Bruno Marchal wrote:
> It is not a question of existence but of definability.
> For example you can define and prove (by Cantor diagonalization) the
> existence of uncountable sets in ZF which is a first order theory of
> Now "uncountability" is not an absolute notion (that is the
> Lowenheim-Skolem lesson).
> Careful: uncomputability is absolute.
Well, 'existence' would certainly be a stronger notion of platonism
than mere 'definability'.
So Bruno, what would your answer be to the question of whether the
universe is a computer or not? I think it all depends on how you
define 'universe' and 'computer' ;)
Personally, my answer is no, I don't think the universe is a computer.
I define 'universe' to mean 'everything which exists' and computer to
mean 'anything which is Turing computable'. Since I think
uncomputables do exist, they are part of the universe and they are not
Turing computable so the universe as a whole can't be a computer.
But one doesn't need to believe in uncomputables to doubt that the
universe as a whole is a computer. There is also the problem of
infinite quantities to contend with. Something which is computable is
most likely finite (by holographic string principles), but if there
exist things with infinite extent or quntification (like space for
instance) it's hard to see how the universe as a whole could be defined
as a computer.
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