Re: What is math? And my thoughts...

On Apr 18, 3:47 am, xbit <xbit....@xxxxxxxxx> wrote:
On 17 ÁÐÒ, 23:16, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

When some people describe mathematics as a 'langugage', it's pretty
clear they're using 'language' in a quite broad and informal way.

Is that means that mathematics in core doesn't formalized?

A great amount of mathematics can be formalized. As far as I know,
virtually all of the mathematics one ordinarily studies can be
formalized. But that doesn't entail that mathematics is best defined
as the study of formal systems.

I started to think that I was wrong in my formulation. Now I can
paraphrase my question. Is formal logic is foundation of math?

In what sense of 'foundation'? Certainly not in the sense of a
foundation as NECESSARY, since obviously people studied mathematics
well before the advent of any formal logic, and even since the
invention of formal logic, many people study mathematics without any
concern for formal logic or formal systems.

MoeBlee

.

Relevant Pages

  • Re: What is dialectics?
    ... My philosophical opinion is that mathematical truth is competely ... truth is established within formal systems, ... quality. ... justify why mathematics might happen to be useful in some cases. ...
    (soc.politics.marxism)
  • Re: Nobody can prove " YOU CANT PROVE ME " therefore its TRUE
    ... Herc seems to consistently miss the difference ... existence, when one seeks to show the existence or non- ... mathematics, ...
    (sci.math)
  • Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?
    ... be a language about describing formal systems. ... Like most mathematics, in ... "mathematical English", i.e., English supplemented with mathematical ...
    (sci.logic)
  • Re: Tolerable "unscience"
    ... >>> or with things which derive directly from mathematics without much dependence ... You must have a different definition of omnipotent than the one I'm ... certain formal systems are much more useful, ... constant that have embedded messages. ...
    (rec.arts.sf.written)
  • Re: Question on formalism
    ... The philosopher is not model driven. ... What you are saying is that the typographical characters of mathematics ... Definitions don't drift in formal systems. ... They drift alright, if you cannot place them anywhere except in their ...
    (sci.logic)