Changes

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>W \subseteq X</math> is the 1-adic relation, that is, the set, associated with the absolute term <math>\mathrm{w} = \text{woman}\!</math> and 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>

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:

 

| height="40" | <math>X\!</math> is the set whose elements form the ''universe of discourse''.

| height="40" | <math>W \subseteq X</math> is the 1-adic relation, or set, whose elements fall under the absolute term <math>\mathrm{w} = \text{woman}.\!</math>  The elements of <math>W\!</math> are sometimes referred to as the ''denotation'' or the set-theoretic ''extension'' of the term <math>\mathrm{w}.\!</math>

| height="40" | <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>

Recalling a few definitions, the ''local flags'' of the relation <math>L\!</math> are given as follows:

Recalling a few definitions, the ''local flags'' of the relation <math>L\!</math> are given as follows:

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<p>(Peirce, CP 3.77).</p>

<p>(Peirce, CP 3.77).</p>

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