Re: Mathematical Logic, Podnieks'page ...

From: Hal Ruhl <HalRuhl.domain.name.hidden>
Date: Tue, 06 Jul 2004 10:31:25 -0400

Hi Bruno:

At 01:15 PM 7/2/2004, you wrote:
>Hi Hal,
>
>At 12:44 02/07/04 -0400, Hal Ruhl wrote:
>
>>By the way if some systems are complete and inconsistent will arithmetic
>>be one of them?
>>
>>As I understand it there are no perfect fundamental theories. So if
>>arithmetic ever becomes complete
>>then it will be inconsistent.
>
>
>Yes, if by "arithmetic" you mean an axiomatic system, or a formal theory,
>or a machine.
>No if by arithmetic you mean a set so big that you cannot define it

"define" appears to be a two sided activity. When you define a thing you
also define the thing which it is not - a bag of the remainder of
"all". Most of the time the latter may not be useful. Since all of
arithmetic [and mathematics] is in the Everything and the Everything in my
system is the definitional pair to the Nothing, defining the Nothing [or
the Everything] automatically defines all of arithmetic along with all of
mathematics.

A "Something" is less than the Everything and may or may not contain
mathematics or a portion thereof.

>in any formal theory,

Well my "theory" seems concerned with the form of its statements that is
the "Somethings" and how they alter.

I think my "theory" defines mathematics the way that "The first number that
can not be described in less than fourteen words" defines a number that we
nevertheless may never actually have in hand.

Hal
Received on Tue Jul 06 2004 - 10:45:12 PDT