Peirce's 1870 “Logic Of Relatives ” • Comment 8.2

Post   : Peirce's 1870 “Logic Of Relatives” • Comment 8.2
http://inquiryintoinquiry.com/2014/02/18/peirces-1870-logic-of-relatives-%e2%80%a2-comment-8-2/
Posted : February 18, 2014 at 3:48 pm
Author : Jon Awbrey

Peircers,

I continue with my commentary on CP 3.73, developing the “Othello” example as a way of illustrating 
Peirce's formalism.

In the development of the story so far, we have a universe of discourse characterized by the 
following equations:

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

b  =  O

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

w  =  B +, D +, E

This much forms a basis for the collection of absolute terms to be used in this example.  Let us now 
consider how we might represent an exemplary collection of relative terms.

Consider the genesis of relative terms, for example:

“lover of ____ ”

“betrayer to ____ of ____ ”

“winner over of ____ to ____ from ____ ”

We may regard these fill-in-the-blank forms as being derived by a kind of ''rhematic abstraction'' 
from the corresponding instances of absolute terms.

The following examples illustrate the relationships that exist among absolute terms, relative terms, 
relations, and elementary relations.

• The relative term “lover of ____ ” can be derived from the absolute term “lover of Emilia” by 
removing the absolute term “Emilia”.

◦ Iago is a lover of Emilia, so the relate-correlate pair I:E is an element of the dyadic relation 
associated with the relative term “lover of ____ ”.

• The relative term “betrayer to ____ of ____ ” can be derived from the absolute term “betrayer to 
Othello of Desdemona” by removing the absolute terms “Othello” and “Desdemona”.

◦ Iago is a betrayer to Othello of Desdemona, so the relate-correlate-correlate triple I:O:D is an 
element of the triadic relation associated with the relative term “betrayer to ____ of ____ ”.

• The relative term “winner over of ____ to ____ from ____ ” can be derived from the absolute term 
“winner over of Othello to Iago from Cassio” by removing the absolute terms “Othello”, “Iago”, and 
“Cassio”.

◦ Iago is a winner over of Othello to Iago from Cassio, so the elementary relative term I:O:I:C is 
an element of the tetradic relation associated with the relative term “winner over of ____ to ____ 
from ____ ”.

To be continued ...

-- 

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