# Anything to be learned from maths, was RE: [FoRK] Re: Anything to be learned from religion?

Wilkin, Kurt Kurt.Wilkin
Fri Aug 12 07:26:56 PDT 2005

```on Friday, 12 August 2005 10:52 p.m. Stephen D. Williams wrote:
> Wilkin, Kurt wrote:
>
>> ...
>> Axioms are unprovable (they were originally 'self-evident truths').
>> Standard example : how many parallel lines are there through a point?
>>
[...]
> Those don't prove the point at all.  You may be pointing out the
> incompleteness of the specification of the axiom,

Rather, the point of axioms being unprovable is that at some
level, your proof will depend on some other axiom which must
then be part of the system within which you are proving
that axiom.

And if you can prove that axiom, you'll depend on some other
axiom which, again, is part of the definition of the system
within which you're proving or disproving the statement.

And if you've proven an axiom, you've at least proved that it
isn't an axiom.

> I think that, just like the meaning(s) of "theory", "prove"
> and "truth"
> have different shades of meaning.
> Truth is really the best, simplest (a la Occam's Razor), most
> consistent, and least disproven theory that has some solid evidence.
> If I create an axiom that says that adding a positive integer to an
> integer makes it bigger than it was before, it is pretty easy
> to decide
> that this is "truth".

If I also create an axiom that says that adding a positive
integer to an integer doesn't always make it bigger, it is
pretty easy to decide that this is also "truth",
but that you are talking about arithmetic, and I'm talking
about modulus or clock arithmetic : its the axioms that
define what we are talking about.
That mine is necessarily false in your system doesn't make
your system any less complete (or incompletely specified)
or make mine false, and vice versa.

Cheers, Kurt.

--
This electronic message together with any attachments is confidential and
intended for the named recipient's use only.  If you are not the intended
recipient (i) do not copy, disclose or use the contents in any way, (ii)
please let us know by return email immediately then destroy the message, and
any hard copies of the message, and any attachments.  The sender of this
message is not responsible for any changes made to this message and/or any
attachments and/or connection linkages to the Internet referred to in this
message after it has been sent.  Unless otherwise stated, any pricing
information given in this message and/or attachments is indicative only, is
subject to change and does not constitute an offer to buy or sell securities
or derivatives at any price quoted.  Any reference to the terms of executed
transactions should be treated as preliminary only and subject to separate
and/or research recommendations, the basis of the provision of such research
material and/or recommendations is set out in the relevant disclaimer.

```