Re: Existence of mathematical entities (Re: Successor Axiom: on what grounds TF?)

examachine_at_gmail.com
Date: 02/28/05 

Date: 28 Feb 2005 12:14:38 -0800

Lester Zick wrote:
> On Mon, 28 Feb 2005 16:44:44 +0100, Mitch Harris
> <harrisq@tcs.inf.tu-dresden.de> in comp.ai.philosophy wrote:
>
> >examachine@gmail.com wrote:
> >> Mitch Harris wrote:
> >>>examachine@gmail.com wrote:
> >>>
> >>>>Nothing exists until you have empirical evidence for it.
> >>>
> >>>Or rewritten to make your context more apparent:
> >>>
> >>> "You don't know anything exists until you have empirical
evidence
> >>>for it"
> >>>
> >>>So what would be empirical evidence for "There exists an even
prime."?
> >>>(maybe I need more clarificatoin of what you mean by "empirical").
> >>
> >> This is quite simple.
> >>
> >> You need nothing more than computational evidence, e.g. facts
about a
> >> simulation in your head, of a *generative* system of numbers.
>
> Technically that's analytical not empirical evidence.

Interesting, Lester, would you care to explain?

> >OK. That, to me, is a reasonable interpretation of "empirical"
(though
> >I'd suppose non-standard).
>
> The ultimate property of empiricism is the presence or absence of
> contradiction between facts and not facts in themselves, whatever a
> fact may be thought to be.

I understand that some radical empiricists do not think they can
"obtain" the reality.
http://www.artsci.wustl.edu/~philos/MindDict/empiricism.html

But what do we mean by absence of contradiction between facts? Is that
really the only standard of a good science? I don't think so.
Self-consistency is not identical to reality. And unfalsifiability has
barely anything to do with true empiricism.

The main tenet of empiricism is that it builds its house on sensory
data:
http://en.wikipedia.org/wiki/Empiricism
===================================================================
 Aristotle argued that all forms of knowing come from induction.
Aquinas wrote the famous quote, "Nihil in intellectu quod prius non
fuerit in sensu" which means "Nothing is in the intellect which was not
first in the senses."
===================================================================

Needless to say, I agree with Aristotle, and my view of computation and
mind is nothing more than a refined Aristotelian theory of motion.

In less philosophical jargon, I think the "strong" form of empiricism,
that there is no reality behind the experiment is sheer hogwash. I
subscribe to Aristotelian Realism, e.g. sensible physicalism instead.
This view is of course much less theological than logical positivism
which is a strange religion with rites of symbolic logic and obscure
formulas.

Regards, 

--
Eray Ozkural

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