[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 5

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| The Signs for Multiplication
|
| I shall adopt for the conception of multiplication
| 'the application of a relation', in such a way that,
| for example, 'l'w shall denote whatever is lover of
| a woman.  This notation is the same as that used by
| Mr. De Morgan, although he apears not to have had
| multiplication in his mind.
|
| 's'(m +, w) will, then, denote whatever is
| servant of anything of the class composed
| of men and women taken together.  So that:
|
| 's'(m +, w)  =  's'm +, 's'w.
|
| ('l' +, 's')w will denote whatever is
| lover or servant to a woman, and:
|
| ('l' +, 's')w  =  'l'w +, 's'w.
|
| ('sl')w will denote whatever stands to
| a woman in the relation of servant of
| a lover, and:
|
| ('sl')w  =  's'('l'w).
|
| Thus all the absolute conditions
| of multiplication are satisfied.
|
| The term "identical with ---" is a unity
| for this multiplication.  That is to say,
| if we denote "identical with ---" by !1!
| we have:
|
| 'x'!1!  =  'x',
|
| whatever relative term 'x' may be.
| For what is a lover of something
| identical with anything, is the
| same as a lover of that thing.
|
| C.S. Peirce, CP 3.68
|
| 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).

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