Peirce’s 1870 “Logic Of Relatives” • Selection 12

On to the next part of §3. Application of the Algebraic Signs to Logic.

The Sign of Involution

I shall take involution in such a sense that x^y will denote everything which is an x for every individual of y.   Thus \mathit{l}^\mathrm{w} will be a lover of every woman.   Then (\mathit{s}^\mathit{l})^\mathrm{w} will denote whatever stands to every woman in the relation of servant of every lover of hers;   and \mathit{s}^{(\mathit{l}\mathrm{w})} will denote whatever is a servant of everything that is lover of a woman.   So that

(\mathit{s}^\mathit{l})^\mathrm{w} ~=~ \mathit{s}^{(\mathit{l}\mathrm{w})}.

(Peirce, CP 3.77)

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One Response to Peirce’s 1870 “Logic Of Relatives” • Selection 12

  1. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

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