Locke's Triangles

One of the most frequently discussed passages from Locke's An Essay Concerning the Human Understanding is that which occurs in IV.vii.9, where he writes:… the Ideas first in the Mind, ‘tis evident, are those of particular Things, from whence, by slow degrees, the Understanding proceeds to some few general ones; which being taken from the ordinary and familiar Objects of Sense, are settled in the Mind, with general Names to them. Thus particular Ideas are first received and distinguished, and so Knowledge got about them: and next to them, the less general, or specifick, which are next to particular. For abstract Ideas are not so obvious or easie to Children, or the yet unexercised Mind, as particular ones. If they seem so to grown Men, ’tis only because by constant and familiar use they are made so. For when we nicely reflect upon them, we shall find, that general Ideas are Fictions and Contrivances of the Mind, that carry difficulty with them, and do not so easily offer themselves, as we are apt to imagine. For example, Does it not require some pains and skill to form the general Idea of a Triangle, for it must be neither Oblique, nor Rectangle, neither Equilateral, Equicrural, nor Scalenon; but all and none of these at once. In effect, it is something imperfect, that cannot exist; an Idea wherein some parts of several different and inconsistent Ideas are put together.I shall not pretend that what Locke is claiming in this passage is wholly clear, nor shall I try to defend the views expressed in it. My intention is to show that what he says here has been widely misinterpreted. It has become common to treat the contents of the passage as aberrant; as presenting a ridiculous variant on his main thesis on abstraction, or that very thesis elaborated with a foolish rhetorical flourish. But what is said in this passage is not something said elsewhere, nor is it an alternative to something said elsewhere. Here, and nowhere else, Locke shows awareness of implications for his doctrine of abstraction, of views he holds about simple ideas.