Re: Hypostatic And Prescisive Abstraction

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HAPA.  Note 12

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| 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.

Incidental Musement:

http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Hom.+Il.+1.172

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