From: Eschatoon Magic (eschatoon@gmail.com)
Date: Wed Feb 25 2009 - 06:54:30 MST
Tough question Stuart.
While I am unable to offer any deeper or more precise formulation,
perhaps I would reword your definition as "maths is the task of
axiomatising basic intuitve concepts (counting bottle-caps, drawing
figures on the sand, watching the planets move) and then pushing the
axioms out as far as they can go, EVEN well beyond the DOMAIN OF
VALIDITY OF THE original intuitve concepts".
The evident explanation of why evolution has shaped our mental
architecture in such a way as to optimize our ability to count
bottlecaps (predators, friends, foes...) do not necessarily explain
why our mental architecture should also be optimized for deeper
mathematical reasoning. So, perhaps, it is not.
G.
On Wed, Feb 25, 2009 at 10:53 AM, Stuart Armstrong
<dragondreaming@googlemail.com> wrote:
>> Godel demonstrated that there must be arithmetic statements which
>> cannot be proven algorithmically, but just "happen to be" true for all
>> natural numbers. I have used the Goldbach conjecture (which may be
>> unprovable in the Godel sense) as an example.
>>
>> If something is true but cannot be proven true, the only thing we can
>> say is that it is "experimentally true".
>
> Ah, I see what you mean. In that sense I agree - Godel did not create
> these "experimentally true" statements, but did show that it might be
> the best you can get.
>
>> I am very intrigued by he suggestion that maths is really the physics
>> of bottlecaps, which seems to me a very pragmatic and sane way to look
>> at it.
>
> As a mathmatician, it seems to be a very poor way of looking at
> things, and bearing little relationship to what I know. I'd say that
> maths is the task of axiomatising basic intuitve concepts (counting
> bottle-caps, drawing figures on the sand, watching the planets move)
> and then pushing the axioms out as far as they can go, well beyond the
> original intuitve concepts.
>
> But that's from an insider - what is your intution for the "physics of
> bottlecaps"?
>
> Stuart
>
-- Eschatoon Magic http://cosmeng.org/index.php/Eschatoon aka Giulio Prisco http://cosmeng.org/index.php/Giulio_Prisco
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