ABSTRACT
The paradigm was mathematical: particular triangles resemble one another precisely, not of course in all respects but 'partially considered', in the particular respect which determines that they are all triangles. Each one of them qua triangle has just what every other one has, and a problem over the boundaries of the class of triangles does not arise for his theory as it does over the boundaries of the class of red things. If we say that all red things have redness in common, 'redness' is not a feature which is precisely the same in each example: it is not a point of precise resemblance. Locke's response to such considerations was to uphold the mathematical paradigm incorporated into his programme for the reform of scientific language. The ideal of precision was thus, like intuitionism, one of the fundamental features of his thought with which the doctrine of abstraction achieved a neat and fully self-conscious fit:
Now because we cannot be certain of the Truth of any general Proposition, unless we know the precise bounds and extent of the Species its Terms stand for, it is necessary we should know the Essence of each Species, which is that which constitutes and bounds it. This, in all simple Ideas and Modes, is not hard to do. For . . . the abstract Idea, which the general Term stands for, being the sole Essence and Boundary, that is or can be supposed, of the Species, there can be no doubt, how far the Species extends, or what Things are comprehended under each Term: which, 'tis evident, are all, that have an exact conformity with the Idea it stands for, and no other.89
