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
JBD:http://web.archive.org/web/20140224152510/http://permalink.gmane.org/gmane.science.philosophy.peirce/11885

Clark, Jeff, List,

We were in the middle of trying to sort out what bearing contemporary mathematical graph theory 
might have on the types of “graphs” that Peirce discussed, for instance especially, his logical 
graphs, entitative and existential, and on the more general run of complex iconic signs that we 
would not be amiss in calling diagrams, figures, illustrations, etc.

I referred to a definition of a graph that is fairly standard among graph theorists and also many 
computer scientists.  There are of course many other ways of defining the same class of mathematical 
objects.  Most of these differ but verbally and most of the rest differ only in their exclusion or 
inclusion of certain boundary cases, like whether to count structures with no points and no lines as 
graphs or not.  One used to see some really silly arguments break out at graph theory conferences 
over these trifles many years ago, but I think a modus vivendi has largely been worked out between 
the different schools of thought by now.

 From this humble root springs a wide variety of graph-theoretical structures.  Some of these are 
simple species within the genus of graphs proper, for example, connected graphs, forests, trees, 
cacti.  Others are genuine variations on the main theme, for example, labeled graphs, colored 
graphs, digraphs (directed graphs), and so on.

Next time we'll look at the definitions of “digraphs” and “digraphs with loops” and that will bring 
us to levels of generality that are suitable for dealing with dyadic relations in general, at least 
in the finite case.

To be continued ...

Jon

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