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| ==Selection 12== | | ==Selection 12== |
| | | |
− | <pre> | + | <blockquote> |
− | | The Sign of Involution
| + | <p>'''The Sign of Involution'''</p> |
− | |
| + | |
− | | I shall take involution in such a sense that x^y
| + | <p>I shall take involution in such a sense that ''x''<sup>''y''</sup> will denote everything which is an ''x'' for every individual of ''y''.</p> |
− | | will denote everything which is an x for every
| + | |
− | | individual of y.
| + | <p>Thus</p> |
− | |
| + | |
− | | Thus
| + | : <p>'l'<sup>w</sup></p> |
− | |
| + | |
− | | 'l'^w
| + | <p>will be a lover of every woman.</p> |
− | |
| + | |
− | | will be a lover of every woman.
| + | <p>Then</p> |
− | |
| + | |
− | | Then
| + | : <p>('s'<sup>'l'</sup>)<sup>w</sup></p> |
− | |
| + | |
− | | ('s'^'l')^w
| + | <p>will denote whatever stands to every woman in the relation of servant of every lover of hers;</p> |
− | |
| + | |
− | | will denote whatever stands to every woman in
| + | <p>and</p> |
− | | the relation of servant of every lover of hers;
| + | |
− | |
| + | : <p>'s'<sup>('l'w)</sup></p> |
− | | and
| + | |
− | |
| + | <p>will denote whatever is a servant of everything that is lover of a woman.</p> |
− | | 's'^('l'w)
| + | |
− | |
| + | <p>So that</p> |
− | | will denote whatever is a servant of
| + | |
− | | everything that is lover of a woman.
| + | : <p>('s'<sup>'l'</sup>)<sup>w</sup> = 's'<sup>('l'w)</sup>.</p> |
− | |
| + | |
− | | So that
| + | <p>(C.S. Peirce, CP 3.77).</p> |
− | |
| + | </blockquote> |
− | | ('s'^'l')^w = 's'^('l'w).
| |
− | |
| |
− | | C.S. Peirce, CP 3.77
| |
− | |
| |
− | | Charles Sanders Peirce,
| |
− | |"Description of a Notation for the Logic of Relatives,
| |
− | | Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic",
| |
− | |'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870,
| |
− | |'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).
| |
− | </pre> | |
| | | |
| ===Commentary Note 12=== | | ===Commentary Note 12=== |