1. The apriority of forms of sensibility
Kant divides representations into concepts and intuitions. Intuitions are divided to a priori intuitions and empirical intuitions. Of these a priori intuitions, the representations of space and time have a special place in Kant’s account of human experience. They are forms of sensibility (Sinnlichkeit). By this Kant means roughly the following. Space and time make it possible for us to be affected by objects outside us. We are affected only spatio-temporally as it were. Thus, space and time are conditions of experience and cannot be acquired by empirical means. Hence, they must a priori representations.
In arguing for conditions of being affected, Kant is departing in an interesting way both from empiricism and rationalism. Descartes and Spinoza can be seen to hold thought and extension as “innate ideas” under which we conceive the reality whereas in Locke’s empiricism mind is endowed with certain faculties but not with any a priori forms of being affected. But whereas Descartes’s and Spinoza’s attributes are both in the world and in the innate conceptual apparatus of the minds, for Kant time and space are only conditions of being affected and for that reason they can be forms of intuition for beings who lack concepts; such as animals.
Even though Kant presents several arguments for the apriority of space and time, the basic line of his argument seems to be a reduction. Suppose we get the idea of space empirically. This might happen in such a way that we first empirically get the concept of a certain length and then we repeat this length in three dimensions and become aware that this repetition can be carried out indefinitely. Thus we have the idea of infinite space—or of space and of its infinity. But the problem with this line of thought is that in order to get an idea of a limited length we have to think of the length as being limited by something, and what this means is that we have to think of the length as being embedded in a greater portion of space, and this greater portion of space still in a greater portion of space and so on indefinitely. Thus, we cannot get the idea of space from empirical representations because these representations require that we have a representation of the infinity of space prior to those representations. Having an empirical representation of space requires that we are having a representation that cannot be given in that representation. The argument for the apriority of time can be presented in an analogous fashion.
2. The apriority of the categories
For Kant, there are certain conditions of experience that are not conditions for being affected. They are general conditions for having thoughts about objects-in-general. These conditions are the categories. As Kant famously says, intuitions without concepts are blind and thoughts without intuitions are empty. Kant wants to connect these categories with the logical forms of judgements by claiming that the table of categories somehow results from the table of judgements. What, then, were Kant’s reasons for rejecting concept-empiricism and postulating a priori concepts. I will consider here different criteria that Kant presents in the Critique of Pure Reason  as well as in the Lectures on Metaphysics .
(A) Argument from necessity and strict universality
For Kant, a priori may qualify at least judgments, concepts, and intuitions. When a judgment is qualified as a priori, it means that the judgment in question is justified without appeal to either outer or inner experience. When a concept is a priori, it means that it is not abstracted from perceptions or empirical representations and when an intuition is a priori, it means that it does not a result from our being affected by external things. It is of some importance to be aware that for Kant a judgment maybe known a priori even though its conceptual content involves empirical items. For example, Kant claims that the principle “Every event has a cause” can be known a priori, even though the concept of an event is a posteriori.
Kant borrows his two different criteria for a priori judgements from Leibniz: strict universality and necessity. Our senses do not tell us the modality of a state of affairs but only simply report of its existence or non-existence. Thus, necessity is something that the understanding adds to a judgement. Moreover, in presenting to itself a strictly universal judgement, the understanding cannot verify it on the basis of empirical observation. This is a platitude, because a strictly universal judgement has, by definition as it were, instances which are possibly not experienced by anybody. Kant sees these different criteria as defining the same class of judgements. Thus, they both are infallible criteria of a priori cognitions. However, Kant claims that it is good to keep these criteria separate, because sometimes it is easier to prove the necessity of a judgment than its universality and sometimes the other way round.
One could now claim that there have to be a priori concepts because there are concepts, such as that of cause, which have necessity as part of their content—these concepts cannot be derived from experience, because of the modal blindness of the senses. Kant only occasionally uses the necessity criterion in showing the apriority of certain concepts, and, in fact, the necessity criterion is not useful in showing the apriority of concepts as the following considerations show: Somebody might, for example, claim that the necessity criterion does not reveal that cause is an a priori concept even if it were granted that perception is modal blind. One could acquire the concept of cause just by adding the necessity operator to the concept of something following something other. It should, then, be argued that “following from” cannot be an empirical concept. But I do not see any easy way to show this. It seems that similar considerations can be applied to other concepts which involve necessity. What the modal blindness of perception shows seems to be only that modal concepts have to be a priori concepts, and Kant is proceeding wisely in reserving the necessity criterion as a criterion for the apriority of judgments.
(B) The peeling argument
In this argument, Kant tries show that simply by peeling off all the empirical and sensible qualities from an empirical intuition we will reach a priori concepts of an object in general. Kant gives several examples of this (e.g. [2, B5-B6]), but maybe the most fully developed version of this argument occurs in his lectures on metaphysics where Kant starts from the intuition of a piece of chalk:
If we omit everything empirical, like weight, density, and color, I still retain the form and shape. Now I ask, can I also omit that? Yes, but then for me no body is left. Through body I think of a substance, so the concept still remains the same for me. Through substance I think of a subject that is not a predicate of another. In that case I am already arriving at concepts. It is a concept which remains when I omit everything else from the object. Every body has a power in it, i.e., a ground of action, that is again a concept. It has form, a multitude of parts – or it is a whole, here I am also not permitted to think of space. Finally, there still remains the concept of a thing, which is substance, has power, parts, is a whole, which presupposes no shape or figure. Thus, pure intuition ultimately remains, and if it is left out, then the pure concept: it is pure because it contains nothing empirical and also has no intuition, is thus transcendental. [4, 151]
The peeling argument has, then, two stages: (I) throw away everything empirical from a perception, reach the sensible intuition! (II) throw away the form of the sensible intuition, reach the a priori concepts that are thought through the perception of the object! In this, way Kant seems to think we would reach the categories of substance-accident, cause (power), and whole.
Kant presents also an argument for a priori concepts that is based on our ability to think and speak. This argument, I believe, can be seen as a variant of the peeling argument. He considers the sentence
Snow has fallen [unto the earth today]
Our common language already contains everything that transcendental philosophy draws out with effort. – These categories are already contained in us, for without them no experience would be possible, e.g. snow has fallen. Herein lies that snow is, substance; fallen means an accident, upon the earth means an influence, that is action <actio> thus belongs to cause <causa>. Today refers to time, fallen to space. If we omit all sensations as well as space and time, substance remains which acts in a certain way, thus they must be connected so that the concept of experience arises. If we posit that we had no such pure concepts of the understanding, then we could not think or speak at all. [4, 158]
What Kant claims here is that if everything empirical is taken away from the thought expressed by the sentence “Snow has fallen upon the earth today”, then pure concepts of a substance and acting remain.
The peeling argument and its linguistic variant seem to suffer from a problem. It seems that before using it, Kant should have available a criterion which would tell how to divide the content of our thoughts into a priori and a posteriori elements.
(C) The argument from concept formation
According to Kant understanding is the faculty of judging. In judging the subject may subsume an object of intuition under a concept of experience (judgment of experience) and judging is also needed in concept acquisition.
For Kant, concept formation is based on three operations of the mind: comparison, reflection, and abstraction. In Jäsche Logik, Kant says of these operations the following:
To make concepts out of representations one must thus be able to compare, to reflect, and to abstract, for these three logical operations of the understanding are the essential and universal conditions for generation of any concept whatsoever. I see, e.g., a spruce, a willow and a linden. By first comparing these objects with one another I note that they are different from one another in regard to the trunk, the branches, the leaves, etc.; but next I reflect on that which they have in common among themselves, trunk, branches, and leaves themselves, and I abstract from the quantity, the figure, etc., of these; thus I acquire the concept of a tree. [3, 592].
Thus, the formation of empirical concepts is judgemental through and through. In order to form an empirical concept of a tree, I have to note, i.e. to judge, that there are differences between several individuals, then I have to reflect on what they have in common (and, of course, to judge what they have in common), and finally to abstract the non-shared properties from the particular representations.
But when the formation of empirical concepts is presented in this way, it is natural to ask how the process of concept formation can ever get started. The minimal requirement seems to be that the objects offered by the sensibility must somehow be able to be identified without any help from the empirical concepts: there must be resources in the mind that enable one to think about those objects. But this seems to be tantamount to saying that these objects must be capable of being subsumed under, at least, the general categories of substance and accident. The point I have in mind here can be presented also as follows: empirical concept getting requires judgement; judgement is not possible without certain concepts; therefore, not all concepts can be empirical. This line of thought would also help to explain why Kant believes that experience is not possible without a priori concepts. It is almost a tautology to say that experience requires empirical concepts. But if it also is true that empirical concepts require a priori concepts, it follows by transitivity that experience requires a priori concepts.
Even though in the Critique of Pure Reason , there is not so much evidence that the argument for the existence of a priori concepts goes the way suggested here, nice confirmation is provided by a passage from “Metaphysik Mrongovius”:
[there are] pure a priori concepts, for since experience is not possible through perception alone, but rather concepts must be added to it, so there must be underlying a priori concepts through which I can bring perceptions under concepts: they underlie experience as substance, and if we did not have a priori concepts then we also would not obtain any concepts at all. [4, 153]
Kant also makes the point about pure concepts of understanding as being presupposed by the fact of experience, in the same way as I have suggested above:
Categories are pure concepts of the understanding without which there would be no concepts of experience, therefore no experience. Through them intuitions are brought into a concept of experience – and then impressions of sensibility must still be added to it. [4, 158]
I believe that this line of thought is fascinating also because a nice analogy would grow out of it: the relation of a priori intuitions to empirical intuitions is in one respect just like the relation of a priori concepts to empirical concepts: without a priori intuitions empirical intuitions are impossible for human beings and without a priori concepts empirical concepts are impossible.
The argument from concept formation has, however, a difficulty. It is not quite clear why all the categories listed in the table of categories should be needed as a priori conditions of empirical concept formation. Showing that, however, is a task I cannot undertake here.
(D) Argument from combination
As we have already seen, Kant got his criteria, necessity and universality, for an a priori judgement from Leibniz. However, there is another strand of thought about a priori in Leibniz. Leibniz is keen to claim that relations are somehow mind dependent. They are not in the things themselves but something the mind places upon the world on the basis of the (monadic) properties of things. This is what Leibniz spokesman, Theophilus, says in one passage [6, Bk. 2 Ch. 25] of the New Essays on Human Understanding, a work Kant knew well:
Relations and orderings are to some extent ‘beings of reason’, although they have their foundations in things; for one can say that their reality, like that of eternal truths and of possibilities, comes from the Supreme Reason.
What is at issue here is that those concepts which relate different things to each other cannot, strictly speaking, correspond to anything that is real. For example, the judgement “ a is taller than b” is such that the one who judges it detects a certain length in a and a certain length in b. But in reality there is no entity that is expressed by the two-place predicate “is taller than”. The correctness of this judgement is dependent on the lengths of a and b, but the relation is added to the world by the mind. Even though this view may sound a bit odd, it makes, I believe, good sense. A relation is ontologically speaking a strange thing. Somehow it should be in several things things at once. A relation would not be a way how some one thing is but it should be able to modify several things simultaneously. Seeing relations as mind dependent beings of reason would liberate one from these kind of ontological difficulties.
From the ideality of relations, there is a small step to the view that all combination is mind dependent. A combined thing could be mind independent only if the relations that do the combining could exist in reality as they exist in the ideas. In the New Essays [6, Bk. II Ch. 12], Leibniz connects the ideality of collections with the ideality of relations by writing as follows:
The unity of the idea of an aggregate is a very genuine one; but fundamentally we have to admit that this unity that collections have is merely a respect or relation, whose foundation lies in what is the case within each of the individual substances taken alone. So the only perfect unity that these ‘entities by aggregation’ have is mental, or phenomenal, like that of the rainbow.
Kant seems to accept what Leibniz says here. In fact, he begins the B-deduction by emphasizing the non-empirical nature of combination:
Yet the combination (conjunctio) of a manifold in general can never come to us through the senses, and therefore cannot already be contained in the pure form of sensible intuition; for it is an act of the spontaneity of the power of representation, and, since one must call the latter understanding, in distinction from sensibility, all combination, whether we are conscious of it or not, whether it is a combination of the manifold of intuition or of several concepts, and in the first case of sensible or non-sensible intuition, is an action of the understanding. [2, B 129-B 130]
Now, it seems that one route for arriving at a priori concepts can be based on the non-empirical nature of combination. If the acts of combination necessarily involve concepts, then it seems clear that these concepts have to be a priori. But now it seems that what is given by the table of judgments are different ways of combining representations. For example, disjunction and implication are two different ways of combining judgments and it is rather plausible to say that these ways to do the combining require the possession of separate concepts; i.e. the concepts of disjunction and implication. Thus, the logical table of judgments gives “logical concepts” which have to be a priori because of their being combining concepts. But if Kant is right in his metaphysical deduction, a question I cannot explore here, that the possession of a logical concept entails the possession of the corresponding category, then he can be seen to have shown that categories are a priori concepts.
This last argument to show the apriority of categories has the following advantage over the first three: with the help of it, it is simple to show the apriority of all categories. The first three ways, on the other hand, require some painstaking piecemeal effort. However, this last method is problematic because much is built on the non-empirical nature of combination. A satisfying evaluation of this method requires a fuller explication of that basis than what has been possible to give here.
- Allison H. Kant’s Transcendental Idealism. Yale U.P., 1983.
- Kant I. Gesammelte Schriften (Akademie-Ausgabe). Berlin: de Gruyter Verlag, 1900 ff.
- Kant I. Lectures on Logic. Translated and edited by J. Michael Young. Cambridge U.P., 1992.
- Kant I. Lectures on Metaphysics. Translated and edited by Karl Ameriks and Steve Naragon. Cambridge U.P., 1997.
- Kant I. Critique of Pure Reason. Translated and edited by Paul Guyer and Allen W. Wood. Cambridge U.P., 1998.
- Leibniz G.W. New Essays on Human Understanding. Translated and edited by Peter Remnant and Jonathan Bennett. Cambridge U.P., 1996.
This article was firstly published in collected articles “Kant zwischen West und Ost” (2005):
Koistinen, Olli. Kant on a priori concepts// Kant zwischen West und Ost. Zum Gedenken an Kants 200. Todestag und 280. Geburtstag. Hrsg. Von Prof. Dr. Wladimir Bryuschinkin. Bd.2. Kaliningrad, 2005. P. 26-34.
 The argument presented here , bears some resemblance to a line of thought presented by Allison (1983) [1, 115-122]. However, I present the point somewhat differently by relying on textual evidence Allison does not use.
 I do not, then, believe that Leibniz wanted reduce relations to monadic predicates.