Changes

<p>The sign of addition is taken by Boole so that</p>

<p>The sign of addition is taken by Boole so that</p>

 

<p>''x'' + ''y''</p>

| align="center" | <math>x + y\!</math>

 

<p>denotes everything denoted by ''x'', and, ''besides'', everything denoted by ''y''.</p>

<p>denotes everything denoted by <math>x\!</math>, and, ''besides'', everything denoted by <math>y\!</math>.</p>

<p>Thus</p>

<p>Thus</p>

 

<p>''m'' + ''w''</p>

| align="center" | <math>\mathrm{m} + \mathrm{w}\!</math>

 

<p>denotes all men, and, besides, all women.</p>

<p>denotes all men, and, besides, all women.</p>

<p>For example,</p>

<p>For example,</p>

 

<p>''f'' + ''u''</p>

| align="center" | <math>\mathrm{f} + \mathrm{u}\!</math>

 

<p>means all Frenchmen besides all violinists, and, therefore, considered as a logical term, implies that all French violinists are ''besides themselves''.</p>

<p>means all Frenchmen besides all violinists, and, therefore, considered as a logical term, implies that all French violinists are ''besides themselves''.</p>

<p>For this reason alone, in a paper which is published in the Proceedings of the Academy for March 17, 1867, I preferred to take as the regular addition of logic a non-invertible process, such that</p>

<p>For this reason alone, in a paper which is published in the Proceedings of the Academy for March 17, 1867, I preferred to take as the regular addition of logic a non-invertible process, such that</p>

 

<p>''m'' +, ''b''</p>

| align="center" | <math>\mathrm{m} ~+\!\!,~ \mathrm{b}</math>

 

<p>stands for all men and black things, without any implication that the black things are to be taken besides the men;  and the study of the logic of relatives has supplied me with other weighty reasons for the same determination.</p>

<p>stands for all men and black things, without any implication that the black things are to be taken besides the men;  and the study of the logic of relatives has supplied me with other weighty reasons for the same determination.</p>

<p>Since the publication of that paper, I have found that Mr.&nbsp;W.&nbsp;Stanley&nbsp;Jevons, in a tract called ''Pure Logic, or the Logic of Quality'' [1864], had anticipated me in substituting the same operation for Boole's addition, although he rejects Boole's operation entirely and writes the new one with a "+" sign while withholding from it the name of addition.</p>

<p>Since the publication of that paper, I have found that Mr.&nbsp;W.&nbsp;Stanley&nbsp;Jevons, in a tract called ''Pure Logic, or the Logic of Quality'' [1864], had anticipated me in substituting the same operation for Boole's addition, although he rejects Boole's operation entirely and writes the new one with a &nbsp;<math>+\!</math>&nbsp; sign while withholding from it the name of addition.</p>

 

 

 

 

 

<p>[0] = 0.</p>

(Peirce, CP 3.67).

<p>It is plain that both the regular non-invertible addition and the invertible addition satisfy the absolute conditions.  But the notation has other recommendations.  The conception of ''taking together'' involved in these processes is strongly analogous to that of summation, the sum of 2 and 5, for example, being the number of a collection which consists of a collection of two and a collection of five. Any logical equation or inequality in which no operation but addition is involved may be converted into a numerical equation or inequality by substituting the numbers of the several terms for the terms themselves &mdash; provided all the terms summed are mutually exclusive.</p>

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