[Inquiry] Re: Logic Of Relatives -- Commentary

[Jon Awbrey]

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LOR.  Commentary Note 8.1

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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'.

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

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).

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:

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

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

1  =  B +, C +, D +, E +, I +, J +, O.

Within this discussion, then, the "individual terms" are
"B", "C", "D", "E", "I", "J", "O", each of which denotes
in a singular fashion the corresponding individual in X.

As "general terms" of this discussion,
we might begin with the following set:

"b"  =  "black"

"m"  =  "man"

"w"  =  "woman"

In Peirce's notation, the denotation of a general term
can be expressed by means of an equation between terms:

b  =  O

m  =  C +, I +, J +, O

w  =  B +, D +, E

Jon Awbrey

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