Re: Peirce’s 1870 “Logic Of Relat ives” • Proto-Graphical Syntax

Thread:
JA:http://inquiryintoinquiry.com/2014/02/12/peirces-1870-logic-of-relatives-%E2%80%A2-proto-graphical-syntax/
HR:http://web.archive.org/web/20140213040631/http://permalink.gmane.org/gmane.science.philosophy.peirce/11753

Helmut, List,

Peirce's sign relations are triadic relations, triadic relations are of course a special sort of 
relations, and so, yes, the logic of relative terms and the mathematics of relations have no small 
application to the theory of signs that we know as Peircean semiotics.  Indeed, it's my own sense 
from reading Peirce's early papers that he was driven by the need to understand the logic of science 
to develop a more realistic theory of inquiry, reflecting the full spectrum of reasoning generated 
by the three principal types of inference, that doing this demanded a more solid, 3-dimensional 
theory of sign relations, and that both the theory of inquiry and the theory of signs required by 
this task forced him to develop the logic of relatives and the mathematics of relations far beyond 
what was given when he set to work.  (He reminds me of Brunelleschi in that way …)

So it's not completely true that the relation denoted by “A gives B to C” is “completely different” 
from the relation denoted by “A brings B into the same sort of correspondence with C as that in 
which A itself stands to C”.  The two relations share the property of being triadic relations and 
there is a lot to be said for what all triadic relations have in common.  Peirce called that 
commonality, that property by the name of “Thirdness” and people do tend to chew the fat about 
Thirdness till Cerberus comes home.  Still, you are right in thinking that invoking Thirdness is but 
the first step, not the be-all end-all in comprehending a given relation.  After “compare” comes 
“contrast” and there is much more to be said about the differentia of specific triadic relations.

Have to break here, will continue later …

Jon

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