Peirce's 1870 “Logic Of Relatives ” • Comment 8.1

Post   : Peirce's 1870 “Logic Of Relatives” • Comment 8.1
http://inquiryintoinquiry.com/2014/02/18/peirces-1870-logic-of-relatives-%e2%80%a2-comment-8-1/
Posted : February 18, 2014 at 12:12 am
Author : Jon Awbrey

Peircers,

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.

Let us invent a concrete example to illustrate the use of Peirce's notation.  Imagine a discourse 
whose universe X will remind us 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 preserving Peirce's 
conventions about capitalization, we may use the alternate terms “u” for the universe X and “Jeste” 
for the character Clown.  This permits the above description of the universe of discourse to be 
rewritten 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 as follows:

“B”, “C”, “D”, “E”, “I”, “J”, “O”

Each of these terms denotes in a singular fashion the corresponding individual in X.

By way of ''general terms'' in this discussion, we may begin with the following set:

“b”  =  “black”
“m”  =  “man”
“w”  =  “woman”

The denotation of a general term may be given by means of an equation between terms:

b  =  O
m  =  C +, I +, J +, O
w  =  B +, D +, E

To be continued ...

-- 

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