Re: Physics is a human construct

[Charles Crummer <ccrummer@cats.ucsc.edu>]

> Godel produced a statement which is formally undecidable and true IF THE
> FORMAL SYSTEM IS CONSISTENT.  Since Godel did not prove the consistency of
> the formal system, what he shows is that "The statement S is true and
> undecidable, if the formal system is consistent.".  That latter statement
> can be PROVED in the formal system--that result is known as godel's Second
> Incompleteness Theorem.
> This misstatement of the Godel result has been around at least since Nagel
> & Newman's book, *Godel's Proof*, in the late 50s, and was recently
> elevated into a bestseller by Penrose, but it is still a mistake.
>
> Turing produced a program and showed that there are inputs for which it
> does not halt and that the non-halting character cannot be proved in the
> formal system, but he did not SPECIFY any particular inputs that he knew
> were not halting and which could not be demonstrated.
>
> Neither Godel nor Turing tell us anything very interesting about
> consciousness.
>
> Richard Grandy
> Philosophy
> Rice University

What Goedel, Turing, and Church did seems to me to be an interesting
demonstration of what humans can do that machines, in principle, can't do.
Whether or not the formal system is consistent doesn't seem to me to be
relevant to their demonstration that a rule-based system is circumscribed
in a way that we are not.

	Charlie