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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 18:16, 27 April 2009
, 18:16, 27 April 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>
Given a universe of discourse <math>X,\!</math> suppose that <math>L \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{l} = \text{lover of}\,\underline{~~~~}.</math>
Recall the definition of the local flags for such a relation:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{lll}
L_{u \,\text{at}\, 1} & = & \{ (u, x) \in L \}
\\[6pt]
& = & \text{the set of ordered pairs in}~ L ~\text{with}~ u ~\text{in the 1st place}.
\\[9pt]
L_{v \,\text{at}\, 2} & = & \{ (x, v) \in L \}
\\[6pt]
& = & \text{the set of ordered pairs in}~ L ~\text{with}~ v ~\text{in the 2nd place}.
\end{array}</math>
|}
===Commentary Note 12.2===
===Commentary Note 12.2===