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

of Empirical

Thought

in General.

I have chosen these names not unadvisedly, so that the difference with regard to the evidence and the application of those principles should not be overlooked. We shall soon see that, both with regard to the evidence and the a priori determination of phenomena according to the categories of quantity and quality (if we attend to the form of them only) their principles differ considerably from those of the other two classes, inasmuch as the [p. 162] former are capable of an intuitive, the latter of a merely discursive, though both of a complete certainty. I shall therefore call the former fnathematical, the latter dynamical principles.^ It should be observed, however, that I do not speak here either of the principles of mathematics, or of those of general physical dynamics, but only of the principles of the pure understanding in relation to the internal sense (without any regard to the actual representations given in it). It is these through which the former become possible, and I have given them their name, more on account of their application than of their contents. I shall now proceed to consider them in the same order in which they stand in the table.

^ Here follows in the Second Edition, Supplement XV.

Transcendefital Analytic 133

p. 1

Principle of the Pure Understanding •

*A11 Phenomena are, with reference to their intuition, extensive quantities ']

I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, and therefore necessarily preceded by it. I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, start- [p. 163] ing from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all portions of time and their addition, a definite quantity of time. As in all phenomena pure intuition is either space or time, every phenomenon, as an intuition, must be an extensive quantity, because it 'can be known in apprehension by a successive synthesis only (of part with part). All phenomena therefore, when perceived in intuition, are aggregates (collections) of previously given parts, which is not the case with every kind of quantities, but with those only which are represented to us and apprehended as extensive.

On this successive synthesis of productive imagination in elaborating figures are founded the mathematics of extension with their axioms (geometry), containing the con1 Here follows, in the later Editions, Supplement XVI.

134 Transcendental Analytic ditions of sensuous intuition a priori^ under which alone the schema of a pure concept of an external phenomenal appearance can be produced ; for instance, between two points one straight line only is possible, or two straight lines cannot enclose a space, etc. These are the axioms which properly relate only to quantities {quanta^ as such.

But with regard to quantity {qiLantitas), that is, with regard to the answer to the question, how large something may be, there are no axioms, in the proper [p. 164] sense of the word, though several of the propositions referring to it possess synthetical and immediate certainty {indemonstj'abiliay The propositions that if equals be added to equals the wholes are equal, and if equals be taken from equals the remainders are equal, are really analytical, because I am conscious immediately of the identity of my producing the one quantity with my producing the other ; axioms on the contrary must be synthetical propositions a priori. The self-evident propositions on numerical relation again are no doubt synthetical, but they are not general, like those of geometry, and therefore cannot be called axioms, but numerical formulas only. That 7 + 5 = 12 is not an analytical proposition. For neither in the representation of 7, nor in that of 5, nor in that of the combination of both, do I think the number 12. (That I am meant to think it in the addition of the two, is not the question here, for in every analytical proposition all depends on this, whether the predicate is really thought in the representation of the subject.) Although the proposition is synthetical, it is a singular proposition only. If in this case we consider only the synthesis of the homogeneous unities, then the synthesis can here take place in one way only, although afterwards

Transcendental Analytic 135