On 07 Sep 2005, at 06:35, Lee Corbin wrote:
> 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/
Received on Wed Sep 07 2005 - 09:55:57 PDT