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==Selection 10==
==Selection 10==
<pre>
<blockquote>
<p>'''The Signs for Multiplication''' (cont.)<p>
<p>The sum 'x' + 'x' generally denotes no logical term. But 'x',<sub>∞</sub> + 'x',<sub>∞</sub> may be considered as denoting some two 'x's.</p>
<p>It is natural to write:</p>
: <p>'x' + 'x' = !2!.'x'</p>
<p>and</p>
: <p>'x',<sub>∞</sub> + 'x',<sub>∞</sub> = !2!.'x',<sub>∞</sub></p>
<p>where the dot shows that this multiplication is invertible.</p>
<p>We may also use the antique figures so that:</p>
: <p>!2!.'x',<sub>∞</sub> = `2`'x'</p>
<p>just as</p>
: <p>!1!<sub>∞</sub> = `1`.</p>
<p>Then `2` alone will denote some two things.</p>
<p>But this multiplication is not in general commutative, and only becomes so when it affects a relative which imparts a relation such that a thing only bears it to ''one'' thing, and one thing ''alone'' bears it to a thing.</p>
<p>For instance, the lovers of two women are not the same as two lovers of women, that is:</p>
: <p>'l'`2`.w</p>
and
: <p>`2`.'l'w</p>
<p>are unequal;</p>
<p>but the husbands of two women are the same as two husbands of women, that is:</p>
: <p>'h'`2`.w = `2`.'h'w</p>
<p>and in general:</p>
: <p>'x',`2`.'y' = `2`.'x','y'.</p>
<p>(Peirce, CP 3.75).</p>
</blockquote>
</pre>
===Commentary Note 10.1===
===Commentary Note 10.1===
