Re: Penrose vs the Robot


Aatu Koskensilta wrote:
> Rupert wrote:
>
> > This sentence leads to paradox. That's a reason for thinking that for
> > the purposes of precise mathematical argument Penrose shouldn't adopt
> > features of our ordinary language like having an unassailable belief
> > predicate which can take as arguments sentences containing itself.
>
> But should instead reason freely from such clear and unproblematic
> statements as "I am F"? As I said, Penrose's second argument seems to me
> to boil down to just the old and well-known problems with belief and
> truth predicates.
>

"I am F" can be expressed by an axiom expressing the equivalence of the
belief predicate with an arithmetical predicate.

One conclusion one can draw from Penrose's second argument, if one
accepts it, is that the set of sentences one unassailably believes in
any given language cannot itself be defined in that language. One
either has to accept this conclusion or find a problem with the
argument.

> --
> Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
>
> "Wovon man nicht sprechen kann, daruber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

.

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