Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller
The text is shown on its own: no facing layer is held for this issue.
The translator’s English as printed (F. Max Müller). The original-language text is not held; names are romanised as the translator printed them.
57^ Discipline of Pure Reason quantities according to their different relations, we represent in intuition according to general rules, every operation which is produced and modified by quantity. Thus when one quantity is to be divided by another, we place the signs of both together according to the form denoting division, etc., and we thus arrive, by means of a symbolical construction in algebra, quite as well as by an ostensive or geometrical construction of the objects themselves in geometry, at results which our discursive knowledge could never have reached by the aid of mere conceptions.
What may be the cause of this difference between two persons, the philosopher and the mathematician, both practising the art of reason, the former following his path according to concepts, the latter according to intuitions, which he represents a priori according to concepts .-* If we remember what has been said [p. 718] before in the Elements of Transcendentalism, the cause is clear. We are here concerned not with analytical propositions, which can be produced by a mere analysis of concepts (here the philosopher would no doubt have an advantage over the mathematician), but with synthetical propositions, and synthetical propositions that can be known a priori. We are not intended here to consider what we are really thinking in our concept of the triangle (this would be a mere definition), but we are meant to go beyond that concept, in order to arrive at properties which are not contained in the concept, but nevertheless belong to it. This is impossible, except by our determining our object according to the conditions either of empirical, or of pure intuition. The former would give us an empirical proposition only, through
Discipline of Pure Reason 577
the actual measuring of the three angles. Such a proposition would be without the character of either generality or necessity, and does not, therefore, concern us here at all. The second procedure consists in the mathematical and here the geometrical construction, by means of which I add in a pure intuition, just as I may do in the empirical intuition, everything that belongs to the schema of a triangle in general and, therefore, to its concept, and thus arrive at general synthetical propositions.
I should therefore in vain philosophise, that is, reflect discursively on the triaogle, without e\er getting beyond the mere definition with which I ought to have begun. There is no doubt a transcendental synthesis, [p. 719] consisting of mere concepts, and in which the philosopher alone can hope to be successful. Such a synthesis, however, never relates to more than a thing in general, and to the conditions under which its perception could be a possible experience. In the mathematical problems, on the contrary, all this, together with the question of existence, does not concern us, but the properties of objects in themselves only (without any reference to their existence), and those properties again so far only as they are connected with their concept.
We have tried by this example to show how great a difference there is between the discursive use of reason, according to concepts, and its intuitive use, through the construction of concepts. The question now arises what can be the cause that makes this twofold use of reason necessary, and how can we discover whether in any given argument the former only, or the latter use also, takes place }
All our knowledge relates, in the end, to possible intui2P
57^ Discipline of Pure Reason tions, for it is by them alone that an object can be given. A concept a priori (or a non-empirical concept) contains either a pure intuition, in which case it can be constructed, or it contains nothing but the synthesis of possible intuitions, which are not given a priori^ and in that case, though we may use it for synthetical [p. 720] and a priori judgments, such judgments can only be discursive, according to concepts, and never intuitive, through the construction of the concept.
There is no intuition a priori except space and time, the mere forms qf phenomena. • A concept of them, as quanta^ can be represented a priori in intuition, that is, can be constructed either at the same time with their quality (figure), or as quantity only (the mere synthesis of the manifold-homogeneous), by means of number. The matter of phenomena, however, by which things are given us in space and time, can be represented in perception only, that is a posteriori. The one concept which a^ priori represents the empirical contents of phenomena is the concept of a thing in general, and the synthetical knowledge which we may have a priori of a thing in general, can give us nothing but the mere rule of synthesis, to be applied to what perception may present to us a posteriori^ but never an a priori intuition of a real object, such an intuition being necessarily empirical.
Synthetical propositions with regard to things in general, the intuition of which does not admit of being given a priori, are called transcendental. Transcendental propositions, therefore, can never be given through a construction of concepts, but only according to concepts a priori. They only contain the rule, according to which we must look empirically for a certain synthetical unity
Discipline of Pure Reason 579
No commentary for this page under the selected tracks.
There is commentary on page 1.