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On Fri, 29 Jul 2005 14:15:27 +0200, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:
>Martin Shobe wrote:
>> On Fri, 29 Jul 2005 11:14:56 +0200, Han de Bruijn
>> <Han.deBruijn@xxxxxxxxxxxxxx> wrote:
>>
>>
>>>Martin Shobe wrote:
>>>
>>>
>>>>On Thu, 28 Jul 2005 15:56:32 +0200, Han de Bruijn
>>>><Han.deBruijn@xxxxxxxxxxxxxx> wrote:
>>>>
>>>>
>>>>>But without the claim that it
>>>>>is the one and only foundation possible. Why not have _several_ pillars
>>>>>that provide a foundation, instead of just one?
>>>>
>>>>Actually, I don't have a problem with that. In a sense, we have that
>>>>now with set theory and category theory (And lets not forget logic).
>>>>But while physics will continue to provide inspirition to mathematics,
>>>>it will not qualify as a foundation for methematics.
>>>
>>>And I don't want that either. Read my lips:
>>>
>>> A little bit of Physics would be NO Idleness in Mathematics
>>>
>>>See? Just that tiny pinch of salt in your otherwise tasteless soup.
>>>
>>>But nevertheless: *IN* your soup.
>>
>>
>> A "tiny pinch of salt"? From the axioms I've seen you proposing that
>> would be more like a ten pound bag of rock salt added to single
>> serving.
>
>No, no. Nobody would like the soup anymore. Just a pinch.
Nobody likes the soup anymore. The axiom that you seem most likely to
want to add (Ax x = {x}), has as a consequence that Ax Ay (x e y) =>
(x = y). (It follows solely from the axiom and the definition of
{x}). After that, you might as well not have sets at all.
Martin
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