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Topic: Then answer to Frege's two objections to formalism.
Replies: 17   Last Post: Apr 9, 2013 7:56 AM

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 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: Then answer to Frege's two objections to formalism.
Posted: Apr 5, 2013 12:26 PM

On Apr 5, 5:22 pm, fom <fomJ...@nyms.net> wrote:
> On 4/5/2013 8:47 AM, Zuhair wrote:
>

> > On Apr 5, 2:25 pm, Zuhair <zaljo...@gmail.com> wrote:
> >> I just want to argue that
>
> >> "Mathematics is analytic processing fictional or real"
>
> Zuhair,
>
> In the link
>
> http://plato.stanford.edu/entries/existence/#FreRusExiNotProInd
>
> you can find the argument for the descriptivist theory of
> names used to address the question of negative existentials.
>
> In the link
>
> http://plato.stanford.edu/entries/logic-free/
>
> you will find the statement that classical logic presupposes
> equivalence between denotation and existence.  This comes
> from the influence of Russellian description theory
> and the analysis of negative existential statements.
>
> This presuppostion is embraced in the axioms for first-order
> logic given by
>
> Ax(P(x)) -> P(t)
>
> P(t) -> Ex(P(x))
>
> The link on free logic will explain how it differs from
> classical first-order logic in relation to names and
> existential import.

No problem at all, all of those are just variants of assumptive
fictional reality (as far as first order logic is concerned, or free
logic), that has nothing to do with mathematics per se, all
mathematics has to do with is the CONSEQUENCES of those assumptions
according to fictional assumed rules of logical inference, so it is of
the kind of If-The-Ism. There is no commitment to any of those
assumptions per se, there is only an assumptive record that has
consequences and it is those consequences in relation to those
assumptions that are the Analytics concerned with those methods that
mathematics is concerned with. All what is in the links you've
referred to is just changing the rules of the game we are to follow
all made in a fictional world. All of those are not matters that
mathematics is ought to be concerned with, they are indeed
philosophical matters, but as said not mathematical.

Zuhair