Peirce's 1870 “Logic Of Relatives ” • Comment 10.1

Post   : Peirce's 1870 “Logic Of Relatives” • Comment 10.1
http://inquiryintoinquiry.com/2014/03/10/peirces-1870-logic-of-relatives-%e2%80%a2-comment-10-1/
Posted : March 10, 2014 at 12:36 am
Author : Jon Awbrey

What Peirce is attempting to do in CP 3.75 is absolutely amazing
and I personally did not see anything on a par with it again until
I began to study the application of mathematical category theory to
computation and logic, back in the mid 1980s.  To completely evaluate
the success of this attempt we would have to return to Peirce's earlier
paper “Upon the Logic of Mathematics” (1867) to pick up some of the ideas
about arithmetic that he set out there.

Another branch of the investigation would require that we examine more
carefully the entire syntactic mechanics of subjacent signs that Peirce
uses to establish linkages among relational domains.  It is important to
note that these types of indices constitute a diacritical, interpretive,
syntactic category under which Peirce also places the comma functor.

The way that I would currently approach both of these branches
of the investigation would be to open up a wider context for
the study of relational compositions, attempting to get at
the essence of what is going on when we relate relations,
possibly complex, to other relations, possibly simple.

-- 

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