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Topic: Interpreting ZFC
Replies: 14   Last Post: Apr 30, 2013 3:45 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Interpreting ZFC
Posted: Apr 30, 2013 3:45 AM

On Apr 30, 2:02 pm, fom <fomJ...@nyms.net> wrote:
> On 4/29/2013 9:29 PM, Graham Cooper wrote:
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> > On Apr 29, 1:30 pm, fom <fomJ...@nyms.net> wrote:
> >> On 4/28/2013 9:36 PM, Graham Cooper wrote:
>
> >>> the problem with mereology is it uses ALL(S) quantifier
> >>> and C (subset) to co-define each other..

>
> >> That is a nice observation Herc.
>
> >> The only problem is that the foundational
> >> investigations for mathematics have a historical
> >> context.

>
> >> What is correct about mereology is that it is
> >> consistent with Leibniz.  In analyzing the notion
> >> of class, Lesniewski concluded that the existential
> >> import of a class and its constituents is
> >> simultaneous.  In describing the difference, he
> >> explained the notion as intensional and contrasted
> >> it with the extensional logic of a Fregean or a
> >> Russellian approach.

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> >> In like fashion, Leibniz contrasted his notion
> >> of logic with the extensional Scholastic logic.
> >> In this respect Leibniz' logic is also intensional
> >> for a different reason.  In Leibniz' case, the sense
> >> of the syllogistic hierarchy had been characterized
> >> by informational complexity.  In other words, a genus
> >> is part of a species because more information is needed
> >> to specify a species than that of the genus with which
> >> it is associated.

>
> >> It is an unfortunate fact that most of modern
> >> foundational mathematics is overly influenced by
> >> Russell without questioning Russell's philosophy.

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> >> For what this is worth, Cantor rejected the "extension
> >> of a concept" formulation used by Frege and Russell.
> >> In fact, Cantor's notion of sets involves a "theory
> >> of ones" approach which suggests a Leibnizian view
> >> of individuation.

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> >> I would argue that the problem with the received
> >> paradigm is that the sign of equality is improperly
> >> characterized.  Leibniz' original introduction of
> >> the principle of identity of indiscernibles involves
> >> geometric intuitions not represented in the logicist
> >> framework of Frege and Russell.

>
> >> Your criticism of mereology will be believed by those
> >> who have not pursued what the original sources have
> >> written.  And, it will be respected by me because of
> >> its insight.  It is, however, a statement that does
> >> not question the alternative which is equally nonsensical.

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> >> Analytical philosophy is based on one thing -- avoid epistemology
> >> at all costs.  When one denies that position, there are
> >> not many choices,

>
> >>http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma
>
> > TODAY!
>
> > Ponytail stunt ends in death
> > A daredevil stuntman has died while attempting to cross a river using
> > just his ponytail.

>
> >http://au.news.yahoo.com/queensland/a/-/world/16933347/Ponytail-stunt...
>
> > That answers that question!
>
> No question had been posed.
>
> But, I like the ad lib.  Feel sorry for the guy, though.
>

Whether you can pull yourself out of the Swamp by your own hair or
not!

I'll have to delve further into that metaphor of the illustration...

Nearly on solid ground!! ?

Herc

Date Subject Author
4/26/13 Zaljohar@gmail.com
4/27/13 Jan Burse
4/27/13 Zaljohar@gmail.com
4/29/13 me 154934
4/29/13 Graham Cooper
4/29/13 me 154934
4/29/13 Graham Cooper
4/30/13 me 154934
4/30/13 Graham Cooper
4/30/13 fom
4/30/13 me 154934
4/30/13 Graham Cooper
4/30/13 Zaljohar@gmail.com