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

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Graham Cooper

Posts: 4,321
Registered: 5/20/10
Re: Interpreting ZFC
Posted: Apr 30, 2013 3:45 AM
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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.

>
> >> 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.

>
> >> 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.

>
> >> 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.

>
> >> 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.
>


yes.. bad way to go...

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



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