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Topic: Mathematics as a language
Replies: 35   Last Post: Nov 8, 2010 1:53 AM

 Messages: [ Previous | Next ]
 Tim Little Posts: 1,793 Registered: 2/7/09
Re: Mathematics as a language
Posted: Nov 6, 2010 4:00 AM

On 2010-11-06, herbzet <herbzet@gmail.com> wrote:
> I guess the problem people are having with my thesis is that they
> are willing to accept (a) the mathematical existence of S, similar
> to that of the object 6, and they are willing to accept (b) the
> mathematical existence of a bijection f from w_1 to P(N), similar
> to that of the object 6, but they are not willing to accept both
> (a) and (b), because the object 6 is special -- it really and truly
> exists in some sense

I'm not sure I believe that N "really exists" in the same sense as the
number 6, let alone objects defined in terms of functions involving
the power set of N.

Even if one accepted that N "really exists", does it really have a
power set? If you accept that all objects definable in any
conceivable consistent mathematical system exist in some sense, then
P(N) does exist in that sense. However almost all of its elements
don't and can't. Is it reasonable for a set to "really exist" in some
sense if it has members that don't exist in that sense?

At some point, most of math seems to me a game of rules and
inferences. One with a very surprising structure and practical
usefulness, which perhaps explains why it seems to have a stronger
sense of existence than arbitrary babble.

- Tim

Date Subject Author
11/2/10 Aatu Koskensilta
11/3/10 herb z
11/3/10 Herman Jurjus
11/3/10 Marshall
11/3/10 Herman Jurjus
11/4/10 herb z
11/4/10 Marshall
11/5/10 herb z
11/5/10 Herman Jurjus
11/6/10 herb z
11/6/10 James Dolan
11/6/10 Tim Little
11/6/10 Daryl McCullough
11/6/10 Marshall
11/6/10 Brian Chandler
11/6/10 Tim Little
11/7/10 lwalke3@lausd.net
11/8/10 Brian Chandler
11/7/10 herb z
11/7/10 Daryl McCullough
11/8/10 herb z
11/3/10 lwalke3@lausd.net
11/3/10 Marshall
11/4/10 herb z
11/4/10 herb z
11/4/10 herb z
11/3/10 Daryl McCullough
11/4/10 Bill Taylor
11/4/10 Daryl McCullough
11/5/10 herb z
11/4/10 herb z
11/4/10 Daryl McCullough
11/5/10 herb z
11/5/10 Daryl McCullough
11/4/10 VK