## 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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