Peirce's 1870 “Logic Of Relatives ” • Comment 8.3

Post   : Peirce's 1870 “Logic Of Relatives” • Comment 8.3
http://inquiryintoinquiry.com/2014/02/18/peirces-1870-logic-of-relatives-%e2%80%a2-comment-8-3/
Posted : February 18, 2014 at 11:10 pm
Author : Jon Awbrey

Peircers,

It is critically important to distinguish a ''relation'' from a ''relative term''.

• The relation is an ''object'' of thought that may be regarded ''in extension''
as a set of ordered tuples that are known as its ''elementary relations''.

• The relative term is a ''sign'' that denotes certain objects, called its ''relates'',
as these are determined in relation to certain other objects, called its ''correlates''.
Under most circumstances the relative term may be taken to denote the corresponding relation.

Returning to the Othello example, let us consider the
dyadic relatives “lover of ____ ” and “servant of ____ ”.

The relative term l equivalent to the rhematic expression
“lover of ____ ” is given by the following equation:

l  =  B:C} +, C:B +, D:O +, E:I +, I:E +, O:D

In the interests of simplicity, let's put aside all distinctions of rank and fealty, collapsing the 
motley crews of servant and subordinate under the heading of a single service, denoted by the 
relative term s for “servant of ____ ”.  The terms of this unified service are given by the 
following equation:

s  =  C:O +, E:D +, I:O +, J:D +, J:O

The elementary relation I:C might be implied by the plot of the play but as it is so hotly arguable 
I will leave it out of the toll.

One thing more that we need to be duly wary about: There are many different conventions in the field 
as to the ordering of terms in their applications and different conventions will be more convenient 
under different circumstances than others, so there does not appear to be much of a chance that any 
one of them can be canonized once and for all. In the current reading we are applying relative terms 
from right to left and so our conception of relative multiplication, or relational composition, will 
need to be adjusted accordingly.

To be continued ...

-- 

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