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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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Posts: 1,635
Registered: 2/27/06
Re: Then answer to Frege's two objections to formalism.
Posted: Apr 7, 2013 12:05 AM
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On Apr 5, 10:22 am, fom <> wrote:
> On 4/5/2013 8:47 AM, Zuhair wrote:

> > On Apr 5, 2:25 pm, Zuhair <> wrote:
> >> I just want to argue that
> >> "Mathematics is analytic processing fictional or real"

1. All you are doing is substituting synonyms that themselves are not
defined. Define "information" to be "data". Define "mathematics" to
be "the science of quantity". Define "logic" to be "formal systems".

Do these accomplish anything? No. You are not unlocking the mystery
of mathematics by referring to other terms of mathematics whose only
difference may be that they are at a different level of abstraction -
lower - than what you are defining.

To "explain" mathematics or logic or formal systems, you need to
define them in terms AS UNMATHEMATICAL AS POSSIBLE. Otherwise you
still have "mathematics" - just more terms.

You need to explain them in informal intuitive terms. Mathematics is
that which we all agree on simply by thinking. Mathematics is the
science that doesn't use the 5 senses. Definitions like these show us
what mathematics really is.

Saying that mathematics is sets or numbers or quantities etc. is just
talking about the aspects of mathematics at various levels of
abstraction but still they are in mathematical terms - you then have
to define those mathematical terms.

It accomplishes nothing. You end up trying to explain the
mathematical terms - the mathematics - of you first explanation.

2. You make a similar mistake when you try to formalize a paradox
without having a clear idea of what that resolution is intuitively.
You don't formalize the solution of an unsolved problem. You
formalize something you already know intuitively.

I could explain the whole concept and process of formalizing in
detail. What does it mean to formalize, Zuhair? Do you have a solid
understanding of the process?


> Zuhair,
> In the link
> you can find the argument for the descriptivist theory of
> names used to address the question of negative existentials.
> In the link
> 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.

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