Relations & Their Relatives : 16

Re: Peirce List Discussions • (1)(2)

First off, we need to be clear about the difference between objects and signs:

  • Relations are formal objects of discussion and thought while relative terms are signs employed to denote relations.  (The shorthand term “relative” is short for “relative term”.)
  • The default meaning for “relative term” is general relative term, that is, a term whose denotation extends over many objects.
  • The default meaning for “relation” is general relation, that is, an aggregate, collection, or set of elementary relations.

Next, we need to be clear about the distinction between relatives (= general relatives) and elementary relatives:

  • Note.  There is a distinction in Peirce’s usage between elementary relatives and individual relatives, but if we factor in what he says about the Doctrine of Individuals and recognize that we are dealing with abstract forms then it becomes a “distinction without a difference”.  So I will tend to use the terms interchangeably.

Here is one place where Peirce exhibits his appreciation of the critical difference between relatives in general and elementary or individual relatives.

Chapter 3. The Logic of Relatives

§4. Classification of Relatives

225.   Individual relatives are of one or other of the two forms

\begin{array}{lll}  \mathrm{A : A} & \qquad & \mathrm{A : B},  \end{array}

and simple relatives are negatives of one or other of these two forms.

226.   The forms of general relatives are of infinite variety, but the following may be particularly noticed.

Relatives may be divided into those all whose individual aggregants are of the form \mathrm{A : A} and those which contain individuals of the form \mathrm{A : B}.  The former may be called concurrents, the latter opponents.

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 7

It needs to be appreciated that classifying relations is vastly more complex than classifying elementary or individual relations.

In particular, classifying sign relations is vastly more complex than classifying elementary or individual sign relations, which is just about all the entire literature on sign taxonomy has been able to touch from Peirce’s time to ours.

Resources

This entry was posted in C.S. Peirce, Dyadic Relations, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations and tagged , , , , , , , , , , . Bookmark the permalink.

2 Responses to Relations & Their Relatives : 16

  1. Pingback: Survey of Relation Theory • 2 | Inquiry Into Inquiry

  2. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

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