- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Russell Standish <R.Standish.domain.name.hidden>

Date: Fri, 13 Apr 2001 09:08:01 +1000 (EST)

Let me try and short circuit this debate, since I had precisely this

debate with Hal about 18 months ago, where I found myself in the same

position Juergen finds himself now.

Basically, Hal believes a finite FAS by definition implies that each

theorem is constrained to be no more than N-bits in length. So by his

definition, number theory is not a finite FAS.

By contrast, almost everyone else believes finiteness in FASes refers

to a finite number of axioms, not that the theorems are bounded in any

fashion.

Whilst I can appreciate diversity of viewpoints, I fail to see how

Hal's position actually yields a useful mathematical object. In

Juergen's chain below, what is the use of a system where a+1=b

(lets say) is a valid theorem, but b+1=c (where c=b+1=a+2) is an

invalid theorem because of an arbitrary cutoff rule?

Cheers

juergen.domain.name.hidden wrote:

*>
*

*> > From: Hal Ruhl Thu Apr 12 14:07:54 2001
*

*> >
*

*> > In case what I tried to say was not clear the idea is that there are no
*

*> > more than 2^(N + c) shortest possible unique proofs in an N-bit FAS. How
*

*> > can number theory if it is a finite FAS contain an infinite number of
*

*> > unique theorems?
*

*>
*

*> Hal, here is an infinite chain of provable unique theorems:
*

*> 1+1=2, 2+1=3, 3+1=4, 4+1=5, ...
*

*>
*

*> Juergen
*

*>
*

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967

UNSW SYDNEY 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Thu Apr 12 2001 - 16:37:31 PDT

Date: Fri, 13 Apr 2001 09:08:01 +1000 (EST)

Let me try and short circuit this debate, since I had precisely this

debate with Hal about 18 months ago, where I found myself in the same

position Juergen finds himself now.

Basically, Hal believes a finite FAS by definition implies that each

theorem is constrained to be no more than N-bits in length. So by his

definition, number theory is not a finite FAS.

By contrast, almost everyone else believes finiteness in FASes refers

to a finite number of axioms, not that the theorems are bounded in any

fashion.

Whilst I can appreciate diversity of viewpoints, I fail to see how

Hal's position actually yields a useful mathematical object. In

Juergen's chain below, what is the use of a system where a+1=b

(lets say) is a valid theorem, but b+1=c (where c=b+1=a+2) is an

invalid theorem because of an arbitrary cutoff rule?

Cheers

juergen.domain.name.hidden wrote:

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967

UNSW SYDNEY 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Thu Apr 12 2001 - 16:37:31 PDT

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:07 PST
*