[FOM] The Lucas-Penrose Thesis

laureano luna laureanoluna at yahoo.es
Thu Oct 5 12:07:34 EDT 2006

Arnon Avron wrote (quoting first Robbie Lindauer):

>> The claim is that it is impossible (logically) for
>>a given machine to
>> determine the truth of (any of) its Godel
>>sentences and that it is 
>> (logically) impossible for humans to do decide the
>>godel sentence 
>> for that given machine.

>If humans are machines, and it is impossible  
(logically) for a given
>machine to  determine the truth of (any of) its
>Godel sentences,
>then (by pure logic) it *is* (logically) impossible
>for humans 
>to decide their own godel sentences. Your argument
>*assumes* that
>humans are not machines - it does not prove it (this
>is typical to the "Proofs for the believers" type of

The point is that we have a proof of the logical
impossibility that a consistent machine proves its own
consistency but we do not have the corresponding proof
regarding a consistent human. 

Let's suppose a human to whom the whole description of
the Turing machine that mirrors him is presented: why
could it be logically (not just physically) impossible
for him to recognise that machine as sound? Since that
description is finite and contains nothing else but
the human's logical and mathematical ability, I cannot
imagine what that impossibility could be. 

As I recently suggested on FOM, mechanists should take
as a scientific challenge the goal of proving that
logical impossibility.

The Lucas-Penrose argument remains inconclusive
because no one has proved the inexistence of that
logical impossibility, but while that existence is
still implausible, mechanism is still implausible.


Laureano Luna Canañero

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