arguments to show how
each of these concepts, and synthetic a priori principles arising from them, are necessary
conditions of the possibility of experience of objects, and hence of the possibility of objects
of experience. The categories of quantity and quality are necessary conditions for the
possibility of magnitudes. The categories of relation – substance, causation, community –
are necessary conditions for the possibility of determinate objective temporal relations. At
least in the second edition of the Critique, the category of actuality – actual existence of
outer objects – is arguably presented as a necessary condition for the possibility of inner
experience (in the Refutation of Idealism). But what argument does Kant offer in this vein
for the (remaining) modal categories, the concepts of possibility and necessity? Standard
accounts of the Critique typically skip over the modal categories. But one should expect to
find an argument here, just as with every other category. My aim in this paper is to
reconstruct a transcendental argument for the principle of possibility from the resources
available to Kant, and to explain how the principle therefore has a crucial role to play in
Kant’s overall critical system.
2. The Principle of Possibility and a Puzzle
Kant discusses the modal categories, and principles arising from them, in the section of
the Analytic of Principles entitled 'The Postulates of Empirical Thinking in General'. A core
claim of the Postulates is that, in contrast to the other categories, which determine what
objects must be like in order to be able to feature in experience, the modal categories
express a relation to our cognitive facilities, to our capacity for having experience of
objects, rather than determining anything about those objects of which we have
experience.

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The categories of modality have this peculiarity: 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. If the concept of a thing is
already entirely complete, I can still ask about the object whether it is merely
possible, or also actual, or, if it is the latter, whether it is also necessary? No further
determinations in the object itself are hereby thought; rather, it is only asked: how is
the object itself (together with all its determinations) related to the understanding
and its empirical use, to the empirical power of judgment, and to reason (in its
application to experience)? (A219/B266)
The postulates themselves accordingly express relations between the concept of a thing
and conditions of experience: agreement with formal conditions for possibility; connection
to material conditions for actuality; and determination in accordance with general
conditions for necessity.
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. (A218/B265-6)
There is a question concerning what the transcendental argument should be in the case of
each of the three principles, but in this paper I will focus on the principle of possibility.
The principle of possibility is the synthetic a priori principle arising from the category
of possibility.
(PP) Whatever agrees with the formal conditions of experience (in accordance
with intuition and concepts) is possible. (A218/B265)
This principle concerns real possibility, the possibility of things, not logical possibility, the
possibility of thoughts or concepts. Kant writes of real and logical 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

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concept is a possible thought, even if I cannot give any assurance whether or not
there is a corresponding object … 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. (Bxxvi)
The Elucidation of the modal categories is put in terms of 'the object', i.e. whether the
object is merely possible, actual, or necessary, by virtue of whether the concept of that
thing bears suitable relations to our cognitive capacities (A219/B266), and not in terms of
whether a concept is thinkable. Hence we can be assured that the modal categories, and
the principle of possibility, are concepts of real, not logical, possibility.
The search for a transcendental argument for the principle of possibility is
accompanied by another kind of puzzle. This principle, along with the other postulates,
makes explicit reference to conditions of experience. I.e. it makes reference not only to
experience, but to the conditions under which experience is possible for us. Given Kant's
view that something can only be an object of experience insofar as it conforms to
conditions of experience arising from the categories and forms of intuition, it makes sense
that the real possibility of a thing should be understood as agreement of (the concept of)
that thing with conditions on experience. If it didn’t thus agree, then it could not be an
object of experience, i.e. there could be no such thing in the empirical world. Indeed, in the
passage quoted above, Kant is a hair’s breadth away from explicitly equating real
possibility with objective validity: `in order to ascribe objective validity to such a concept
(real possibility …)’ (Bxxvi). What is puzzling is the claim that the concept of this should be
a category; that not only this agreement, but the concept of this agreement, should be
required for possible experience. A category is a concept the possession and deployment
of which is a necessary condition of the very possibility of experience. We should then ask
why the very possibility of experience presupposes our grasp of a concept so
sophisticated as to make reference to the conditions under which experience is possible
for us. Why should we be required to conceptually reflect upon our cognitive capacities
(formal conditions of experience) and the relation between these capacities and the
concepts of things (agreement) to make experience possible? In sketching an argument
for the principle, I hope to also provide a solution to this puzzle, i.e. to shed light on why,
according to Kant, we require such a sophisticated concept as a prerequisite to
experience.
There is a bad solution to the puzzle, which should be dismissed from the outset.
Kant’s project, in the Critique of Pure Reason, is to examine our ability to form objective

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representations, ultimately to learn what it is possible for beings like us to know. It is of
crucial importance to the project that we be able to justify our concepts as having content
and being applicable to the world. The concept of possibility allows us to assess whether
our concepts—including the categories—could be instantiated in reality, and thereby
underwrites the critical project. Without it, we could never be sure if our concepts were
capable of contributing to objective representations of the world at all. One might put the
point: without a concept of possibility with the kind of content evinced by the principle of
possibility, Kant's transcendental philosophy would not be possible at all. It is this concept
that allows us to think about the legitimacy of our concepts. This boils down to something
like the following transcendental argument: (1) We can do transcendental philosophy; (2) a
necessary condition of the very possibility of transcendental philosophy is a concept of real
possibility; (3) therefore, we have a concept of real possibility. But (1) is hardly a
convincing starting point. Even the most committed Kantian must admit that
transcendental philosophy isn't an ineliminable condition of the very possibility of empirical
experience at all.1
So whilst modal concepts may allow us to reflect upon our cognitive
abilities, e.g. to think about the possibility of experience, it isn’t at all clear why we should
need to do that. We need to find a better reason to explain why modal concepts are built
into our capacity for cognition at a fundamental level.
There are two slightly different questions in the vicinity, which it will help to
distinguish: (1) What is the role of the modal categories in Kant’s account of experience?
(2) Does Kant give a transcendental argument – similar to the Analogies of Experience –
for the modal concepts? The first question is largely philosophical, the second largely
interpretive. My focus in this paper will be on the former: I will present an argument that
would be available to Kant, which makes sense of the role of modality in Kant’s system.
Given that there are good philosophical reasons for including this in our understanding of
Kant’s philosophy, it seems to me likely that Kant had something like this in mind, in
answer to question (2). But I will not go so far here as to fully defend that claim.
3. The Argument
Here is the key passage, in which the main inspiration for an argument can be
found.
1 Although it may be considered a welcome by-product of such conditions.

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[T]he principles of modality are also nothing further than definitions of the concepts
of possibility, actuality, and necessity in their empirical use, and thus at the same
time restrictions of all categories to merely empirical use, without any permission
and allowance for their transcendental use. For if they are not to have a merely
logical significance [Denn, wenn diese nicht eine bloß logische Bedeutung haben]
and analytically express the form of thinking, but are to refer to things and their
possibility, actuality, and necessity, then they must pertain to possible experience
and its synthetic unity, in which alone objects of cognition are given.
(A219/B266-7, translation amended)
From this, along with the considerations I offer below, we can construct the following
argument.
1. The categories are restricted to an empirical use: to application to objects of
experience. (Otherwise they would have a merely logical significance).
2. If the categories are to be restricted to an empirical use, then they must pertain only to
possible experience and its synthetic unity (in which alone objects of cognition are
given).
3. If the categories are to pertain only to possible experience and its synthetic unity, then
the application of the categories must agree with the formal conditions of experience.
4. Therefore, if the categories are to be restricted to an empirical use, then the application
of the categories must agree with the formal conditions of experience.
5. That a concept agrees with the formal conditions of experience just is an instance of
the principle of possibility.
6. Therefore, the principle of possibility is a transcendental condition of the restriction of
the categories to an empirical use.
This argument seems, at least prima facie, to take the form of a valid transcendental
argument (or at least as valid as any transcendental argument can be). Premise 1 states
an assumed actual truth about the meaning or significance of the categories. Premises 2-4
present a chain of transcendental conditions of 1. 5 notes that the ultimate transcendental
condition of this chain is equivalent to the principle of possibility. Hence the conclusion in 6
that the principle of possibility is a transcendental condition of the assumed fact in premise
1, that the categories have a restricted use.

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Premise 1 is particularly important, as it starts off the whole argument. I understand
this starting point in terms of Kant’s account of the origin of the categories as arising from
the functions of judgment. A plausible way to understand the content of the categories, as
explained in the 'Metaphysical Deduction' is as the functions of judgment when applied to
our conditions of sensibility, i.e. the conditions under which objects can be given to us in
experience. The logical forms of judgment, laid out in the Table of Judgments (A70/B95),
comprise conditions on thinking, i.e. on the well-formedness of a thought or judgment. The
different forms of judgment—the different forms that the content of a judgment can take—
are the result of the different functions of unity of the understanding—the different ways
that the understanding is able to unify representations together into a judgment (A69/B93-
4). These are merely conditions on thinking, the activity of the understanding alone. But
when these functions of unity of the understanding are applied outside of the
understanding, to intuitions, the result is the categories.
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.
(A79/B104-5)
But now the categories are nothing other than these very functions for judging,
insofar as the manifold of a given intuition is determined with regard to them. (B143)
When combined with the formal conditions of our becoming aware of objects, the logical
forms of judgment transform into pure concepts of the understanding, forms that our
experience of objects must take. This explains why it is so important for the categories to
bear an appropriate relation to possible experience. Without this they would simply be
logical conditions on well-formed thoughts, not real conditions on objects of possible
experience. This explains Kant’s remark, that if the categories are 'not to have a merely
logical significance and analytically express the form of thinking', they then need to 'pertain
to possible experience and its synthetic unity, in which alone objects of cognition are
given'. Without a restriction to the conditions of possible experience, to the conditions
under which objects can be given to us in intuition, the categories just are the logical forms
of judgment. A restriction to 'empirical use' is imperative for there to be categories, properly
speaking, at all.

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Kant elaborates on this requirement for the significance of the categories in the
Schematism. The Schematism appears soon after the Transcendental Deduction. At this
point in the Critique, Kant takes himself to have shown that the categories are applicable
to possible experience (objectively valid), but not how or where they do apply. Following
the Schematism we have the main sections of the Analytic of Principles which, as I have l
already noted, give a detailed account of the particular content and application of each
category, e.g. the application of a causal principle to account for determinate objective
temporal succession. We can thus read the Schematism as charting the general transition
from the Deduction—an argument that the categories are in general applicable to
experience—to the Principles—particular arguments for how each category applies to
experience. Again, the crucial claim is that the categories need to be restricted to empirical
application to be afforded a real, not a merely logical, significance.
[T]he schemata of the concepts of pure understanding are the true and sole
conditions for providing them with a relation to objects, thus with significance, and
hence the categories are in the end of none but of a possible empirical use.
(A145-6/B185)
Another way to put the point is that, whilst in the transcendental deduction Kant is
concerned with the objective validity of the categories, i.e. applicability to possible
experience, in the following sections he is concerned with the objective reality of the
categories, i.e. where they in fact do apply to experience. He moves from a concern about
whether the categories can be true of objects of possible experience, to the claim that the
categories are true of objects of experience, and necessarily so, as elaborated by the
principles.
Following premise 1, premises 2-4 elaborate on what the necessary conditions are
for the categories to have their full meaning, as opposed to a merely logical meaning.
These conditions are the categories being in agreement with the formal conditions of
experience. If they are to pertain only to possible experience, then they must be
compatible with the conditions under which experience is possible, i.e. the forms of
intuition and the other categories. In other words, they must agree with these formal
conditions of experience. The final step is then definitional. This condition is just what Kant
has defined the principle of possibility to be. Hence the principle of possibility is the
ultimate condition of the possibility of the categories having full meaning, not merely logical
significance.

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My focus in this paper will not be to show that such an argument makes good sense
of the role that the modal categories – or at least the principle of possibility – have to play
in Kant’s theoretical philosophy. First, I will offer textual evidence to support the claim that
such an argument coheres with Kant’s writings. Second, I will offer a philosophical account
of how I take this argument to fit in with Kant’s overall critical system. Finally, I will consider
some alternative approaches to incorporating modal concepts as categories into Kant’s
theoretical philosophy.
4. Kant's applications of the principle of possibility
First, I want to consider evidence to show that my proposed argument coheres with Kant's
text. In the passages following the key passage quoted above, Kant effectively applies the
principle of possibility to every kind of a priori representation.
We shall now make obvious the extensive utility and influence of this postulate of
possibility. (A221/B268)
He does not only make the general claim that the principle of possibility is required to
explain the meaning of the categories, as restricted to an empirical use; he also proceeds
to demonstrate this use of the principle.
To start, he covers the three categories of relation: substance, causation, and
community.
[Substance] If I represent to myself a thing that persists, so that everything that
changes merely belongs to its states, I can never cognize from such a concept
alone that such a thing is possible. (A221/B268)
[Causation] Or, if I represent something to myself that is so constituted that if it is
posited something else always and inevitably succeeds it, this may well be able to
be so thought without contradiction; but whether such a property (as causality) will
be encountered in any possible thing cannot thereby be judged. (A221/B2689)
[Community] Finally, I can represent various things (substances) to myself that are
so constituted that the state of one is followed by a consequence in the state of the
other, and conversely; but whether such a relation can pertain to any things cannot

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be derived from these concepts, which contain a merely arbitrary synthesis.
(A221/B269)
We can already note how strange it is that Kant should now query the objective reality of
these concepts. Not only has the transcendental deduction already purportedly shown the
objective validity in general of the categories, but these categories of relation have already
been subject to further argumentation in the Analogies of Experience, where Kant has
argued that these concepts are necessary conditions of objective temporal relations. The
concepts discussed here are clearly those concepts, already tied to temporal relations:
they are concepts explicitly concerning persistence and succession. They are already
implicated in conditions of experience.
The general lesson offered by Kant is that only in relation to the formal conditions of
experience can we cognize the `objective reality’ or `transcendental truth’ of these
categories.
Thus only from the fact that these concepts express a priori the relations of the
perceptions in every experience does one cognize their objective reality, i.e., their
transcendental truth, and, to be sure, independently of experience, but yet not
independently of all relation to the form of an experience in general and the
synthetic unity in which alone objects can be empirically cognized. (A212/B269)
What is transcendental truth? Whereas empirical truth requires an agreement of the
cognition with its object (A58/B82), transcendental truth is different.
All of our cognitions, however, lie in the entirety of all possible experience, and
transcendental truth, which precedes all empirical truth and makes it possible,
consists in the general relation to this. (A146/B185)
Transcendental truth makes empirical truth possible, and requires a relation to the entirety
of experience. Empirical truth involves a cognition which is about an object with which it
agrees (A58/B82). It is the forms of intuition and the categories, formal conditions of
possible experience, which, according to Kant, make cognitions about the world and
objects of experience possible. I suggest that we should understand the transcendental
truth of a cognition as making cognition and objects of experience possible through
application to possible experience. When Kant writes that transcendental truth `consists in

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the general relation to the entirety of all possible experience’, he means that
transcendentally true cognitions apply to all possible experience. Hence, in order to
demonstrate the transcendental truth of a cognition, we need to show that it agrees with
conditions on possible experience. This is to apply the principle of possibility.
Following the categories of relation, Kant then presents us with an application of the
principle of possibility to the concepts of magnitudes, covering the categories of quantity
and quality.
And thus the possibility of continuous magnitudes, indeed even of magnitudes in
general, since the concepts of them are all synthetic, is never clear from the
concepts themselves, but only from them as formal conditions of the determination
of objects of experience in general. (A224/B271-2)
This is followed by an application to the concept of a triangle – an example of a
mathematical concept, another kind of a priori concept.
It may look, to be sure, as if the possibility of a triangle could be cognized from its
concept in itself (it is certainly independent of experience); for in fact we can give it
an object entirely a priori, i.e., construct it. But since this is only the form of an
object, it would still always remain only a product of the imagination, the possibility
of whose object would still remain doubtful, as requiring something more, namely
that such a figure be thought solely under those conditions on which all objects of
experience rest. (A223-4/B271)
Even though we can construct the concept of a triangle in pure intuition, Kant presses the
point that we still need an assurance that such a figure could be instantiated in empirical
experience. Without this, it would `remain only a product of the imagination’. Hence
another application of the principle of possibility is required. We need to be assured that
the concept of a triangle can be `thought solely under those conditions on which all objects
of experience rest’. It must be in agreement with formal conditions of experience. In the
case of the triangle, the crucial element of these conditions is space, as an a priori form of
intuition. It is because space is itself a formal necessary condition of the possibility of
experience, that the triangle, as constructed through our pure intuition of space, is
guaranteed agreement with formal conditions of experience.

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[S]pace is a formal a priori condition of outer experiences ... it is this alone that
connects with this concept [triangle] the representation of the possibility of such a
thing. (A224/B272)
Note that the claim is that it can be thought `solely’ under those conditions. Why is it not
enough that it can be thought under these conditions, never mind whether it can be
thought under others? I will return to this point below.
One might object at this point that Kant's arguments of the Axioms of Intuition and
the Anticipations of Perception (earlier in the Principles) are already supposed to have
shown that mathematics is applicable to experience, in showing that the magnitudes
studied in mathematics are necessary features of experience. However, the fact that Kant
has offered an application of his principle of possibility to the concepts of magnitude
suggests that he does not, after all, take the work to be already complete. This goes for
the categories of relation too. This compounds the puzzle introduced above. Kant is
supposed already in the transcendental deduction to have shown us that the categories
are objectively valid. Given that he offers further arguments in the Analytic of Principles –
the Analogies, Axioms and Anticipations – it is doubly puzzling that he takes the work to be
incomplete.
To explain what work is left for the principle of possibility to do, then, I need to turn
to a more detailed discussion of the role the principle could play in Kant’s theoretical
philosophy.
5. Making concepts
The application Kant makes of the principle of possibility, in determining a proper
restriction of the categories to objects of possible experience, suggests that he takes it to
play an important role in our account of concepts. I will argue that there is a role to be
played by the principle in Kant's account of the formation and acquisition of concepts.
According to Kant, concepts are characteristically general. They relate to an object
'by means of a feature which several things may have in common' (A320/B337). Moreover,
the generality of a concept is 'made', not given.
All concepts, as to matter, are either given (conceptus dati) or made (conceptus
factitii). The former are given either a priori or a posteriori. ... The form of a concept,
as that of a discursive representation, is always made. (Logic, Ak. 9:94)

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Concepts that have a 'made' matter, are constructed concepts (a.k.a. factitious concepts),
typically mathematical concepts (see Dunlop (2012)). Concepts with a given matter divide
into those with a matter given in experience (empirical concepts) and those with a matter
given independently of experience (pure concepts).
We can think of the generality of a concept as the concept having a sphere or
extension – a domain of things to which it applies.
The general logical account of concept-formation concerns only the conditions that
make possible the sphere or extension [Umfang ] of a concept (i.e., its form). The
issue here is not the determination of the limits of the concept's sphere, but merely
the (positive) conditions under which it has a sphere at all or is a general
representation. (Newton, forthcoming, 18)
In explaining how the generality of a concept is made, then, the challenge is to explain
how a concept comes to have a sphere or extension. Proposals for this explanation vary
(see e.g. Longuenesse (1998) and Newton (forthcoming)). To endorse a particular
approach here would take us too far from present purposes. Besides, my explanation of
the principle of possibility should be available regardless of the account one chooses here.
My interest here is not with the generality of a concept as such, but with the other
side of generality – that a concept must not only have a sphere, but an appropriately
limited sphere. Through some cognitive capacity, our concepts are assured generality – a
sphere. Through the transcendental deduction, we are assured that the sphere of our pure
concepts covers objects of possible experience. But the worry remains that the sphere of
these pure concepts may overrun the bounds of possible experience. Indeed,
[If] I leave out all intuition, then there still remains the form of thinking, i.e., the way
of determining an object for the manifold of a possible intuition. Hence to this extent
the categories extend further than sensible intuition, since they think objects in
general without seeing to the particular manner (of sensibility) in which they might
be given. (A254/B309)
It is only in application to intuition, and within the bounds of the possibility of receiving a
manifold of intuition, that a category can count as determining an object. If these
conditions are not fulfilled, the form of thinking still remains. But whatever representations
we have no longer determine an object, they merely determine the form of a thought.

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They do not thereby determine a greater sphere of objects, since one cannot
assume that such objects can be given without presupposing that another kind of
intuition than the sensible kind is possible, which, we are by no means justified in
doing. (A254/B309)
(See also A286/B342.)
The application of the categories – with their full, schematized meaning – is
restricted to the empirical world, the world of possible experience. If we consider the
categories apart from the sensible conditions of being given objects in experience, Kant
maintains that they retain 'only a logical significance' (B186). They retain some kind of
meaning, but this is different to their full-blooded, schematized meaning. In particular, the
pure or unschematized categories, considered apart from the conditions on sensibility, no
longer give rise to the principles discussed in the Analytic of Principles. For example, the
pure category of substance—'a something that can be thought as a subject (without being
a predicate of something else)' (B186)—doesn’t give rise to a principle of the permanence
of substance unless time as a pure form of sensibility is introduced.
In short, the categories—full-blooded, schematized categories—have a sphere of
application, an extension, which is restricted to objects of possible experience. Something
must explain this limitation of the sphere of these concepts. We have seen that concepts
have both matter and form. The form, generality, is made. In the case of an empirical
concept, the matter is derived from empirical experience of the relevant kind, e.g.
experience of various trees for acquiring the concept tree. The matter of the concept
serves to limit the sphere or extension of the concept, e.g. to applicability to trees. But
what is to serve as the matter of a pure concept, a category? The logical functions of
judgment provide the basis for the content of the categories, but, as we have just seen,
these alone are not sufficient to limit the sphere of the categories to the empirical world:
they 'extend further than sensible intuition', as they are forms of thinking, and do not take
into account conditions of intuition.
An additional element is therefore required to ensure that the sphere of these
concepts is restricted to possible objects of experience. One might think that this addition
is the manifold of intuition, or rather, the pure form of intuition (the categories are pure
concepts, and so must have pure beginnings). After all, it is through application to intuition
that the functions of judgments become categories. However, this merely shifts the
problem to the pure forms of intuition: how can we be assured that they provide the right

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constraints on the sphere of a category? Recall: Kant also felt he needed to apply the
principle of possibility to the concept of a triangle, even though we can construct a triangle
in pure intuition.
The most plausible candidate for this additional element is thus the principle of
possibility. When a concept is formed, it must be formed in agreement with the formal
conditions of experience, i.e. the conditions under which we can have intuitions and
concepts. In the case of an empirical concept this condition is satisfied by the fact that any
concept acquired from actual experience is a fortiori in agreement with possible
experience. In the case of a pure concept, not derived from experience, agreement with
these conditions requires an additional principle: the principle of possibility. Given the
fundamental role that such a principle plays, prior even to schematized categories, such a
principle must be a priori.
A simpler way to put the point is as follows: we need concepts. In particular,
according to Kant, we need the categories as a condition of the possibility of experience.
One way to think of a concept is as a rule for picking a set of possible things, e.g. the
extension of the concept tree is the set of all possible trees. Hence the principle of
possibility expresses a constraint in forming concepts, that one must adhere to the formal
conditions of experience to ensure that the extension of the concept is indeed of possible
things.
This account of the role of the principle of possibility helps us to make better sense
of one of Kant’s remarks noted earlier, that the possibility of the concept of a triangle
having an object required 'that such a figure be thought solely under those conditions on
which all objects of experience rest.' (A224/B271) We can now understand why he restricts
us to thinking the figure solely under conditions of experience. It is to restrict the sphere of
the a priori concept to objects of possible experience, to ensure that the concept has the
right kind of meaning.
But returning to this example also raises the question: the concept of a triangle is
not one of the categories, so how should we explain Kant’s application of the principle
here? The proposal is that Kant sees a need to explain the limitation of the extension of a
priori concepts to the bounds of possible experience. Whilst our fundamental presentation
of space is as a pure form of intuition, and not a concept, it seems right that we do then
form geometrical concepts, such as the concept of a triangle. The pedigree of a concept
such as triangle is thus pure all the way down. And so we need to give an account of the
limitation of its sphere. Again, the answer offered, is that it must agree with conditions of
possible experience. Insofar as it is generated from the pure intuition of space, and our

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intuition of space is a necessary condition of the possibility of outer experience of objects,
the concept of a triangle is assured agreement with the conditions of the possibility of
experience. Hence the principle of possibility is fulfilled.
If this account of concept formation in Kant’s system is correct, then we can see
how the transcendental argument outlined above might be generated. The very possibility
of categories with proper schematized content depends upon an application of the
principle of possibility in the exercise of our capacity for concept formation.2
Moreover, this
account provides the key to the solution of the puzzle I posed above. Why on earth do we
need such a sophisticated concept as a prerequisite of the very possibility of experience?
Because the categories are conditions of the very possibility of experience. And the
principle of possibility is implicated in the categories having the right kind of content to do
their job. Our following this principle ensures that the categories do not have a merely
logical significance, but are properly restricted to their empirical use.
This connection to the possibility of objectively valid concepts also suggests a way
to understand why Kant calls the principle of possibility a postulate of empirical thinking.
This is in stark contrast to, for example, the principles arising from the categories of
relation, which are entitled analogies of experience. Why call the former a postulate of
empirical thinking, rather than of experience (empirical cognition)? I suggest: because of
the role that the principle of possibility plays in concept formation, together with the relation
between thinking and concepts.
Earlier in the Critique, Kant states that the understanding is a faculty for thinking of
objects of sensible intuition, i.e. empirical thinking.
The faculty for thinking of objects of sensible intuition ... is the understanding.
(A51/B75)
The characteristic representation-type of the understanding—the application of which turns
intuitions into thoughts about objects—is the concept (A50-1/B74-5). A necessary
condition, then, of empirical thinking, is our having concepts which are applicable to
objects of sensible intuition. This is what the principle of possibility guarantees us. Hence,
2 One might worry that this makes it sound like the principle of possibility is only applicable to pure concepts,
but it seems to present us with a general criteria for the possibility of any kind of thing. However, just
because the reason that the principle is a transcendental condition rests on its application to pure concepts,
does not mean that it can’t be applied more widely. It may well apply trivially to empirical concepts that are
acquired directly from experience. But its application to more complex, invented concepts is not at all trivial.
See A222-3/B269-70.

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16
it is a pre-condition, or a postulate (of which more below), of empirical thinking at all (i.e.
empirical thinking in general).
One might respond: experience, as Kant understands it, also requires the
application of concepts, so why not call the principle a postulate of experience, rather than
empirical thinking? Because this highlights the very different role that the Postulates have
to play, compared to the other principles. The first three kinds of principle—the Axioms,
Anticipations, and Analogies—are concerned with building up direct conditions of
experience. The Axioms and Anticipations present conditions on our having appropriate
intuitions of objects, and the Analogies present conditions on relations between these
objects of experience. By contrast, the principle of possibility, I have argued, is concerned
with the conditions of there being these conditions of experience at all. Hence specifying
that the Postulates are of empirical thinking emphasises this difference in role, i.e. it
distinguishes them from the Analogies of Experience. Moreover, the first three kinds of
principle are largely concerned with the spatio-temporal conditions of experience, in
particular specifying principles for magnitudes and temporal relations. As such, they are
closely connected to sensible conditions of experience. Insofar as the principle of
possibility is closely connected to the possibility of objectively valid pure concepts, it is tied
up with our capacity for thinking, rather than for sensing. As such, it seems appropriate to
call it a postulate of empirical thinking.
6. Making modal concepts
If this account of the genesis of concepts, and in particular pure concepts, is correct, and if
the modal categories are pure concepts, then the account should also apply to the modal
categories. How should we understand the application of the principle of possibility to the
concept of possibility itself? Kant offers an answer to this question when he explains why
the principles of modality are called 'postulates'.
The character of the modal categories is very different to that of the others. Recall,
the modal categories do not determine a property of an object, but concern only the
relation between the concept of an object and our cognitive capacities.
The categories of modality have this peculiarity: 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. (A219/B266)

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Kant takes this to imply that the modal categories are, in an important sense, not objective,
but rather subjectively 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. (A233-4/B286)
To count as objective, the categories of modality would have to say something about what
the objects to which they apply are like. Instead of this, they only say something about the
relation between the representation of the object and our cognitive faculties.
The modal categories are thus importantly different to other categories. As a
consequence, we don't require the same kind of justification of content and applicability as
for the others. The first nine categories purport to predicate properties of objects of
experience, and so we need to be assured that they properly apply to such objects. The
principle of possibility plays a key role in ensuring this. But the modal categories do not
predicate properties of objects, and so do not need to be held to the same standard. What
then is the appropriate alternative standard? Kant likens the status of the principles of
modality to that of postulates in mathematics.
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.
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.
(A234-5/B287)
We can't prove the proposition which tells us how to draw a circle, because it is only on the
basis of this that we can start to prove anything about circles. Likewise, we cannot prove

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the principle of possibility, because it is only on the basis of this principle that we can prove
anything about concepts, in particular the concept of possibility, at all. Such propositions or
principles cannot be proved or justified in the usual way, but this is not in virtue of their
merely appearing to us to be 'self-evident' or 'certain' (A233/B285-6).3
It is because they
constitute a prerequisite for proofs or justifications of the usual kind.
Just as the definition of a circle provides a rule for drawing a circle in the first place,
and hence is not something that can be proved about circles, so the principle of possibility
provides us with a rule for forming a general concept which is objectively valid, and hence
is not a concept that is open to the same kind of justification as other concepts. Kant writes
in a letter to Herz that
the possibility is given in the definition of a circle, since the circle is actually
constructed by means of the definition, that is, it is exhibited in intuition ... The
proposition “to inscribe a circle” is a practical corollary of the definition (or so-called
postulate), which could not be demanded at all if the possibility—yes, the very sort
of possibility of the figure—were not already given in the definition. (Ak. 11:53)
The postulate which defines a circle itself ensures the possibility of the circle: no further
justification is required. This is because the definition itself involves a construction of a
circle in pure intuition. The concept of possibility is not a constructed mathematical
concept, but it shares the feature of ensuring its own possibility as somehow given. The
possession of any concept requires that the form of that concept be made. In the case of
pure concepts, the making of that form requires a principle of constraint, the principle of
possibility. So one might say: whereas the definition of a mathematical concept involves
the construction of its own object, thereby ensuring its own possibility, the possession of a
pure concept involves the construction of its general form within the bounds of possible
experience, thereby ensuring its possibility, and also the possibility of the concept
implicated in that construction, namely the concept of possibility itself.
Finally, one might wonder, if the modal categories—or at least the concept of
possibility—do not require justification in the same way as the other categories, then why
is Kant's transcendental deduction—intended to justify or prove the applicability of the
categories to objects of experience—extended to the modal categories at all? Why doesn't
3
This is because often things that are taken to be ‘self-evident’ or ‘certain’ turn out to be wrong. As Kant
writes: ‘since there is no lack of audacious pretensions that common belief does not refuse … our
understanding would therefore be open to every delusion’, (A233/B285-6) if we took these as
fundamental grounds for knowledge.

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Kant restrict its scope? In response to this question, we should recall the aims of the
Deduction as compared to those of the Principles. The Deduction offers us a quite general
argument for why pure concepts of the understanding must be applicable to objects of
experience. Throughout the Principles Kant offers particular arguments for how and why
each category does, and must, apply to possible experience. These latter arguments
hardly render the initial, general argument obsolete. One might say: the Deduction shows
us that these concepts are conditions on the possibility of experience, the Principles tells
us in more detail how these concepts are conditions on the possibility of experience. The
category of possibility, like any pure concept, is shown to be applicable to objects of
experience. When we consider the details of the particular contribution that this concept
makes, it emerges that the reasons for thinking that it is a condition of experience are
different in form to those of the other categories, but for all this, it is no less a condition on
the possibility of experience. A kind of justification is offered in the Postulates, it is just a
very different kind of justification to that of the other categories.
7. Alternative arguments for a principle of possibility
My proposed transcendental argument, connecting the principle of possibility to Kant’s
account of concept formation, is not the only Kantian route to the importance of the modal
concepts. In this paper, I have attempted to stay fairly close to the text of the Postulates in
formulating an argument. In this section I will briefly survey some alternative routes to
establishing the principle of possibility as an a priori principle, which are perhaps more in
the spirit of Kant's philosophy, than adhering closely to the letter of the text. However, I do
not see these as competitors to my suggestion in this paper, but rather as distinct yet
complementary lines of thought leading to a similar conclusion.
First, a Kant-inspired link between concept possession and the concept of
possibility has been explored elsewhere. Baldwin (2002) and Brandom (2008) in particular
bill their theories of modality as being Kantian. They both argue that it is a necessary
prerequisite of our possessing concepts at all that we have some modal reasoning abilities
that can be expressed in terms of our familiar modal concepts. They argue that possession
or deployment of (empirical) concepts presupposes some grasp of modal concepts.
Baldwin (2002) draws a link to Evan's Generality Constraint.
[I]f a subject can be credited with the thought that a is F, then he must have the
conceptual resources for entertaining the thought that a is G, for every property of

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being G of which he has a conception. This is the condition that I call `The
Generality Constraint'. (Evans, 1982, 104)
If, in order to possess the concept F in thoughts of the form Fa, we also need to be able to
entertain thoughts such as Ga and Fb, this suggests that concept possession presupposes
some capacity to entertain non-actual alternative situations (Ga and Fb).4
But non-actual
situations do not yet count as possible. Baldwin extends the point by considering cases
where concepts are applied together.
[A]lthough non-actuality is an ingredient of mere possibility, not everything non-
actual is possible and more needs to be said to fill out the role of modality in
characterising concept possession. We get closer to this, I think, by considering
what is characteristic of the ability to understand what it would be for something to
be both F and G. For the obvious account is that it involves an ability to reason
concerning the implications, both positive and negative, of the hypothesis that
something is both F and G, where the ability to identify these implications does not
require knowledge of whether or not they actually obtain. This suggestion connects
concept-possession with a capacity for reasoning, and this is, I think, the
fundamental aspect of the matter. The ability to employ concepts to frame objective
thoughts about the world … is inseparable from the ability to employ these concepts
in reasonings in which a grasp of these concepts is deployed through a grasp of
their implications. (Baldwin, 2002, 9-10)
Concept possession requires an ability to reason regarding non-actual and possible
situations. For example, arguably, one does not count as possessing the concepts
bachelor and married if one thinks that they can be applied to the same subject in the
same thought (at the same time etc.) and possibly result in something true. Such a
scenario counts as non-actual – but we must also be able to recognize it as impossible, if
we are to count as properly understanding those concepts. So possession of concepts
presupposes an ability to reflect upon and reason about such potential applications.
A similar argument is to be found in Brandom (2008), in his discussion of the 'Kant-
Sellars Thesis' about modality. He argues that the practices and abilities which underlie the
4 Note that one can also read into this a link between the Generality Constraint and Kant's view that
concepts are essentially general.

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ability to deploy alethic modal vocabulary are practices and abilities which are required for
the deployment of any empirical vocabulary at all.
The ability to use ordinary empirical descriptive terms such as `green', `rigid', and
`mass' already presupposes grasp of the kinds of properties and relations made
explicit by modal vocabulary. (Brandom, 2008, 96-7)
This is because the ability to understand the vocabulary (possess the requisite empirical
concepts) requires the ability to assess the robustness of material inferences in
counterfactual situations involving those concepts, which in turn requires the ability to think
counterfactually, i.e. modally. For example,
One grasps the claim “the lioness is hungry” only insofar as one takes it to have
various consequences (which would be true if it were true) and rule out some others
(which would not be true if it were true). And it is not intelligible that one should
endorse as materially good an inference involving it, such as the inference from “the
lioness is hungry” to “nearby prey animals visible to and accessible by the lioness
are in danger of being eaten,” but be disposed to make no distinction at all between
collateral premises that would, and those that would not, if true infirm the inference.
One must make some distinction such as that the inference would still go through if
the lioness were standing two inches to the East of her actual position, the day
happened to be a Tuesday, or a small tree ten miles away cast its shadow over a
beetle, but not if she were shot with a tranquillizing dart, the temperature instantly
plummeted 300 degrees, or a plane crashed, crushing her. The claim is not that one
could not fail to assess some or even all of these particular counterfactuals correctly
and still count as grasping the claim that is their premise, but that one could not so
qualify if one made no such distinctions. (Brandom, 2008, 105)
In other words, properly understanding a concept or a piece of vocabulary involves some
grasp of the consequences of different scenarios for instances of the concept. That grasp
of consequences involves the ability to reason counterfactually. And the ability to reason
counterfactually, or the practice of reasoning counterfactually, is sufficient to account for
the introduction of modal vocabulary.
Whilst both Baldwin and Brandom make interesting connections between concepts
and possibility, it seems to me that Kant himself – or at least my reconstruction – brings

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out a slightly different link. Both alternative accounts rest on relations (material or logical)
between concepts – such as that between the hungry lioness, nearby prey, danger, and so
on – whereas my proposed argument rests on the relation between a concept and
conditions of possible experience. At the outset of the Postulates, Kant stresses that they
concern `the relation to the faculty of cognition’ (A219/B266), rather than a relation
amongst concepts. The proposal is that the extension or sphere of concepts must be
restricted by conditions of the possibility of experience; not that our proficiency with
concepts depends upon modal inferences involving other concepts.5
A second alternative route to understanding why, for Kant, the modal concepts are
categories takes seriously Kant’s transition from the functions of judgment to the
categories. In section 3 I outlined the relationship between the functions of judgment—
conditions on the activity of the understanding alone—and the categories—these functions
of judgment applied to intuition.
But now the categories are nothing other than these very functions for judging,
insofar as the manifold of a given intuition is determined with regard to them. (B143)
One might therefore construct an argument for the modal concepts being categories on
the basis of the modal functions of judgment. Roughly:
1. The functions of judgment are essential elements of judging.
2. There are modal functions of judgment.
3. The categories are nothing other than functions of judgment, insofar as the manifold of
a given intuition is determined with regard to them.
4. Therefore, there are modal categories (corresponding to the modal functions of
judgment).
Such an argument raises several questions. Why think that there are modal functions of
judgment that are essential elements of judging? What form do these modal functions of
judgment take? And what kind of concepts should we expect to result when they’re applied
to intuition? Are the modal concepts, as defined in the Postulates, of the form one would
therefore expect? To answer these questions would go beyond the scope of the present
5 This is not to say that Kant's account of concepts couldn't accommodate the claim that our mastery of a
concept depends upon our ability to assess modal inferences involving that concept. However, I don't think
this helps us to understand the role of the principle of possibility as expounded in the Postulates.

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paper.6
But note that if the claims of this paper are plausible, then this may provide a
constraint on the answers. They would have to be compatible with the suggested role of
the concept of possibility in the formation of concepts.
Finally, in the Critique of Judgment Kant appears to argue that it is something about
the cognitive capacities of a discursive understanding like ours, as opposed to an intuitive
understanding, which generates our need for modal concepts.
It is absolutely necessary for the human understanding to distinguish between the
possibility and the actuality of things. The reason for this lies in the subject and the
nature of its cognitive faculties. For if two entirely heterogeneous elements were not
required for the exercise of these faculties, then there would be no such distinction
(between the possible and the actual). That is, if our understanding were intuitive, it
would have no objects except what is actual. … Thus the distinction of possible
from actual things is one that is merely subjectively valid for the human
understanding. (Ak. 5:401-2)
In Leech (forthcoming) I explore in more detail how the functioning of our cognitive
capacities relates to modal concepts, and provide a model of the intuitive understanding, in
order to draw some general lessons for our ability to make modal judgments, and the
function of such judgments. In brief, Kant’s view seems to be that we need a distinction
between possibility and actuality to cope with the consequences of our divided cognitive
architecture. Our ability to have experience of or to make judgments about objects splits
into two distinct cognitive capacities—sensibility for intuition, and understanding for
thought. As such, there is a potential gap between our thoughts of things—what we can
conceptualise—and the existence of those things—what we are given in intuition.
Therefore, if we are to account for the possibility of knowledge of objects (where our
thoughts about things and their existence matches up), we need to be able to distinguish
between cases where our thoughts correspond to actual things, and cases of mere
possibility. If we can conceptualize such a distinction, then we will be able to express
sceptical worries, and formulate strategies to improve knowledge and avoid error.
This is evidently a very different route to the importance of modal concepts for Kant
to that presented in this paper, but one that is nevertheless complementary. In brief, the
6 I develop an answer to the first question elsewhere (Leech, ms.). See also Allison (2004, 139) for a brief
proposal for an answer to this first question. In Leech (2012) I propose an answer to the second question in
terms of the position of a judgment in a course of reasoning. See also Longuenesse (1998, 157-161).

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Critique of Judgment argument calls for a distinction between the possible and the actual
that is appropriately connected to discursive cognitive capacities – what things are or could
be objects of experience for us. This call is answered by the account proposed in this
paper: that of a concept of possibility which is implicated in the formation of objectively
valid concepts, i.e. those concepts which could apply to objects of experience for us.
8. Conclusion
If the Postulates are to follow the pattern set by previous sections of the Principles, we
should expect to find transcendental arguments which purport to show that the principles
of modality are necessary conditions for the possibility of experience. In this paper I have
sketched what I take to be a plausible candidate for a transcendental argument for the
principle of possibility. This argument rests on Kant’s account of the nature of concepts in
general, and the nature of pure concepts in particular. In short, the principle of possibility is
required as part of the account of concept formation. Insofar as the generality of concepts
is made, not given, an additional principle is required to ensure that pure concepts—in
themselves unbound by empirical constraints—are not too general, and are appropriately
restricted to empirical application. This is the role of the principle of possibility. Such an
argument helps us to understand passages in which Kant appears to apply the principle to
pure concepts to precisely this end. If this account is correct, then it would seem that the
modal categories play a much more central role in Kant’s theoretical philosophy than has
previously been recognized. They are not a mere oddity to be overlooked in favour of the
more exciting Refutation of Idealism that is buried in their midst. Rather, at least the
principle of possibility plays a fundamental role in ensuring that the core elements of Kant’s
philosophy—pure concepts of the understanding—have the right kind of content. In other
worlds, the principle of possibility ensures that there are categories at all.7
References
Baldwin, T. (2002) “The Inaugural Address: Kantian Modality." Proceedings of the
Aristotelian Society, Supplementary Volumes 76:1-24.
Brandom, R. B. (2008) Between Saying & Doing: Towards an Analytic Pragmatism.
Oxford: Oxford University Press.
7 Thanks go to audiences in Cambridge and Miami for invaluable feedback and discussion on earlier
versions of the paper.

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Dunlop, K. ( 2012) “Kant and Strawson on the Content of Geometrical Concepts.” Nous
46:86-126.
Evans, G. (1982) The Varieties of Reference. Oxford: Clarendon Press.
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------. (1992b) Correspondence. Cambridge University Press.
------. (1998) Critique of Pure Reason. Cambridge University Press. Translated and edited
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Leech, J. (2012) “Kant’s Modalities of Judgment”, European Journal of Philosophy, 20:2,
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------, ms. “Judgment: what does modality have to do with it?”
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