[Inquiry] Logic Of Relatives

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

LOR.  Note 1

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| The letters of the alphabet will denote logical signs.
| Now logical terms are of three grand classes.
|
| The first embraces those whose logical form involves only the
| conception of quality, and which therefore represent a thing
| simply as "a ---".  These discriminate objects in the most
| rudimentary way, which does not involve any consciousness
| of discrimination.  They regard an object as it is in
| itself as 'such' ('quale');  for example, as horse,
| tree, or man.  These are 'absolute terms'.
|
| The second class embraces terms whose logical form involves the
| conception of relation, and which require the addition of another
| term to complete the denotation.  These discriminate objects with a
| distinct consciousness of discrimination.  They regard an object as
| over against another, that is as relative;  as father of, lover of,
| or servant of.  These are 'simple relative terms'.
|
| The third class embraces terms whose logical form involves the
| conception of bringing things into relation, and which require
| the addition of more than one term to complete the denotation.
| They discriminate not only with consciousness of discrimination,
| but with consciousness of its origin.  They regard  an object
| as medium or third between two others, that is as conjugative;
| as giver of --- to ---, or buyer of --- for --- from ---.
| These may be termed 'conjugative terms'.
|
| The conjugative term involves the conception of 'third', the relative that of
| second or 'other', the absolute term simply considers 'an' object.  No fourth
| class of terms exists involving the conception of 'fourth', because when that
| of 'third' is introduced, since it involves the conception of bringing objects
| into relation, all higher numbers are given at once, inasmuch as the conception
| of bringing objects into relation is independent of the number of members of the
| relationship.  Whether this 'reason' for the fact that there is no fourth class
| of terms fundamentally different from the third is satisfactory of not, the fact
| itself is made perfectly evident by the study of the logic of relatives.
|
| C.S. Peirce, CP 3.63
|
| 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).

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o