Dr. Chong-Fuk Lau
Method means the procedure or way for attaining something. Just as every path will lead to its particular destination, what can be attained by a method also depends on what the method is. The development of modern natural science documents a success story of the application of inductive method based on experimental observations. Kant himself does attach great value to developing a method (modus logicus) which is suitable for philosophy, or more precisely, for his transcendental philosophy. He even regards the Critique of Pure Reason as a whole as “a treatise on the method” [B XXII]. Recognizing the importance of designing a proper method for philosophy, Kant dedicates an entire section, Transcendental Doctrine of Method, to this problem, which constitutes the second half of the Critique. Yet, important as it is, the Doctrine of Method has been widely neglected in the Kant literature. This paper, therefore, tries to analyze some key passages of the Doctrine of Method, especially the guidelines offered by Kant for the so-called “transcendental proofs,” in order to review the fundamental concerns and presuppositions of transcendental philosophy.
It is a common conviction among rationalists that mathematics provides a splendid example of how to arrive at rational knowledge with absolute certainty. The success of mathematics leads many a sophisticated mind to attempt to replicate the mathematical method in philosophy. This is demonstrated to the utmost by Spinoza’s Ethics, which is based on a deductive method derived from Euclidean geometry . Kant, however, is of the opinion that the mathematical method, no matter how promising it is, can never be adopted to philosophy because of the fundamental differences between the two disciplines:
Philosophical cognition is rational cognition from concepts, mathematical cognition that from the construction of concepts. But to construct a concept means to exhibit a priori the intuition corresponding to it. … Philosophical cognition thus considers the particular only in the universal, but mathematical cognition considers the universal in the particular, and indeed even in the individual. [7, A 713-4/B 741-2]
The difference between philosophical and mathematical cognition is more fundamental than what is usually believed to be a difference between qualitative and quantitative determinations. Kant suggests that it is primarily a difference in how to gain objective reality of concepts. According to Kant, mathematical cognition is based on the construction of concepts, i.e., the exhibition of a general concept in an individual intuition. It is legitimate to define a mathematical concept as long as it is constructible in the intuition. It does not matter whether something can be found in the empirical intuition that corresponds to what is constructed a priori in the intuition. It is, for instance, legitimate for a mathematician to construct a perfect circle in the pure form of space and to study its properties, even if a perfect circle can never be found in our empirical world.
The objectivity of mathematical construction is grounded on the fact that every empirical object must conform to the pure forms of appearance in space and time, and thus all possible intuitions must also agree with the concepts that are constructed in accordance with these forms. The particularly constructed circle, for example, is a demonstration of certain properties of the universally valid form of pure space. Mathematics has, in this respect, the “freedom” to create its own concepts or objects of cognition as long as the construction fulfills the formal conditions given in pure intuition. With the freedom in using concepts, a system of mathematical propositions can be based on definitions and axioms that are “absolute” in the sense that they are not in need of any further proofs.
Instead of being cognition from the construction of concepts, philosophy is rational cognition from concepts. In contrast to the intuitive nature of mathematical cognition, philosophical cognition is discursive in nature. There is no a priori intuition available which could serve as a basis for the use of concepts; for instance, the question whether every event has a cause cannot be settled by constructing an example in intuition. Philosophers cannot lay claim to knowledge by constructing an object with the concepts at their disposal, and philosophy can never imitate mathematics in establishing a system on the basis of definitions and axioms either. For, to define means to exhibit a concept exhaustively within its bounds, and it is therefore impossible for philosophy to yield absolutely precise definitions. In the case of empirical concepts, one cannot be sure that the object referred to by the concept actually has all the characteristics described by the definition, while, in the case of pure or a priori concepts, it is questionable whether the concept, even if it is clearly and adequately defined, has objective validity in regard to the reality at all. “Philosophy thus,” according to Kant, “has no axioms and can never simply offer its a priori principles as such, but must content itself with justifying their authority through a thorough deduction” [7, A 733-4/B 761-2].
Instead of modeling transcendental philosophy on mathematics or other sciences, Kant’s tries to develop its own methodology. In the section The Discipline of Pure Reason with Regard to its Proofs, Kant proposes three guiding rules for transcendental proofs. The first rule is:
to attempt no transcendental proofs without having first considered whence one can justifiably derive the principles on which one intends to build and with what right one can expect success in inferences from them. [7, A 786/B 814]
The point here concerns the nature of reasoning in transcendental philosophy. It is a rule against dogmatic thinking. Dogmatic disciplines are, according to Kant, those which begin straightforwardly with cognition of objects by applying the concepts they have without first clarifying the objective validity of the concepts and the legitimacy of using them [7, A 712ff./B 740ff.]. In this sense, not only traditional metaphysics but also mathematics is dogmatic in nature. The most important question in the discussions of transcendental philosophy is what we are justified to do with the concepts at our disposal. It must be clarified under what conditions and to what extent the concept in question can be applied. Transcendental proofs are, therefore, essentially self-referential, insofar as they are bound to deal with the very conditions under which the proofs themselves are to be carried out. This point will be covered in more detail later.
“The second peculiarity of transcendental proofs is,” according to Kant, “this: that for each transcendental proposition only a single proof can be found” [7, A 787/B 815]. Once more, this rule is directed primarily against dogmatic metaphysics, which often comes forward with a dozen of proofs, say, for the existence of God. It is asked, if a single valid proof has been found, then what are the others good for? In the case of mathematics or empirical sciences, there can be different ways to prove a proposition, since the proposition is founded on pure or empirical intuitions which can be constructed or given in different ways. Accordingly, a proposition can be justified by any of the grounds which suffices to show the objective validity of the use of the concept. “Every transcendental proposition, however,” as Kant claims, “proceeds solely from one concept, and states the synthetic condition of the possibility of the object in accordance with the concept” [7, A 787/B 815].
In the case of transcendental cognition, it is concerned with the conditions of the possibility of an object. The proof must proceed by showing that the object would not be possible without presupposing the concept in question. It must be shown that the concept is constitutive for the unique set of conditions that alone make the object possible, and that there are no other possible alternatives, since the conditions would otherwise not be necessary. Therefore, a transcendental proof is unique in the sense that it can only be reached by unfolding the unique set of conditions of the possibility of the object. This, however, does not mean that there can only be one way to present or formulate the proof. The uniqueness does not restrict the way of presentation or formulation of the proof to one single scheme. It would, therefore, be overhasty to accuse Kant of violating his own rule by presenting two versions of transcendental deduction of categories in the first and the second of the Critique respectively. In addition to these two rules, Kant suggests that:
The third special rule of pure reason, if it is subjected to a discipline in regard to transcendental proofs, is that its proofs must never be apagogic but always ostensive. [7, A 789/B 817]
An apagogic proof is an argument in the form of modus tollens, i.e., proving a certain proposition to be true by showing that the logical consequences of its opposite are false. An ostensive proof is, by contrast, an argument in the form of modus ponens: it proves a proposition by analyzing the consequences or conditions of that proposition directly. Such a proof has the advantage over an apagogic one that the latter, even if it is flawless, can only show that a proposition is valid, but not why and under what conditions it is so. In other words, it only shows the certainty, but not the comprehensibility of the truth of a proposition, whereas an ostensive proof combines the conviction of the truth with insight into the source of this truth. In terms of persuasiveness, however, the apagogic proof is superior to the ostensive one, for “a contradiction always carries with it more clarity of representation than the best connection, and thereby more closely approaches the intuitiveness of a demonstration” [7, A 790/B 818].
Nevertheless, the reason why the apagogic proof, despite its advantages, is not suitable for transcendental philosophy is the potential error in substituting “that which is subjective in our representations for that which is objective” [7, A 791/B 819]. There is the possibility that one wrongly applies a subjectively originated concept to determine something to which the concept has no objective relevance, which means that the concept may be inapplicable to the object at all. For instance, as shown in the First Antinomy, since it is wrong to assume that the empirical world as a whole can be given in its totality, it is from the very beginning wrong to presuppose that the world must either be finite or infinite. Therefore, refuting the thesis does not prove the antithesis, nor vice versa, for the conditions of employing an apagogic proof are not fulfilled in this circumstance. Nevertheless, this rule should not be over-interpreted. Kant does not claim that the apagogic proof is logically incorrect and totally unfeasible in transcendental philosophy. What is crucial is that one must be cautious enough not to fall into the above-mentioned subreption and ensure the applicability of the concept to the object in question. For this reason, Kant himself also employs numerous apagogic proofs in the Critique, for instance, in the Refutation of Idealism. Nevertheless, the major arguments in the Critique, the transcendental deduction of categories in particular, adopt the ostensive strategy in showing the necessary conditions of possible experience.
Yet, it is doubtful whether these three rules suffice to demarcate a special method or a class of proofs deserving to be called “transcendental.” It can be objected that the rules do not specify any logical property that can distinguish the transcendental method from other forms of argument. However, this objection misses the crucial point of Kant’s analysis which aims at emphasizing the necessity of clarifying what can justifiably be achieved with the concepts at our disposal. Kant does not claim that, with respect to the logical form, there is a clear-cut distinction between “dogmatic” and “transcendental” proofs. The difference is rather in the way they deal with their concepts. Without clarifying the presuppositions and limitations of applying a concept, even if the analysis of the concept is logically flawless, the argument as a whole may still be useless or irrelevant. Therefore, the three rules are not to be understood as “criteria” for a logically distinctive form of arguments that can be called transcendental, but rather as the guiding principles, or we may say, “maxims” against dogmatic reasoning.
Nevertheless, it is true that, without determining the formal characteristics of transcendental proofs, the three rules discussed above do not really explain how such proofs could proceed from premise to conclusion. While mathematics has a priori intuitions to serve as a basis for the synthetic connection of concepts, transcendental philosophy also needs its own guideline in achieving objective synthesis:
In transcendental cognition … this guideline is possible experience. The proof does not show, that is, that the given concept … leads directly to another concept … ; rather it shows that experience itself, hence the object of experience, would be impossible without such a connection. The proof, therefore, had to indicate at the same time the possibility of achieving synthetically and a priori a certain cognition of things which is not contained in the concept of them. [7, A 783/B 811]
But what does Kant mean by “experience” and “possible experience”? Indeed, Kant’s concept of experience differs both from the empiricist and the rationalist conception, maintaining that experience is neither, as the empiricists suggest, a mere aggregate of sensations or impressions, nor, as the rationalists believe, the source of illusion. “Experience consists,” according to Kant, “in the synthetic connection of appearances (perceptions) in a consciousness, insofar as this connection is necessary” [7, B 4. 305]. In other words, experience is not merely a rhapsody of perceptions, but always a structurally connected and ordered presentation of objects, which lays claim to objectivity; that is to say, experience is cognition of objects, or what Kant calls Erfahrungserkenntnis.
This concept of objective experience occupies a crucial position in Kant’s thought; Kant even declares that “the supreme problem of transcendental philosophy is … : How is experience possible?” [7, 275] Unlike Descartes, Kant does not attempt to establish his philosophical system on an Archimedean point, on an allegedly absolutely indubitable foundation. Instead, he begins with the objective reality of experience and explores the conditions for its possibility. The possibility of experience, or possible experience, is indeed the point of departure of transcendental philosophy. The possibility of experience itself does not necessitate any external proofs, since “the possibility of experience is … that which gives all of our cognition a priori objective reality” [7, A 156/B 195]. Without referring to possible experience, a concept would not have any objective reality and thus be nothing but an “empty” concept, regardless of how clear and distinct it is. In this connection, possible experience turns out to be the criteria and reference point of objectivity.
However, it does not mean that the possibility of experience cannot and need not be justified. The peculiarity of the transcendental deduction of categories consists precisely in the fact that the analysis of the necessary conditions of possible experience is on the one hand the proof of the objective reality of categories, but on the other hand, it also serves as a justification for the possibility of experience. Kant himself certainly recognizes this distinctive feature of a transcendental proof. He points out the following requirement for a transcendental proof:
although it must be proved, it is called a principle and not a theorem because it has the special property that it first makes possible its ground of proof, namely experience, and must always be presupposed in this. [7, A 737/ B 765]
The most crucial characteristic of a transcendental proof is that it refers to its own conditions reflectively. Although the possibility of experience must first be presupposed in the proof, this presupposition is precisely what has yet to be justified in the proof. Put differently, the proof justifies the very conditions under which the proof itself is made possible. This peculiar characteristic can be called self-referentiality  and . However, does this not simply lead to a vicious circle? It is, indeed, a circle – but a necessary one. In denying the possibility of imitating the mathematical, axiomatic method in philosophy, Kant rejects the rationalistic project in searching for an absolutely indubitable foundation of knowledge. He states clearly that “since philosophy is merely rational cognition in accordance with concepts, no principle is to be encountered in it that deserves the name of an axiom” [7, A 732/B760]. If there is no ultimate and secure foundation, only two alternatives are left for philosophical knowledge: either it involves an infinite regression, or it is circular. Understanding the fact that an infinite regression would only put aside, but never solve the problem, Kant adopts a method which is, to a certain extent, circular. It is to be noted that a circular method does not necessarily result in a vicious circle. The idea of “hermeneutic circle,” for example, shows us how helpful it can be to view the nature of human understanding by taking into account its circular structure [3, 265].
Indeed the structure of self-referentiality is already implicitly contained in Kant’s concept of “transcendentality,” for transcendental does not simply refer to an ordinary kind of knowledge about objects, but rather a kind of knowledge that deals reflectively with the a priori possibility of knowledge itself. Kant calls “all cognition transcendental that is occupied not so much with objects but rather with our mode of cognition of objects insofar as this is to be possible a priori” [7, A 11-2/B 25]. If the transcendental proof is a proof that aims at “transcendental knowledge,” it must be one that goes back to the conditions of its own operation in justifying a certain conclusion. Accordingly, the transcendental proof is circular, or self-referential, in the sense that proving the conditions for the possibility of using certain concepts must, at the same time, also show how such a proof is possible. Rüdiger Bubner explains:
one should not talk of transcendentality if only an unspecified precondition for knowledge is at stake, nor if only some knowledge is meant which is independent of the empirical and consequently prior to all experience. According to Kant, only that knowledge is transcendental, in which knowledge is thematized concerning its specific possibilities. If this is true, then that knowledge which is called transcendental takes as its object, together with the general conditions of knowledge, the conditions of its own genesis and functioning. [1, 461-462]
The concept of transcendentality is Kant’s answer to dogmatic reasoning. Transcendental reasoning does not rely on any principles which are alleged to be self-evident, but deals with the conditions for knowledge in general as well as for this very reasoning in particular. In contrast to the rationalistic tradition, on the basis of which Kant develops his transcendental philosophy, Kant does not adopt an analytic or deductive method in justifying his position; instead his whole project of justifying the possibility of objective knowledge revolves around possible experience, which on the one hand must be presupposed and on the other has yet to be accounted for in the Critique. The circular structure of this method of reasoning is not merely connected with, but even, according to Heidegger’s interpretation, originates from the essence of possible experience:
The proof consists in showing that the principles of pure understanding are possible through that which they themselves make, through the nature of experience. This is an obvious circle, and indeed a necessary one. The principles are proved by recourse to that whose arising they make possible, because these propositions are to bring to light nothing else than this circularity itself; for this constitutes the essence of experience. [5, 241-242]
It may be helpful to summarize the above discussions from another point of view. Contemporary epistemologists usually distinguish between two possible positions regarding the justification of knowledge, namely between foundationalism and coherentism. It is also widely accepted that almost all traditional philosophers, from Aristotle through Descartes to Kant, are basically foundationalists, whereas Hegel is regarded as the first philosopher who introduces a theory of coherentist epistemology. In the case of Kant, it seems indisputable that the categories established in the Critique together with the principles derived from them are to be taken as foundations for all human knowledge, since it is the categories that determine the formal structure of all possible objects as well as the knowledge of objects.
The Doctrine of Method of the Critique, however, seems to suggest another picture. Kant’s arguments against the mathematical method and the dogmatic reasoning in traditional metaphysics are indeed arguments against foundationalism, for they are clearly directed against the possibility of establishing a philosophical system on certain absolute foundations. Moreover, by showing the necessary circularity, or self-referentiality, of transcendental proofs, Kant does seem to be suggesting a certain form of coherentism that revolves around the possibility of experience. Admittedly, a much more detailed discussion would be required in order to support the interpretation of Kant as a coherentist, but the analysis of Kant’s Doctrine of Method given above at least shows that the traditional interpretation of Kant is due for reconsideration.
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This article was first published in collection of articles «Kant zwischen West und Ost»:
Lau, Chong-Fuk. The Problem of Method in Transcendental Philosophy// Kant zwischen West und Ost. Zum Gedenken an Kants 200. Todestag und 280. Geburtstag. Hrsg. Von Prof. Dr. Wladimir Bryuschinkin. Bd.1. Kaliningrad, 2005. S.189 – 199.
 References to Kant’s Critique of Pure Reason are to the first and second edition, cited in the standard way with the abbreviation “A” and “B” respectively. All other references to Kant’s texts are to the Akademie-Ausgabe , cited with the abbreviation “Ak.” followed by the volume and page number. English translations are from  and .
 Our main concern here is not Kant’s philosophy of mathematics, but to clarify the philosophical method by comparing it with the mathematical one. A detailed analysis of Kant’s conception of mathematics can be found in .
This is the objection raised by Moltke Gram in his detailed study of transcendental arguments .
 In the current context, Kant employs the two terms “possible experience” and “possibility of experience” synonymously [10, 90].
 See additionally another passage which uses the term “possible experience” instead of the “possibility of experience”: “It is possible experience alone that can give our concepts reality; without it, every concept is only an idea, without truth and reference to an object” [7, A 489/B 517].
 It is to be noted that there is an essential distinction between “possible” and “actual experience.” In a passage criticizing Hume, Kant points out that Hume “confused going beyond the concept of a thing to possible experience … with the synthesis of the objects of actual experience, which is of course always empirical” [7, A 766/B 794]. While particular and contingent determinations of objects are given in actual experience, the term “possible experience” does not refer to any single instance of experience that we encounter in the empirical world, but the structured unity of experience as a whole. Accordingly, a proof guided by “possible experience” is not empirical in nature.
 See additionally this passage in the Prolegomena: “The word transcendental … with me never signifies a relation of our cognition to things, but only to the faculty of cognition” [7, B. 4. 293].