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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 15:32, 20 April 2009
, 15:32, 20 April 2009→Selection 12
==Selection 12==
==Selection 12==
===The Sign of Involution===
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
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<p>I shall take involution in such a sense that <math>x^y\!</math> will denote everything which is an <math>x\!</math> for every individual of <math>y.\!</math></p>
<p>I shall take involution in such a sense that ''x''<sup>''y''</sup> will denote everything which is an ''x'' for every individual of ''y''.</p>
<p>Thus</p>
<p>Thus</p>
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| align="center" | <math>\mathit{l}^\mathrm{w}\!</math>
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<p>will be a lover of every woman.</p>
<p>will be a lover of every woman.</p>
<p>Then</p>
<p>Then</p>
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| align="center" | <math>(\mathit{s}^\mathit{l})^\mathrm{w}\!</math>
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<p>will denote whatever stands to every woman in the relation of servant of every lover of hers;</p>
<p>will denote whatever stands to every woman in the relation of servant of every lover of hers;</p>
<p>and</p>
<p>and</p>
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| align="center" | <math>\mathit{s}^{(\mathit{l}\mathrm{w})}\!</math>
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<p>will denote whatever is a servant of everything that is lover of a woman.</p>
<p>will denote whatever is a servant of everything that is lover of a woman.</p>
<p>So that</p>
<p>So that</p>
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| align="center" | <math>(\mathit{s}^\mathit{l})^\mathrm{w} ~=~ \mathit{s}^{(\mathit{l}\mathrm{w})}.</math>
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<p>(C.S. Peirce, CP 3.77).</p>
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<p>(Peirce, CP 3.77).</p>
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