Peirce's 1870 “Logic Of Relatives ” • Selection 1

Post   : Peirce's 1870 “Logic Of Relatives” • Selection 1
http://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-%e2%80%a2-selection-1/
Posted : January 27, 2014 at 4:00 pm
Author : Jon Awbrey

Peircers,

The first selection doesn't have too much formatting to run through email, so I will go ahead and do
that this time.  As an aid to study and mental eupepsia I will follow the practice of breaking up
long paragraphs into bite-size chunks.

We pick up the text at §3. Application of the Algebraic Signs to Logic.

<quote>

Use of the Letters
------------------

The letters of the alphabet will denote logical signs.

Now logical terms are of three grand classes.

The first embraces those whose logical form involves only the conception of quality, and which
therefore represent a thing simply as “a ──”.  These discriminate objects in the most rudimentary
way, which does not involve any consciousness of discrimination.  They regard an object as it is in
itself as such (quale);  for example, as horse, tree, or man.  These are absolute terms.

The second class embraces terms whose logical form involves the conception of relation, and which
require the addition of another term to complete the denotation.  These discriminate objects with a
distinct consciousness of discrimination.  They regard an object as over against another, that is as
relative;  as father of, lover of, or servant of.  These are simple relative terms.

The third class embraces terms whose logical form involves the conception of bringing things into
relation, and which require the addition of more than one term to complete the denotation.  They
discriminate not only with consciousness of discrimination, but with consciousness of its origin.
They regard  an object as medium or third between two others, that is as conjugative;  as giver of
── to ──, or buyer of ── for ── from ──.  These may be termed conjugative terms.

The conjugative term involves the conception of third, the relative that of second or other, the
absolute term simply considers an object.  No fourth class of terms exists involving the conception
of fourth, because when that of third is introduced, since it involves the conception of bringing
objects into relation, all higher numbers are given at once, inasmuch as the conception of bringing
objects into relation is independent of the number of members of the relationship.  Whether this
reason for the fact that there is no fourth class of terms fundamentally different from the third is
satisfactory of not, the fact itself is made perfectly evident by the study of the logic of relatives.

(Peirce, CP 3.63)

</quote>

What strikes me about the initial installment this time around is a certain pattern of argument I
can recognize as invoking a closure principle.  This is a figure of reasoning that Peirce uses in
three other places:  his discussion of continuous predicates [1}, his definition of a sign relation
[2], and his formulation of the pragmatic maxim [3] itself.

[1] http://intersci.ss.uci.edu/wiki/index.php/Continuous_predicates
[2] http://intersci.ss.uci.edu/wiki/index.php/Sign_relations
[3] http://intersci.ss.uci.edu/wiki/index.php/Pragmatic_maxim

One might also call attention to the following two statements:

<quote>

Now logical terms are of three grand classes.

No fourth class of terms exists involving the conception of fourth, because when that of third is
introduced, since it involves the conception of bringing objects into relation, all higher numbers
are given at once, inasmuch as the conception of bringing objects into relation is independent of
the number of members of the relationship.

</quote>

Regards,

Jon

-- 

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