Hume and Abstract General Ideas

17. HUME AND ABSTRACT GENERAL IDEAS In his discussion of abstract ideas in the Treatise, Hume offers what "...may... be thought... a plain dilemma, that decides concerning the nature of those abstract ideas..." He states the dilemma in these words: The abstract idea of a man represents men of all sizes and all qualities; which 'tis concluded it cannot do, but either by representing at once all possible sizes and all possible qualities , or by representing no particular one at all. Now it having been esteemed absurd to defend the former proposition, as implying an infinite capacity in the mind, it has been commonly infer'd in favour of the latter; and our abstract ideas have been suppos'd to represent no particular degree either of quality or quantity. (T, 1,1,7, ?.18) However, with respect to this dilemma, Hume says: But that this inference is erroneous , I shall endeavor to make appear, first , by proving, that 'tis utterly impossible to conceive any quantity or quality, without forming a precise notion of its degrees: And secondly by showing, that tho' the capacity of the mind be not infinite, yet we can at once form a notion of all possible degrees of quantity and quality, in such a manner at least, as, however imperfect , may serve all the purposes of reflexion and conversation. (T, 1,1,7, p. 18) The second item Hume claims he is about to prove is aimed at the first disjunct of the above-stated dilemma; more specifically, it is aimed at the claim that (1) An abstract idea (e.g. , of a man) represents all possible degrees of quantity and quality (in men) only if the human mind is infinite in capacity. To show that (1) is false, Hume offers his own positive account of how ideas which are particular in nature may nevertheless be general in representation, even though the mind's capacity is finite. The first item Hume sets out to prove is aimed at the second disjunct, and conclusion, of the dilemma; it is aimed, that is, at 18. (2)Abstract ideas represent no particular degree of either quantity or quality. In this paper I will be concerned solely with Hume's attack on (2); it is this attack in which Hume says I "place my chief confidence." (T, I, I, 7, p. 24) I_ As stated, (2) is ambiguous, since it might be taken to mean that abstract ideas fail to represent altogether, or that they fail to represent any quantity or quality however construed. But, I believe, Hume means neither of these; he means, instead, that (2a) Abstract ideas represent non-particular, indeterminate degrees of quantity or quality. Now recall that Hume tries to refute (2a) by establishing, as he says, that (3)It is impossible to conceive any quantity or quality without forming a precise notion of its degrees. But how, by establishing (3) , would Hume thereby refute or aid in the refutation of (2a)? And, for that matter, how does he support (3)? Hume's case for (3) consists of three arguments, the respective conclusions of which are most pertinent here. He concludes his first argument by saying that (4)...the general idea of a line .. .has in its appearance in the mind a precise degree of quantity and quality. (T, 1,1,7, p. 19) The conclusion of the second argument is this : (5)An idea is a weaker impression; and as a strong impression must necessarily have a determinate quantity and quality, the case must be the same with its copy or representative.(T, 1,1,7, p. 19) 19. and of the third it is this: (6)Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, tho' the application of it in our reasoning be the same, as if it were universal.(T, 1,1,7, p. 20) Construed in a fully general way, these conclusions assert that (7)Each idea is determinate with respect to öegree of) quantity and quality. But notice that (7) is not equivalent to, and does not obviously imply, (3). Hence, Hume...