MyWikiBiz, Author Your Legacy — Friday November 08, 2024
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, 15:10, 22 April 2009
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| In ordinary arithmetic the ''involution'' <math>x^y,\!</math> or the ''exponentiation'' of <math>x\!</math> to the power of <math>y,\!</math> is the repeated application of the multiplier <math>x\!</math> for as many times as there are ones making up the exponent <math>y.\!</math> | | In ordinary arithmetic the ''involution'' <math>x^y,\!</math> or the ''exponentiation'' of <math>x\!</math> to the power of <math>y,\!</math> is the repeated application of the multiplier <math>x\!</math> for as many times as there are ones making up the exponent <math>y.\!</math> |
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− | In analogous fashion, the logical involution <math>\mathit{l}^\mathrm{w}\!</math> is the repeated application of the term <math>\mathit{l}\!</math> for as many times as there are individuals under the term <math>\mathrm{w}.\!</math> | + | In analogous fashion, the logical involution <math>\mathit{l}^\mathrm{w}\!</math> is the repeated application of the term <math>\mathit{l}\!</math> for as many times as there are individuals under the term <math>\mathrm{w}.\!</math> According to Peirce's interpretive rules, the repeated applications of the base term <math>\mathit{l}\!</math> are distributed across the individuals of the exponent term <math>\mathrm{w}.\!</math> In particular, the base term <math>\mathit{l}\!</math> is not applied successively in the manner that would give something like "a lover of a lover of … a lover of a woman". |
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| For example, suppose that a universe of discourse numbers among its contents just three women, <math>\mathrm{W}^{\prime}, \mathrm{W}^{\prime\prime}, \mathrm{W}^{\prime\prime\prime}.</math> This could be expressed in Peirce's notation by writing: | | For example, suppose that a universe of discourse numbers among its contents just three women, <math>\mathrm{W}^{\prime}, \mathrm{W}^{\prime\prime}, \mathrm{W}^{\prime\prime\prime}.</math> This could be expressed in Peirce's notation by writing: |
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− | This says that a lover of every woman in this particular 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> |
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| ==References== | | ==References== |