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

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Graham Cooper

Posts: 4,495
Registered: 5/20/10
Re: Interpreting ZFC
Posted: Apr 29, 2013 10:29 PM
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On Apr 29, 1:30 pm, fom <> 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,


Ponytail stunt ends in death
A daredevil stuntman has died while attempting to cross a river using
just his ponytail.

That answers that question!


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