From: Ben Goertzel (ben@goertzel.org)
Date: Mon May 31 2004 - 15:48:42 MDT
> If you have some broad class of well defined
> mathematical problem people might call it
> 'uncomputable', but any particular finite sub-set of
> that class will in fact be entirely computable. So
> there is really no constructive way of defining an
> 'uncomputable' entity. All mathematical entities with
> objective existence are computable. It is simply the case
> that there is an infinite number of such entities.
>
Marc,
But the puzzling thing I mentioned is that it is often useful to
provisionally introduce mathematical entities that are UNCOMPUTABLE and
consequently LACK OBJECTIVE EXISTENCE, as intermediate stages in an
explanation of computable, "objectively existent" phenomena. For
example, the use of differential calculus (with its uncomputable
continua) to explain patterns among finite measurements.
-- Ben G
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