Scott Stapleford. Kant’s Transcendental Arguments and Conditions of Instantiation

In this paper I ask what a transcendental argument is for Kant. I will argue that a transcendental argument seeks to connect two concepts by disclosing their joint conditions of instantiation in a possible experience. One of my goals is to explain what that means.

There is a large body of literature on transcendental arguments in which Kant’s work is given pride of place.[1] But this literature lies largely outside the mainstream of Kant scholarship. As a rule, commentators in this offshoot field have been very selective in their use of Kant. They typically try to find historical support for some up-to-date conception of what a transcendental argument is by isolating one of Kant’s famous proofs and then drawing parallels with the position that they support. A shortcoming of this anti-systematic approach is that it has left relatively unexplored Kant’s own account of his procedure as set out explicitly in the second major division of the Critique under the heading, ‘The Discipline of Pure Reason’.

In my view, this neglect is unwarranted, since the chapter contains several canonical sounding descriptions of the transcendental method in philosophy that could be turned to good account in interpreting one or more of the difficult proofs in the Analytic of Principles. So I propose that we take a look at Kant’s own sketch of his proof procedure and then try to apply it to the second Analogy of Experience for the sake of illustration. There is a catch to this plan, however, in that many of the statements Kant makes in the Discipline have all the appearance of outright inconsistency. A second goal is therefore to remove these apparent contradictions.

Let’s make a start by considering the principal contrast that interests Kant in this chapter. Kant opposes the philosophical or transcendental method to the method that pure reason employs in mathematics. “Philosophical knowledge,” he says, “is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts” [3, A 713/B 741]. Alternatively, philosophy is “the discursive employment of reason in accordance with concepts,” mathematics “its intuitive employment by means of the construction of concepts” [3, A 719/B 747].

To construct a concept, Kant tells us, “means to exhibit a priori the intuition which corresponds to the concept” [3, A 713/B 741]. This is really just an elaborate way of saying that mathematics makes or produces particular objects instantiating its concepts in the imagination. And since the imagination is an “intuitive” faculty (meaning a capacity to represent particular objects), mathematics is thus dependent upon intuition: “mathematics can achieve nothing by concepts alone but hastens at once to intuition, in which it considers the concept in concreto” [3, A 715/B 743]. Furthermore, since mathematics is an a priori science, the intuition it works with must also be a priori. In its constructive proofs, therefore, mathematics neither starts out from concepts given a priori, nor acquires them empirically, but takes some stipulated concept and shows that it can only be constructed in accordance with the universal rules of intuitive representation (in space and time).

Compare this with the method of proof in philosophy. Transcendental, that is to say, properly philosophical propositions are synthetic a priori [3, A 722/B 750]. And synthesis, so Kant, requires intuition: “If we are to judge synthetically in regard to a concept, we must go beyond this concept and appeal to the intuition in which it is given” [3, A 721/B 749]. Now mathematics has no difficulty in getting on synthetically, for its concepts are constructed in pure intuitions (space and time), which impose their own (necessary) structure on the objects thus constructed, thereby giving them something that belongs to them synthetically and yet necessarily. There is thus a vast supply of intuitive content (in the imagination) from which synthetic principles are easily derived.

But philosophy, a conceptual science, appears to have no intuitive resources: “While philosophical knowledge must do without this advantage [the advantage of intuition], inasmuch as it has always to consider the universal in abstracto (by means of concepts) [durch Begriffe] ” [3, A 734/B 762]. So philosophy both requires intuition and has to do without it, and thus the philosophical method seems to be out of keeping with itself.[2] Unfortunately, the textual difficulties do not stop there.

Here are some of the troubling statements. “Philosophy,” Kant says at one point, “confines itself to universal concepts” [3, A 715/B 743]. Then later we get, “…philosophy is simply what reason knows by means of concepts” [3, A 732/B 760]. Similarly, in its pure employment reason proceeds “by means of mere concepts” [3, A 738/B 766]. Particularly striking is Kant’s claim that philosophical proofs “may be conducted by the agency of words alone [nur durch lauter Worte] (the object in thought)” (3, A 735/B 763), which might touch off the idea that criticism can be compared, even reduced, to linguistic analysis. And Kant occasionally portrays the principles of the understanding in terms that suggest analyticity sooner than the synthetic a priori. For instance, after running through a list of the questions addressed by each of the principles he sums up thus: “[they] one and all belong altogether to knowledge obtained by reason from concepts, such knowledge being termed philosophical” [3, A 724/B 752]. And at [3, A 733/B 761] Kant refers to the proposition ‘everything which happens has a cause’ as a “synthetic principle derived from concepts alone” (although it is not immediately certain). The qualifier ‘synthetic’ is confusing here since the principle is allegedly “derived from concepts alone.” Finally, Kant says quite clearly that the Axiom of Intuition “is itself no more than a principle derived from concepts” [3, A 733/B 762].

Now for the other side of the coin. Take this starkly contrasting statement from the Progress of Metaphysics: “By mere concepts we can produce no synthetic a priori propositions” [5, 416]. Has Kant changed his view? Not a jot. Just look at what he says about the principle of the second Analogy in the very text I have just been quoting: “Thus no one can acquire insight into the proposition that everything which happens has its cause, merely from the concepts involved” [3, A 737/B 765]. And again, “I cannot obtain knowledge of such a principle directly and immediately from the concepts alone” [3, A 733/B 761]. Likewise, in the ‘General Note on the System of the Principles’, he says, “no synthetic proposition can be made from mere categories,” and, where intuition is lacking, “there is nothing which can enable us to go out beyond a given concept, and to connect another with it” [3, B 289], the connecting of concepts being in my view the primary function of transcendental arguments. Kant concludes: “No one, therefore, has ever yet succeeded in proving a synthetic proposition merely from pure concepts of the understanding—as, for instance, that everything which exists contingently has a cause” [3, B 289]. So while the first set of claims has philosophy restricted in its proofs to bare concepts, the second set tells us that it cannot even make a start with its special task of furnishing synthetic a priori principles if it does not take a step outside of the conceptual circle. The question, therefore, is where it can step, if not to intuition.

In order to clear some of the fog I think we need to introduce another distinction that Kant makes, this time between the genuine transcendental proofs of critical philosophy and what he disparagingly calls the ‘dogmatic’ proofs of traditional metaphysics.

Kant defines a dogma as follows: “A synthetic proposition directly derived from concepts is a dogma” [3, A 736/B 764]. And he believes that synthetic judgments directly derived from concepts are one and all specious: “Now in the whole domain of pure reason, in its merely speculative employment, there is not to be found a single synthetic judgment directly derived from concepts” [3, A 736/B 764]. So the difference between the two kinds of philosophical proof will have to be that while the conclusions of dogmatic proofs are derived directly from concepts, transcendental propositions (the conclusions of transcendental arguments) are not.

This is in fact Kant’s view. Consider what he calls the ‘criterion’ of the possibility of transcendental proofs: “This criterion consists in the requirement that proof should not proceed directly to the desired predicate but only by means of a principle that will demonstrate the possibility of extending our given concept in an a priori manner” [3, A 785/B 813]. Transcendental proofs are only cogent if there is a non-conceptual route from the subject concept to the predicate concept, and the proof must actually show us how such connection is possible (vide [3, A 789/B 817], third rule).

The non-conceptual stuff that binds the two concepts is possible experience:

In transcendental knowledge, so long as we are concerned only with concepts of the understanding, our guide is possible experience [die mögliche Erfahrung]. Such proof does not show that the given concept (for instance, of that which happens) leads directly to another concept (that of a cause); for such a transition would be a saltus which could not be justified. The proof proceeds by showing that experience itself, and therefore the object of experience, would be impossible without a connection of this kind [3, A 783/B 811]—I have changed Kemp Smith’s ‘possibility of experience’ to ‘possible experience’.

It is difficult to say exactly how concepts get connected indirectly through possible experience. A superficial explanation might be that we make the connection by reflecting on the conditions that make experience in accordance with a certain concept possible. But that is really unhelpful, for what is it that we are reflecting on here? It cannot simply be the meanings of the concepts involved, nor can it be an intuition in which the objects corresponding to them are actually present.

For Kant, there is one, and only one way to get from a given concept to an empirical concept completely a priori. The object of a philosophical concept is not given a priori. The concept itself has a meaning that makes up its (very slender) content. So if any proof is possible, it can only proceed by investigating the conditions of presenting an object answering to that content. In other words, transcendental proofs seek to uncover the conditions of instantiating certain concepts. As Kant puts it: “In the case of transcendental propositions…we start always from one concept only, and assert the synthetic condition of the possibility of the object in accordance with this concept [3, A 787/B 815]”. The proof specifies what it would be like for an object to fall under the given concept: “[It] can contain nothing more than the determination of an object in general in accordance with this one single concept” [3, A 788/B 816]. So transcendental proofs do not investigate simply the meanings of terms, but the conditions of their application.

The third thing that is needed to connect the concepts in a philosophical proof is called indifferently the ‘possibility of experience’ [3, A 217/B 264] or ‘possible experience’ [3, A 783/B 811]. I don’t think that Kant is talking about some concept, ‘possibility of experience’, but is talking rather about the possibility of experiencing an object corresponding to some concept. In other words, the proof does not analyse the meaning of the phrase ‘possibility of experience’ to see if the concept ‘event’, for instance, is analytically contained in it.

Instead, it begins from a concept that is given a priori and considers the possibility of experiencing an object falling under it, or, as I am expressing it here, the possibility of instantiating it. The only way to do that, I suggest, is to try to supply the concept with an intuitive content, that is to say, to give it a ‘possible intuition’ in order to see if it is the sort of thing that can be represented in the spatio-temporal world. So supplying a concept with an intuitive content shows that and how it can be instantiated in our experience.

If it turns out that a condition of instantiating one concept is the simultaneous application or instantiation of another, and if, further, this can be established through an examination of a merely possible experience—that is, the representation of a possible object without the actual presence of that object in sensation—then Kant will have found a way to connect a given concept and an acquired concept a priori and synthetically. The proof will be a priori, since no perception of an actually present object is required, and it will be synthetic because it goes beyond the intension of a concept to its possible object and finds a connection there rather than in the concept itself. We try to abstract from the empirically contingent features of a sensible image and consider only those features that pure intuition would impose on any object corresponding to the concept. So without the object actually needing to be given in a perception, the transcendental proof considers the a priori conditions of its presentation.

Now that we have an outline of a theory let’s test how it works when applied to the second Analogy. There are two basic types of perceptual sequences. In the first, one perception is thought of as following upon another in a chance order. We think that the order of the sequence could just as well have been reversed. In the other type of sequence, the order is not thought of as reversible. The perception that follows could not, so we think, have preceded the first. This second type of sequence, the one conceived as necessarily one-directional, represents what we call an event. If we think that a sequence of perceptions could have been inverted, then we do not think that that sequence counts as the representation of an event. Put positively, the sequence gives an instance of the concept ‘event’ only insofar as we think that it is ordered objectively.

But a sequence of perceptions thought of as ordered is really nothing but a sequence conceived as representing a causal succession. That is what the schema judgment tells us.[3] So the perceptual sequences we think of as representing events just are those sequences we think of as representing causal series. The proof, in other words, is supposed to show that where the concept ‘event’ applies, then necessarily, so does the concept ‘cause’ (and contrariwise). That means that the second Analogy proves both that the application of the concept ‘event’ requires the application of the concept ‘cause’ and that the application of the concept ‘cause’ requires the application of the concept ‘event’: The two converge in the object.

How does Kant prove this? I’m going to put this bluntly: He proves it by telling us to think about the difference between perceiving, for instance, the sides of a house successively and perceiving a ship moving down stream. It is this example, I believe, or an example of this type—which we picture—that allows us to grasp the difference between subjective and objective succession. We try to represent to ourselves an event, and we recognize that it cannot be done without introducing a conception of determinateness, for without thinking the order of perceptions as determinate, there is no phenomenological difference between events and non-events. As Kant puts it, “the apprehension of an event is not yet thereby distinguished from other apprehensions” [3, A 192/B 237].

But bringing a conception of determinateness to the object is equivalent to conceiving it as subject to a causal rule. “This,” he tells us, “is the sole possible ground of proof; for the event, in being represented, has objective validity, that is, truth, only in so far as an object is determined for the concept by means of the law of causality” [3, A 788/B 816—emphasis added]. The representation of an event has ‘objective validity’—that is, is distinguished from a non-event or merely subjective sequence—just insofar as it is thought of as being ordered (again, not just having an order, but being ordered in such a way that the sequence couldn’t have been reversed).

This conceptual criterion for representing events confronts us as it were in the possible object. In trying to envision a perceptual sequence that we would be willing to call the representation of an event, we are forced to recognize that this particular conception of the possible object (as an event) likewise—or equivalently—commits us to a conception of it in terms of causality (as ordered). This recognition of course presupposes that we have already made the schema judgment that gives us the temporal translation of the pure concept ‘cause’. And we grasp the conceptual difference between objective and subjective sequences in an example with sensory content (see [3, A 715/B 743]). ‘Cause’, as a pure concept, connotes “something from which we can conclude to the existence of something else” [3, A 243/B 301]. But as a rule for organizing sense data—that is, as applied to objects of experience—it is tantamount to the imposition of a determinate order on perceptions, which is the very criterion for distinguishing events from non-events.

That perceptual sequences of the type ‘event’ represent a determinate order in the object is not an intuitive quality that they bear—transcendental proofs are not demonstrations, after all (see [3, A 734/B 762]). Rather, in reflecting on the possibility of instantiation we notice a conceptual difference between one type of sensible image and another (the kind that we think counts as the representation of an event and the kind that we do not think counts as the representation of an event). What I am in fact doing in attempting to represent a possible object for the concept ‘event’ is merely identifying my own way of conceiving or thinking about events, not my manner of intuiting them.

That means I don’t have to check every event to see, literally, if it represents a causal order. All Kant wants to say is that we cannot think of a perceptual sequence as the apprehension of an event without also thinking of it as representing a causal order. And in a sense all the proof does is prompt us to try it. It’s not that I find I am unable in this case to represent an event without applying the concept ‘cause’ and cannot therefore be completely certain about any others. I am made aware by representing possible objects that this is just what I mean by an event’s taking place in time and space. So it is not unfair to say that transcendental proofs are concerned with the extensional meanings of certain cognitively fundamental concepts. And that is why we need to consult possible intuitions or sensible images, which take us beyond connotations to the conditions of instantiation. The use of possible intuitions is what makes the proof synthetic. It also shifts the point of convergence away from the concepts and into their objects. They overlap in our experience, but not in themselves.

I want to finish by pointing out an architectonic bonus of this interpretation. On the account developed here, the conclusions of transcendental arguments will serve to undercut dogmatism and empiricism at one stroke, and the transcendental method will thus contain an implicit critique of the dogmatic and empirical methods. This is something that is clearly in line with Kant’s programmatic concerns. Here is what I mean.

The fact that the a priori concept ‘cause’ is tied through intuition to the empirical concept ‘event’ as a condition of its instantiation means that there can be no dogmatic or non-experiential use of the a priori concept (in theoretical philosophy, at any rate). But the fact that the empirical concept ‘event’ is also tied by conditions of instantiation to the a priori concept ‘cause’ means that there is no experience of events that lacks an a priori element. So empiricism is defeated in that an empirical concept that is fundamental to our experience is shown to depend for its instantiation upon the prior application of some a priori concept. And dogmatism is defeated in that a traditional philosophical concept is shown to be applicable only in conjunction with a corresponding empirical concept in sensory intuition.

Since the method described in the Discipline of Pure Reason is apparently meant to be a general account of what Kant is doing in the Analytic of Principles, we can say that each proof in the Analogies of Experience counts simultaneously as an argument against the two main ‘non-critical’ options in philosophy, and that Kant’s method is therefore precisely adapted to his dialectical aims.


1. Allison H. Kant’s Transcendental Idealism: An Interpretation and Defense. New Haven: Yale University Press, 1983.

2. Bieri P., Horstmann R., and Krüger L. (eds.) Transcendental Arguments and Science: Essays in Epistemology. Dordrecht: D. Reidel, 1979.

3. Kant I. Gesammelte Schriften (Akademie-Ausgabe). Berlin: de Gruyter Verlag, 1900 ff.

4. Kant I. Critique of Pure Reason. St. Martin’s Press, New York. 1929.

5. Kant I. Theoretical Philosophy after 1781. New York: Cambridge University Press, 2002.

6. Rohs P. Immanuel Kant: Kritik der reinen Vernunft // Die Disziplin der reinen Vernunft, 1. Abschnitt / Ed. G. Mohr and M. Willaschek. Akademie Verlag. Berlin, 1998.

7. Schaper E., Vossenkuhl W. (eds.) Bedingungen der Möglichkeit: ‘Transcendental Arguments’ und transzendentales Denken. Stuttgart: Klett-Cotta, 1984.

8. Schaper E. Reading Kant: New Perspectives on Transcendental Arguments and Critical Philosophy. New York: Basil Blackwell, 1989.

9. Stern R. Transcendental Arguments: Problems and Prospects. Oxford University Press, Oxford. 1999.

10. Stern R. Transcendental Arguments and Scepticism: Answering the Question of Justification. Oxford University Press, Oxford. 2000.

This article was firstly published in collected articles “Kant zwischen West und Ost” (2005):

Stapleford, Scott. Kant’s Transcendental Arguments and Conditions of Instantiation// 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. 74-82.

[1] See [9], [10] for some of the newest literature and for extensive bibliographies. Also relevant are [7], [8] and [2]

[2] Rohs, has identified this problem. [6, 557]


[3] ‘Schema judgment’ is Allison’s term for “a judgment that asserts that a certain schema pertains to, or is the sensible expression of, a certain category.” [1, 185]