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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 6 Feb 2008 14:14:41 -0600
Message-id: <p06230909c3cfc2df00f9@[]>
At 1:15 PM -0600 2/6/08, Christopher Menzel wrote:
>On Feb 6, 2008, at 6:41 AM, Avril Styrman wrote:
>>  Chris,
>>  I'll have to explain the background a little. The overall mathematical
>>  ideology that I'm holding is finitism, and I argue that finitism is 
>>  not just
>>  an alternative to platonism and transfinitism, no more than slavery 
>>  is an
>>  alternative to freedom. Slavery is wrong, and so is uncontrolled 
>>  platonism.
>>  The reason for this is that it is better for the human kind to throw 
>>  away
>>  the abracadabraic things from mathematics. And that's a good enough
>>  justification for finitism.
>Ah, I see, well, you are clearly more interested in ideology than 
>mathematics or knowledge engineering, and that is not something that 
>ought to be debated in this forum.  You might try your luck on the 
>USENET groups sci.logic and sci.math, where actual mathematicians 
>entertain themselves arguing with extremists, ideologues, and assorted 
>crackpots who believe that there are deep logical or conceptual flaws 
>in classical mathematics.  Just for the record, I do think the sort of 
>"strict" finitism (a.k.a. "ultra-intuitionism") you appear to be 
>advocating is an interesting philosophical ideology,    (01)

And I agree, BTW, just for the record.    (02)

Avril, you might enjoy "Ad Infinitum" by Brian 
Rotman, Stanford U. Press 1993.  BTW, you make 
one logical error in an earlier post. An infinite 
series of finite things can grow indefinitely 
without any one of them actually becoming 
infinite. This is true even with a strict 
finitist understanding of "infinite".    (03)

Pat Hayes    (04)

>though only when 
>argued by those who have a deep understanding of classical mathematics 
>(e.g., Alexander Yessenin-Volpin, David Isles).
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