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

concept in any proposition is its being referred to things in general and to things by themselves, while its empirical use refers to phenomena only, that is, to objects of a possible experience.

That the latter use alone is admissible will be clear from the following considerations, [p. 239] What is required for every concept is, first, the logical form of a concept (of thought) in general ; and, secondly, the possibility of an object to which it refers. Without the latter, it has no sense, and is entirely empty, though it may still contain the logical function by which a concept can be formed out of any data.

The only way in which an object can be given to a concept is in intuition, and though a pure intuition is possible a priori and before the object, yet even that pure intuition can receive its object, and with it its objective validity, by an empirical intuition only, of which it is itself nothing but the form.

All concepts, therefore, and with them all principles, though they may be possible a priori, refer nevertheless to empirical intuitions, that is, to data of a possible experience. Without this, they can claim no objective validity, but are a mere play, whether of the imagination or of the understanding with their respective representations. Let us take the concepts of mathematics as an example, and, first, with regard to pure intuitions.

Although such principles as ' space has three dimensions,' ' between two points there can be only one straight line,' as well as the representation of the object with which that science is occupied, may be produced in the mind a priori, they would have no meaning, if we were not able at all times [p. 240] to show their meaning as applied to phenomena (empirical objects).

It is for this reason that an abstract concept is required to be made sensnons, that is, that its correspond196 Transcejidental Analytic 2ing object is required to be shown in intuition, because, without this, the concept (as people say) is without sense, that is, without meaning. Mathematics fulfil this requirement by the construction of the figure, which is a phenomenon present to the senses (although constructed a priori). In the same science the concept of quantity finds its support and sense in number ; and this in turn in the fingers, the beads of the abacus, or in strokes and points which can be presented to the eyes. The concept itself was produced a priori, together with all the synthetical principles or formulas which can be derived from such concepts ; but their use and their relation to objects can nowhere be found except in experience, of which those concepts contain a priori the (formal) possibility only.

That this is the case with all categories and with all the principles drawn from them, becomes evident from the fact that we could not define any one of them (really, that is, make conceivable the possibility of their object),^ without at once having recourse to the conditions of sensibility or the form of phenomena, to which, as their only possible objects, these categories must necessarily be restricted, it being impossible, if we take away [p. 241] these conditions, to assign to them any meaning, that is, any relation to an object, or to make it intelligible to ourselves by an example what kind of thing could be intended by such concepts.

[When representing the table of the categories, we dispensed with the definition of every one of them, because at that time it seemed unnecessary for our purpose, which concerned their synthetical use only, and because entail1 Additions of the Second Edition.