[ FWD:Fwd: SUO: Re: Ontology ]
Hi Jay,
You wrote:
> Peirce had done what 'all'? Invented the Theory of
> Types, for instance?
> Found the conradiction in Frege? Invented the
> semantical definition of
> truth? Proved the Completeness Theorem? Invented
> Godel numbering? Proved the
> Incompleteness Theorem? None of these. Shall I
> mention the Contradiction in
> Frege again? There have been many developments in
> logic since Peirce -- and
> since Russell and Whitehead, for that matter.
Not many people know this, but Peirce proved Cantor's famous result independently (using a version of the diagonalisation argument)!! The proofs are in a collection of Peirce's mathematical writings called "New Elements of Mathematics" (ed. Carolyn Eisele). When Peirce got wind of Cantor's work he read it thoroughly and sent him a series of excited letters trying to engage him in discussion but I think Cantor was too far gone at that stage in isolation/illness to really engage.
As far as I understand it, Goedel's Incompleteness Proof relies crucially on the diagonalisation argument, so it wasn't too far off.
Re. the contradiction in Frege, Peirce refused to call "Russell's Paradox" "Russell's Paradox" because he said it was only a trivial extension of ideas already expressed by Cantor.
The issue of the semantic definition of truth is an interesting one. I have a feeling there might be something in Peirce along these lines, but I don't have any references to hand.
> 'Anticipated in Latin' covers a multitude of sins.
> Without the symbolic
> logic -- variable binding quantifiers -- which
> hadn't been invented, the
> significance of Russell's analysis is lost.
>
>
> I will mention once again that Peirce did not invent
> the Theory of Types,
> nor discover
> the Contradiction. Nor invent set theory, for that
> matter.
There is a set theory in the "New Elements of Mathematics" also.
> "Unfortunately Peirce was like Leibniz, not only in
> his originality as a
> logician, but also in his constitutional inability
> to finish the many
> projects he conceived." (P.410), Kneale and Kneale,
> The Development of
> Logic)
I actually find the overall trajectory of his thought much more of a slow steady development than Russell's frequent changes of mind.
> "Working on some suggestions of De Morgan, Perice
> explored this new field,
> and shortly after the publication of the
> Begriffschrift he even produced
> independently a doctrine of functions with a
> notation adequate for
> expressing all the principles formulated by Frege;
> but he never reduced his
> thoughts to a system nor set out a number of basic
> principles like those
> given [by Frege]. (P. 510, Kneale and Kneale, The
> Development of Logic)
Again, the "New Elements of Mathematics" gives the lie to this statement. Check out Peirce's Existential Graphs, for instance.
>
>[...]But your`s is very much a
> minority opinion, as Google,
> for instance, demonstrates: "Bertrand Russell" -
> 236,000; "Charles Peirce" -
> 6,250. (Unsurprisingly, neither one compares well
> with "Bill Gates" -
> 2,270,000).
Is this meant to be an argument?
Best regards,
Cathy.