
Re: Then answer to Frege's two objections to formalism.
Posted:
Apr 7, 2013 12:05 AM


On Apr 5, 10:22 am, 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"
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?
CB
> 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/logicfree/ > > 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 firstorder > 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 firstorder logic in relation to names and > existential import.

