Changes

To my way of thinking, CP 3.73 is one of the most remarkable passages in the history of logic.  In this first pass over its deeper contents I won't be able to accord it much more than a superficial dusting off.

To my way of thinking, CP 3.73 is one of the most remarkable passages in the history of logic.  In this first pass over its deeper contents I won't be able to accord it much more than a superficial dusting off.

As always, it is probably best to begin with a concrete example.  So let us initiate a discourse, whose universe ''X'' may remind us a little of the cast of characters in Shakespeare's ''Othello''.

As always, it is probably best to begin with a concrete example.  So let us initiate a discourse, whose universe <math>X\!</math> may remind us a little of the cast of characters in Shakespeare's ''Othello''.

: ''X'' = {Bianca, Cassio, Clown, Desdemona, Emilia, Iago, Othello}.

| <math>X = \{ \operatorname{Bianca}, \operatorname{Cassio}, \operatorname{Clown}, \operatorname{Desdemona}, \operatorname{Emilia}, \operatorname{Iago}, \operatorname{Othello} \}.</math>

The universe ''X'' is "that class of individuals ''about'' which alone the whole discourse is understood to run" but its marking out for special recognition as a universe of discourse in no way rules out the possibility that "discourse may run upon something which is not a subjective part of the universe;  for instance, upon the qualities or collections of the individuals it contains" (CP 3.65).

The universe <math>X\!</math> is "that class of individuals ''about'' which alone the whole discourse is understood to run" but its marking out for special recognition as a universe of discourse in no way rules out the possibility that "discourse may run upon something which is not a subjective part of the universe;  for instance, upon the qualities or collections of the individuals it contains" (CP 3.65).

In order to provide ourselves with the convenience of abbreviated terms, while staying a bit closer to Peirce's conventions about capitalization, let us rename the universe "''u''", the Clown "Jeste", and then rewrite the above description of the universe of discourse in the following fashion:

In order to provide ourselves with the convenience of abbreviated terms, while staying a bit closer to Peirce's conventions about capitalization, let us rename the universe <math>^{\backprime\backprime} u ^{\prime\prime},\!</math> the Clown "Jeste", and then rewrite the above description of the universe of discourse in the following fashion:

: ''u'' = {B, C, D, E, I, J, O}.

| <math>u = \{ B, C, D, E, I, J, O \}.\!</math>

This specification of the universe of discourse could be summed up in Peirce's notation by the following equation:

This specification of the universe of discourse could be summed up in Peirce's notation by the following equation: