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

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Posts: 1,968
Registered: 12/4/12
Re: Interpreting ZFC
Posted: Apr 30, 2013 12:02 AM
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On 4/29/2013 9:29 PM, Graham Cooper wrote:
> 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!

No question had been posed.

But, I like the ad lib. Feel sorry for the guy, though.

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