[Arisbe] Re: Peirce Through The Looking Glass

[Jon Awbrey]

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PLG.  Note 47

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| The definition [of the singular description] was one of the many deft contributions
| of Whitehead and Russell's three forbidding volumes of 'Principia Mathematica',
| which appeared in 1910-13.  Their heroic project was to clarify the whole
| intricate structure of classical mathematics by deriving its principal
| concepts, step by step and definition after definition, from a slender
| basis of clear and simple primitive terms, and deriving its principal
| laws pari passu from a few postulates.
|
| Such a project had seemed feasible because of the revolutionary
| advances in logic in the latter half of the nineteenth century,
| at the hands mainly of Gottlob Frege, Charles Sanders Peirce, and
| Giuseppe Peano.  Progress in clarifying basic mathematical concepts
| had already been made by Richard Dedekind, Georg Cantor, and, again
| and especially, Frege and Peano.  But it had remained to Russell
| and Whitehead to organize, refine, and extend these beginnings
| and integrate them into an organic and imposing whole.  The
| economical foundation achieved in 'Principia', and further
| reduced by subsequent logicians, now comprises only the
| truth functions and quantification of elementary logic
| plus the two-place predicate `e` of class membership.
| The whole conceptual conceptual scheme of classical
| mathematics boils down to just that.
|
| Quine, S->S, p. 8-9.
|
| W.V. Quine, 'From Stimulus To Science',
| Harvard University Press, Cambridge, MA, 1995.

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