On 07 Sep 2005, at 06:35, Lee Corbin wrote:

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Bruno writes[Hal wrote]I wouldn't be surprised if most people who believe that minds can be simulated on TMs also believe that everything can be simulated on a TM.They are wrong.Note that this is just Bruno's opinion.

No. It is Bruno's theorem :-)

Hal's statement really is true: most people don't agree with Bruno on this.

`My sad discovery is that many people can hardly follow a deductive`

`argumentation when it goes too much again their (not always`

`conscious) prejudice.`

But UDA is more easy than many imagine. Also.

If minds are turing-emulable then indeed minds cannot perceive something as being provably non-turing-emulable, but minds can prove that 99,999...% of comp-Platonia is not turing-emulable.I don't pretend to understand this at all. You are saying that minds (e.g. we) cannot *perceive* something as being provably non-turing-emulable, yet minds can nonetheless *prove* that something is non-turing-emulable.

Russell has given a good answer.

`More generally: If you accept the use of the excluded middle`

`principle you can prove disjunctions, A V B, without being able to`

`prove neither A nor B. You can prove the existence of a number n`

`having some property without being able to prove, whatever n is, that`

`n has that property.`

`If C represents a modality of proof, you are confusing C(ExP(x)) with`

`ExCP(x). E = "it exits" quantifier.`

I (very naively, of course) would have supposed that as soon as a mind proved that X was Y, then that very mind would have perceived that X was provably Y. How confusing.

`Since Godel, Brouwer ... we know that the notions of formal and`

`informal provability are quite subtle and counter-intuitive notions.`

`That is why modal logic, mainly through Solovay's theorem, is an`

`incredible relief, by axiomatizing soundly and completely (at the`

`propositional level) the logic of provability and their variants. But`

`the simpler UDA argument gives already an intuitive feel of the`

`oddities.`

Bruno http://iridia.ulb.ac.be/~marchal/