Re: Peirce's 1870 “Logic Of Relatives ” • Comment 8.5

Re:
JA:http://inquiryintoinquiry.com/2014/02/20/peirces-1870-logic-of-relatives-%E2%80%A2-comment-8-5/
CG:http://web.archive.org/web/20140222153200/http://permalink.gmane.org/gmane.science.philosophy.peirce/11855

Clark, List,

At the present point in our run-through of Peirce's paper, we have been introduced but briefly to 
triadic relations, inasmuch as they are denoted by Peirce's third “grand class” of logical terms, 
the “conjugative terms”.

Cf:
http://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-%E2%80%A2-preliminaries/
http://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-%E2%80%A2-selection-1/
http://inquiryintoinquiry.com/2014/02/05/peirces-1870-logic-of-relatives-%E2%80%A2-selection-6/

Peirce illustrated the issues surrounding the application of conjugative terms by way of his “giver 
of a horse to a lover of a woman” example and we did have quite a bit of discussion about how to 
distinguish various species, especially sign relations, within the genus of triadic relations:

Cf:
http://inquiryintoinquiry.com/2014/02/07/peirces-1870-logic-of-relatives-%E2%80%A2-selection-7/
http://inquiryintoinquiry.com/2014/02/12/peirces-1870-logic-of-relatives-%E2%80%A2-proto-graphical-syntax/
http://web.archive.org/web/20140222172815/http://comments.gmane.org/gmane.science.philosophy.peirce/11531
http://web.archive.org/web/20140222172402/http://comments.gmane.org/gmane.science.philosophy.peirce/11753

But that's about as far as we've got with the category of triadic relations.

Graphs in the sense of mathematical graph theory fall into the category of dyadic relations, being 
either dyadic relations themselves or equivalence classes of dyadic relations.  Representing triadic 
relations in general or sign relations in particular on analogy with matrices requires 3-dimensional 
arrays or something equivalent in information like relational data tables.  There are a few schools 
of thought that treat relations of arity 3 and higher as “hyper-graphs”, but even they are forced to 
admit that the human knack for visual intuition that gets us so much mileage in the case of graphs 
is all but lost in the hypering thereof.

“But what of Peirce's logical graphs?”, you ask.  Aren't they supposed to help us reason about any 
sorts of relations whatever?  To answer those questions and all their kin will depend on us looking 
a lot more carefully at several other questions, like the difference between direct representation 
and indirect description of mathematical form and the exact class of forms to which Peirce's graphs, 
or the best of all possible logical forms, must belong.

So we have our work cut out for us ...

Regards,

Jon

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