Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

1 Philosophy swarms with faulty definitions, particularly such as contain some true elements of a definition, but not all. If, therefore, it were impossible to use a concept until it had been completely defined, philosophy would fare very ill. As, however, we may use a definition with perfect safety, so far at least as the elements of the analysis will carry us, imperfect definitions also, that is, propositions which are not yet properly definitions, but are yet true, and, therefore, approximations to a definition, may be used with great advantage. In mathematics definitions belong ad esse, in philosophy ad melius esse. It is desirable, but it is extremely difficult to construct a proper definition. Jurists are without a definition of right to the present day.

588 Discipline of Pure Reason we can never be quite certain of the completeness of our analysis. It is on these accounts that the method of mathematics cannot be imitated in the definitions of philosophy.

II. Of Axioms. These, so far as they are immediately certain, are synthetical principles a priori. One concept cannot, however, be connected synthetically and yet immediately with another, because, if we wish to go beyond a given concept, a third connecting knowledge is required ; and, as philosophy is the knowledge of reason based on concepts, no principle can be found in it deserving the name of an axiom. Mathematics, on the other hand, may well possess axioms, because here, by means of the construction of concepts in the intuition of their object, tlie predicates may always be connected a priori and immediately ; for instance, that three points always lie in a plane. A synthetical principle, on the contrary, made up of concepts only, can never be immediately certain, [p. 733] as, for example, the proposition that everything which happens has its cause. Here I require something else, namely, the condition of the determination by time in a given experience, it being impossible for me to know such a principle, directly and immediately, from the concepts. Discursive principles are, therefore, something quite different from intuitive principles or axioms. The former always require, in addition, a deduction, not at all required for the latter, which, on that very account, are evident, while philosophical principles, whatever their certainty may be, can never pretend to be so. Hence it is very far from true to say that any synthetical proposition of pure and transcendental reason is so evident (as people sometimes emphatically maintain) as the statement that twice

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two are four. It is true that in the Analytic, when giving the table of the principles of the pure understanding, I mentioned also certain axioms of intuition ; but the principle there mentioned was itself no axiom, but served only to indicate the principle of the possibility of axioms in general, being itself no more than a principle based on concepts. It was necessary in our transcendental philosophy to show the possibility even of mathematics.

Philosophy, therefore, is without axioms, and can never put forward its principles a priori with absolute authority, but must first consent to justify its claims by a thorough deduction, [p. 734] III. Of Demonstrations. An apodictic proof only, so far as it is intuitive, can be called demonstration. Experience may teach us what is, but never that it cannot be otherwise. Empirical arguments, therefore, cannot produce an apodictic proof.

From concepts a priori, however (in discursive knowledge), it is impossible that intuitive certainty, that is, evidence, should ever arise, however apodictically certain the judgment may otherwise seem to be. Demonstrations we get in mathematics only, because here our knowledge is derived not from concepts, but from their construction, that is, from intuition, which can be given a priori, in accordance with the concepts.

Even the proceeding of algebra, with its equations, from which by reduction both the correct result and its proof are produced, is a construction by characters, though not geometrical, in which, by means of signs, the concepts, particularly those of the relation of quantities, are represented in intuition, and (without any regard to the heuristic method) all conclusions are secured against errors by submitting each of them to intuitive evidence. PhilosophSgo Disciplme of Pure Reason