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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 17:54, 4 May 2009
, 17:54, 4 May 2009→Commentary Note 12.3
===Commentary Note 12.3===
===Commentary Note 12.3===
Peirce next considers a pair of compound logical involutions, stating an equation between them that amounts to a form of associative law:
Peirce next considers a pair of compound involutions, stating an equation between them that is roughly analogous to an associative law:
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<p>(Peirce, CP 3.77).</p>
<p>(Peirce, CP 3.77).</p>
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Converting the relative term <math>\mathit{s}^{(\mathit{l}\mathrm{w})}\!</math> into its set-theoretic equivalent is fairly immediate:
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| <math>\mathit{s}^{(\mathit{l}\mathrm{w})} ~=~ \bigcap_{x \in LW} \operatorname{proj}_1 (S \star x) ~=~ \bigcap_{x \in LW} (S \cdot x)</math>
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