ONT Re: Hypostatic And Prescisive Abstraction
HAPA. Note 12
| One branch of deductive logic, of which from the nature of
| things ordinary logic could give no satisfactory account,
| relates to the vitally important matter of abstraction.
| Indeed, the student of ordinary logic naturally regards abstraction,
| or the passage from "the rose smells sweet" to "the rose has perfume",
| to be a quasi-grammatical matter, calling for little or no notice from
| the logician. The fact is, however, that almost every great step in
| mathematical reasoning derives its importance from the fact that it
| involves an abstraction.
| For by means of abstraction, the transitory elements of thought,
| the 'epea pteroenta' [winged words], are made substantive elements,
| as James terms them, 'epea apteroenta' [plucked words].* It thus
| becomes possible to study their relations and to apply to these
| relations discoveries already made respecting analogous relations.
| In this way, for example, operations become themselves the subjects
| of operations.
|* William James, 'Principles of Psychology', vol. 1, p. 243.
| C.S. Peirce, 'Collected Papers', CP 3.642, in dictionary entry for "Relatives",
| J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 447-450.