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http://www.yorku.ca/dept/psych/classics/Lovelace/menabrea.htm

http://www.yorku.ca/dept/psych/classics/Lovelace/lovelace.htm

On Wed, 16 Feb 2000, Cliffe, Owen wrote:

*> Cliffe:
*

*> MENEBREA starts by saying that there are areas of mathematics that can
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*> be automated and those that can't, this distinction is interesting
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*> because in a sense I think it captures in some way the distinction
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*> between intellect and automation, in that it implies that the process
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*> of 'reasoning' cannot be automated (at least not sufficiently to do
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*> proper math, by which I assume he is indicating proof and discovery).
*

Yes, but is the distinction valid? and is it true that reasoning

(thinking) cannot be automated (computational).

When it comes to mathematical proof and discovery, there was "Hilbert's

Programme," which was meant to discover the rules by which all true

theorems could be mechanically proven from their axioms. Goedel (see

next week's reading by Lucas) showed that Hilbert's Programme could not

be fully realized, because it was provable that every axiomatic system

(if it was consistent, and included arithmetic) would have theorems

that were true but not provable. Lucas argued that because our minds

can KNOW this, they cannot be just computational:

J.R. Lucas (1961) Minds, Machines and Goedel. Philosophy 36 112-127.

http://cogprints.soton.ac.uk/abs/phil/199807022

There are problems with this idea, as we will see next week, but even

if we leave it open whether Lucas's Goedel-argument is right or wrong,

there is no formal argument for mathematical discovery and intuition in

general, is there? Isn't it still just as possible that the processes

that generate those discoveries and intuitions are computational,

even though we don't know happen to know (yet) what algorithm they are

using? That would not mean that our minds can think everything, but

what they can think, they could still think through (unconscious)

computation.

In dealing with Lady Lovelace, you passed over the "objection" that

Turing himself singled out for discussion:

Lady LOVELACE:

"The Analytical Engine has no pretensions to originate anything. It

can do whatever we know how to order it to perform"

Is it true that computation cannot do anything "new"? What does "new"

mean? Can WE do anything new? If it takes us by surprise, does that

mean it could not have been computable? Does it even mean that it was

not actually computed (unconsciously) by our brains?

If you are interested in creativity, have a look at:

Harnad, S. (in prep.) Creativity: Method or Magic?

http://www.cogsci.soton.ac.uk/~harnad/Papers/Harnad/

Stevan

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