[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 30

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| The Signs for Multiplication (cont.)
|
| The sum 'x' + 'x' generally denotes no logical term.
| But 'x',_oo + 'x',_oo may be considered as denoting
| some two 'x's.
|
| It is natural to write:
|
| 'x' + 'x'  =  !2!.'x'
|
| and
|
| 'x',_oo + 'x',_oo  =  !2!.'x',_oo
|
| where the dot shows that this multiplication is invertible.
|
| We may also use the antique figures so that:
|
| !2!.'x',_oo  =  `2`'x'
|
| just as
|
| !1!_oo  =  `1`.
|
| Then `2` alone will denote some two things.
|
| But this multiplication is not in general commutative,
| and only becomes so when it affects a relative which
| imparts a relation such that a thing only bears it
| to 'one' thing, and one thing 'alone' bears it to
| a thing.
|
| For instance, the lovers of two women are not
| the same as two lovers of women, that is:
|
| 'l'`2`.w
|
| and
|
| `2`.'l'w
|
| are unequal;
|
| but the husbands of two women are the
| same as two husbands of women, that is:
|
| 'h'`2`.w  =  `2`.'h'w
|
| and in general:
|
| 'x',`2`.'y'  =  `2`.'x','y'.
|
| C.S. Peirce, CP 3.75
|
| 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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