Part One: that Abstract Ideas are Impossible
(In Three Arguments)
a.) Abstraction is separation
b.) By contraposition, the inseparable cannot be abstracted.
c.) But the impression or idea of line cannot be separated from its definite endpoints.
d.) But if anything could be abstracted, it would be an abstract quantity from a concrete one.
e.) So nothing can be abstracted.
a.) A merely faint and muddled idea that could be confused with its instances is not an abstract one
b.) But all ideas are merely faint impressions (from sec. 1-3)
c.) Therefore there are no abstract ideas.
a.) What is impossible to be understood by a clear and coherent idea in the mind is really impossible.
b.) Therefore, What is absurd for reality outside the mind is absurd for the reality within it.
c.) But abstract existence is impossible for reality outside the mind
d.) Therefore, abstract existence is impossible within the mind.
Part Two: What Supposedly Abstract Ideas Actually Are
(Prologue with Four Explanations)
The putatively abstract idea is particular in its existence, but general in representation. By “general” we mean “we are accustomed to associate it with many”
So what is the basis of this “custom” that makes us associate some idea with many particulars? This is, for Hume, “the only difficulty that can remain on this subject”. His prologue to a proposed solution is fascinating:
The most proper method, in my opinion, of giving a satisfactory explication of this act of the mind, is by producing other instances, which are analogous to it, and other principles, which facilitate its operation. To explain the ultimate causes of our mental actions is impossible.
a.) When things are hard to imagine, we invent symbol systems in order to make them more concrete. No one can visualize a chiliagon, but we can all understand a thousand-sided figure. The symbol is a remedy for the weakness of visualization.
b.) A single idea often sets off a cascade effect of evoking others, like a smell bringing back the idea of childhood, or a word that reminds us of a whole sentence, viz. “four-score” or “unalienable”.
c.) [I simply don’t get what description he is trying to give here, so I’ll just block-quote it]
Thirdly, I believe every one, who examines the situation of his mind in reasoning, will agree with me, that we do not annex distinct and compleat ideas to every term we make use of, and that in talking of government, church, negotiation, conquest, we seldom spread out in our minds all the simple ideas, of which these complex ones are compos’d. ’Tis however observable, that notwithstanding this imperfection we may avoid talking nonsense on these subjects, and may perceive any repugnance among the ideas, as well as if we had a full comprehension of them. Thus if instead of saying, that in war the weaker have always recourse to negotiation, we shou’d say, that they have always recourse to conquest, the custom, which we have acquir’d of attributing certain relations to ideas, still follows the words, and makes us immediately perceive the absurdity of that proposition; in the same manner as one particular idea may serve us in reasoning concerning other ideas, however different from it in several circumstances.
d.) Imagination is a prodigious genius at suggesting fit ideas for our use. It ranges freely over all concrete instances by a power, that we might never be able to explicate. But just because we can’t understand how this power works does not require us to say that it has recourse to something that has no concrete existence, any more than our failure to understand how a jet engine works requires us to say that it has parts with no concrete existence.