On 23 Aug 2012, at 18:11, benjayk wrote:

Or how can you determine whether to program a particular program or not? To
do this computationally you would need another program, but how do you
determine if this is the correct one?

You don't.

In theoretical inductive inference theory (Putnam, Gold, Blum, Case and Smith, Oherson, Stob, ...), you can show this: The more machines can be wrong, and relies on other machines, and change their minds, and (amazingly enough) change their mind wrongly (changing a correct theory for the know facts by an incorrect one), from times to times, the more larger are the classes of phenomena that they are able to recognize (build correct theories fro them).

And those theorem are non constructive, meaning that in the world of inference inductive machine, a machine capable of being wrong is already non computably more powerful than an error prone machine.

if like some people, you define intelligence by an ability to extrapolate series, there is something transcendentally (non- computably, even with strong oracles) more powerful than any inference inductive machine, it is a couple of inference inductive machines.

All machines evolves, in a non predictable way, through errors, notably.



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