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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 01:44, 9 April 2009
, 01:44, 9 April 2009→The Signs for Multiplication (cont.)
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{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
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<p>The sum <math>x + x\!</math> generally denotes no logical term. But <math>{x,}_\infty ~+~ {x,}_\infty</math> may be considered as denoting some two <math>x\!</math>'s.</p>
<p>The sum <math>x + x\!</math> generally denotes no logical term. But <math>{x,}_\infty + \, {x,}_\infty</math> may be considered as denoting some two <math>x\!</math>'s.</p>
<p>It is natural to write:</p>
<p>It is natural to write:</p>
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| <p>and</p>
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| align="right" | <math>{x,}_\infty ~+~ {x,}_\infty</math>
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| and
| align="right" | <math>{x,}_\infty + \, {x,}_\infty</math>
| align="center" | <math>=\!</math>
| align="center" | <math>=\!</math>
| align="left" | <math>\mathit{2}.{x,}_\infty</math>
| align="left" | <math>\mathit{2}.{x,}_\infty</math>
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| <p>just as</p>
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| just as
| align="right" | <math>\mathit{1}_\infty</math>
| align="right" | <math>\mathit{1}_\infty</math>
| align="center" | <math>=\!</math>
| align="center" | <math>=\!</math>
<p>For instance, the lovers of two women are not the same as two lovers of women, that is:</p>
<p>For instance, the lovers of two women are not the same as two lovers of women, that is:</p>
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| width="25%" align="right" | <math>\mathit{l}\mathfrak{2}.\mathrm{w}</math>
| width="10%" align="center"| and
| width="25%" align="left" | <math>\mathfrak{2}.\mathit{l}\mathrm{w}</math>
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<p>are unequal; but the husbands of two women are the same as two husbands of women, that is:</p>
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<p>are unequal;</p>
| width="25%" align="right" | <math>\mathit{h}\mathfrak{2}.\mathrm{w}</math>
| width="10%" align="center"| <math>=\!</math>
<p>but the husbands of two women are the same as two husbands of women, that is:</p>
| width="25%" align="left" | <math>\mathfrak{2}.\mathit{h}\mathrm{w}</math>
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<p>and in general:</p>
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| and in general,
| align="right" | <math>x,\!\mathfrak{2}.y</math>
| align="center" | <math>=\!</math>
| align="left" | <math>\mathfrak{2}.x,\!y</math>
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<p>(Peirce, CP 3.75).</p>
<p>(Peirce, CP 3.75).</p>