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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

Date: Tue, 06 Jul 2004 10:31:25 -0400

Hi Bruno:

At 01:15 PM 7/2/2004, you wrote:

"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.

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

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