1 May
2018
1 May
'18
1:14 p.m.
On Tue, May 1, 2018 at 7:19 AM, Cris Moore <moore@santafe.edu> wrote:
... For any set of axioms, there is a Turing machine which 1) never halts and 2) that set of axioms cannot prove that it never halts. ...
But don’t you agree that the Halting Problem has a definite truth value? In other words, that a given Turing machine (with a given input) either runs forever or doesn’t, regardless of our ability to prove it? ...
To answer the question posed, shouldn't we ask if, given any *particular* TM, there exists *some* consistent system/set of axioms that can prove whether it halts or not? I was under the impression that the answer here was "yes", regardless of any individual consistent system being unable to tackle the general problem.