Re: SUO: Re: Extension x Comprehension
Leo,
I think that we have a strong agreement on many, if not most of the basic
issues of logic. I just wanted to clarify some of the historical
relationships
between the main protagonists.
LO> Actually, some of us think that Goedel was the best logician after
> Aristotle/Plato, ok, maybe Leibniz, and that Russell was the best
> philosopher of language after ..., ok, maybe Leibniz and maybe Frege.
I certainly agree with you about Goedel. Most logicians consider Goedel
the greatest logician of the 20th century. I also have a very high opinion
about Leibniz (and so did Goedel).
But I can't agree with you about Russell. I consider Russell a very
intelligent (i.e., high IQ) person whose creativity and good sense were
both mediocre. In philosophy of language, Russell was decidedly inferior
to the medieval Scholastics. Just compare him to William of Okham.
For more about Russell vs. Ockham, see Section 4 of my paper on signs,
processes, and language games:
http://www.jfsowa.com/pubs/signproc.htm
In logic, I agree with Peirce's assessment of Russell's _Principles of
Mathematics_, which CSP said was "superficial to the point of nauseating me."
For more about what Peirce wrote in 1909 in comparison the the Principia
Mathematica in 1910, see my commentary on Peirce's manuscript:
http://www.jfsowa.com/peirce/ms514.htm
Whitehead was by far a superior philosopher, logician, and mathematician.
After Russell revised the PM for the second edition, Whitehead published
a letter disagreeing with Russell's new preface and disavowing any
responsibility for the changes.
LO> Maybe some of us would put Tarski somewhere in there, if only as a
> bridge into new worlds. And those in natural language would possibly put
> Montague in there, for letting us linguistic semanticists know there was
> something better than your or my "semantic features", called model
> theory.
I like Tarski and Montague, who did some very important work. However, I
would also like to draw people's attention to the work of the Scholastics,
who had developed a model-theoretic semantics for language (which Peirce
adopted for the semantics of existential graphs). Tarski had to fight an
uphill battle against the entrenched Frege-Russellism of his day, but his
work (and Montague's) were obvious extensions of Ockham's model theory
combined with the notation of predicate calculus. For further discussion
of these topics (with references), see my commentary on Peirce's MS 514.
John Sowa