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.

"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.

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