Re: Mathematics, Pseudomathematics, Artificial Intelligence

From: JXStern (JXSternChangeX2R_at_gte.net)
Date: 02/17/05 

Date: Thu, 17 Feb 2005 06:00:18 GMT

On 16 Feb 2005 07:32:16 -0800, stevendaryl3016@yahoo.com (Daryl
McCullough) wrote:
>I don't see how it's relevant. Do you mean that you believe that
>the semantics of natural language involves constructive or otherwise
>nonclassical interpretations of quantifiers and connectives?

I do.

> That
>very well may be true (even though I would say that natural language
>doesn't fit very well with first-order logic, period, regardless of
>whether it is constructive or classical logic).

That's consistent.

> But even if it is
>true, it doesn't say anything about the sort of mathematics that should
>be used to *analyze* brains or natural language.

Not with certainty, but it's suggestive, if intelligence is itself
constructive, it increases the hope that the mechanisms for
instantiating intelligence are also constructive.

> Classical mathematics
>is perfectly capable of describing and analyzing constructive reasoning.

Because constructive is a subset of classical?

>The tools used to analyze a system don't need to be closely related
>to the tools used *by* that system. We can use digital cameras to
>record people making sand paintings, after all.

But on the other hand, one doesn't construct castles out of thin air.

J.

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