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Directory talk:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 02:22, 1 May 2009
, 02:22, 1 May 2009→Commentary Note 12.1
This says that a lover of every woman in the given universe of discourse is a lover of <math>\mathrm{W}^{\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math> In other words, a lover of every woman in this context is a lover of <math>\mathrm{W}^{\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math>
This says that a lover of every woman in the given universe of discourse is a lover of <math>\mathrm{W}^{\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math> In other words, a lover of every woman in this context is a lover of <math>\mathrm{W}^{\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math>
To get a better sense of why the above formulas hold, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the following materials and definitions:
To get a better sense of why the above formulas mean what they do, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the following materials and definitions:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
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| height="40" | <math>S \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{s} = \text{servant of}\,\underline{~~~~}.</math>
| height="40" | <math>S \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{s} = \text{servant of}\,\underline{~~~~}.</math>
|}
{| align="center" cellspacing="6" width="90%"
| height="40" | <math>\mathfrak{W} = \operatorname{Mat}(W) = \operatorname{Mat}(\mathrm{w})</math> is the matrix representaion of the set <math>W\!</math> and the term <math>\mathrm{w}.\!</math>
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| height="40" | <math>\mathfrak{L} = \operatorname{Mat}(L) = \operatorname{Mat}(\mathit{l})</math> is the matrix representaion of the relation <math>L\!</math> and the relative term <math>\mathit{l}.\!</math>
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| height="40" | <math>\mathfrak{S} = \operatorname{Mat}(S) = \operatorname{Mat}(\mathit{s})</math> is the matrix representaion of the relation <math>S\!</math> and the relative term <math>\mathit{s}.\!</math>
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