Jon, (01)
Yes, Peirce gave very general foundations for much, much,
more than classical FOL. (02)
JA> I'm sure you must know, if you think about it, that many
> of the statements that you make below are not exactly so.
> Peirce's interpretation of basic logical symbols was far more
> abstract, formal, or general than our conventional readings
> of boolean syntax, as evidenced among many other facts by the
> deep duality between the entitative interpretation and the
> existential interpretation of logical graphs. (03)
The fact that Peirce did much more than classical FOL does
not contradict the fact that the FOL subset of his 1885 paper
on the Algebra of Logic is exactly compatible with the FOL
subset of his existential graphs of 1906 and exactly compatible
with the FOL subset of Frege's publications. (04)
That is a truly remarkable point that is *not* true of *any*
programming language or system that has been defined by purely
behavioral methods. It's importance cannot be overstated. (05)
JA> It is also evident in the fact that Peirce gave axioms for
> boolean algebra in dual symmetric form, even writing them in
> the fashion that was customary to present dual axiomsets for
> projective geometry. This leads to a very distinctive way of
> regarding the interpretation of logical calculi, where symbols
> that we once regarded as "logical constants" take on variable
> meanings. (06)
Indeed, Peirce had profound insights into logic that are worth
much more study than most logicians have bothered to give them. (07)
But it is also true that the ISO standard for classical FOL with
the extensions in the CL standard is already far beyond what most
people are using today. (08)
Let's take it one step at a time. (09)
John (010)
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