ONT Re: Logic Of Relatives
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LOR. Discussion Note 24
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HC = Howard Callaway
HC: I might object that "teridentity" seems to come
to a matter of "a=b & b=c", so that a specific
predicate of teridentity seems unnecessary.
Howard,
I am presently concerned with expositing and interpreting
the logical system that Peirce laid out in the LOR of 1870.
It is my considered opinion after thirty years of study that
there are untapped resources remaining in this work that have
yet to make it through the filters of that ilk of syntacticism
that was all the rage in the late great 1900's. I find there
to be an appreciably different point of view on logic that is
embodied in Peirce's work, and until we have made the minimal
effort to read what he wrote it is just plain futile to keep
on pretending that we have already assimilated it, or that
we are qualified to evaluate its cogency.
The symbol "&" that you employ above denotes a mathematical object
that qualifies as 3-adic relation. Independently of my own views,
there is an abundance of statements in evidence that mathematical
thinkers from Peirce to Goedel consider the appreciation of facts
like these to mark the boundary between realism and nominalism in
regard to mathematical objects.
Jon Awbrey
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