Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller
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The translator’s English as printed (F. Max Müller). The original-language text is not held; names are romanised as the translator printed them.
586 Discipline of Pure Reason an arbitrary synthesis that can be constructed a priori. It follows, therefore, that mathematics only can possess definitions, because it is in mathematics alone that we represent a priori in intuition the object which we think, and that object cannot therefore contain either more or less than the concept, because the concept of [p. 730] the object was given by the definition in its primary character, that is, without deriving the definition from anything else. The German language has but the one word Erkldrung (literally clearing up) for the terms exposition, explication, declaration, and definition ; and we must not therefore be too strict in our demands, when denying to the different kinds of a philosophical clearing up the honourable name of definition. What we really insist on is this, that philosophical definitions are possible only as expositions of given concepts, mathematical definitions as constructions of concepts, originally framed by ourselves, the former therefore analytically (where completeness is never apodictically certain), the latter synthetically. Mathematical definitions make the concept, philosophical definitions explain it only. Hence it follows, a. That we must not try in philosophy to imitate mathematics by beginning with definitions, except it be by way of experiment. For as they are meant to be an analysis of given concepts, these concepts themselves, although as yet confused only, must come first, and the incomplete exposition must precede the complete one, so that we are able from some characteristics, known to us from an, as yet, incomplete analysis, to infer many things before we come to a complete exposition, that is, the definition of the concept. In philosophy, in fact, the defini- [p. 731] tion in its complete clearness ought to conclude rather
Discipline of Pure Reason 587
than begin our work ; ^ while in mathematics we really have no concept antecedent to the definition by which the concept itself is first given, so that in mathematics no other beginning is necessary or possible.
b. Mathematical definitions can never be erroneous, because, as the concept is first given by the definition, it contains neither more nor less than what the definition wishes should be conceived by it. But although there can be nothing wrong in it, so far as its contents are concerned, mistakes may sometimes, though rarely, occur in the form or wording, particularly with regard to perfect precision.
Thus the common definition of a circle, that it is a curved line, every point of which is equally distant from one and the same point (namely, the centre), is faulty, [p. 732] because the determination of curved is introduced unnecessarily.
For there must be a particular theorem, derived from the definition, and easily proved, viz. that every line, all points of which are equidistant from one and the same point, must be curved (no part of it being straight). Analytical definitions, however, may be erroneous in many respects, either by introducing characteristics which do not really exist in the concept, or by lacking that completeness which is essential to a definition, because
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