[Inquiry] Re: Relatives Of Second Intention

[Jon Awbrey]

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ROSI.  Note 12

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| Section 4.  Classification of Relatives (cont.)
|
| These different classes have the following relations.
| Every negative of a concurrent and every alio-relative
| is both an opponent and the negative of a self-relative.
| Every concurrent and every negative of an alio-relative
| is both a self-relative and the negative of an opponent.
| There is only one relative which is both a concurrent and
| the negative of an alio-relative;  this is "identical with __".
| There is only one relative which is at once an alio-relative
| and the negative of a concurrent;  this is the negative of the
| last, namely, 'other than __".  The following pairs of classes
| are mutually exclusive, and divide all relatives between them:
|
|    Alio-relatives and self-relatives,
|
|    Concurrents and opponents,
|
|    Negatives of alio-relatives and negatives of self-relatives,
|
|    Negatives of concurrents and negatives of opponents.
|
| No relative can be at once either an alio-relative
| or the negative of a concurrent, and at the same time
| either a concurrent or the negative of an alio-relative.*
|
|* [Note added in proof]  The relative 0 ought to be considered as at once a
|  concurrent and an alio-relative, and the relative oo [infinity symbol] as
|  at once the negative of a concurrent and the negative of an alio-relative.
|  The statements in the text require to be modified to this extent.
|
| C.S. Peirce, 'Collected Papers', CP 3.227
|
| C.S. Peirce, "On the Algebra of Logic",
|'American Journal of Mathematics', vol. 3, pp. 15-57 (1880), reprinted in:
|'Collected Papers' (CP 3.154-251), 'Chronological Edition' (CE 4, 163-209).

NB.  The infinity symbol "oo" is here used to denote the "relative universe",
     which is the logical sum of all the relevant "dual individual relatives",
     elsewhere called the "elementary dyadic relatives" for the given universe.

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