Re: Peirce List Discussion • HR

The immediate task is to get clear about the critical relationship between relations as sets and elementary relations as elements of those sets.  What’s at stake is understanding the extensional aspect of relations.  Beyond its theoretical importance, the extensional aspect of relations is the interface where relations make contact with empirical phenomena and ground logical theories in observational data.

The relationship between tokens and types, under one pair of terms or another, has been pervasive in science and knowledge-oriented philosophy from the time of Plato and Aristotle at least, arising from the observation that knowledge is of forms and generalities, not haecceities or individuals in themselves.

There is a communication problem that arises here, because the words “token” and “type” tend to be used differently outside Peirce studies, referring to objects that aren’t always signs.  So I have found it less confusing to use more neutral terms, like “instance of a type” or “element of a set”.

In that sense, we can say that the ordered pair (Cain, Abel) is an instance of the type B, where B is a particular subset of all ordered pairs of biblical figures.