Re: Is the Halting Problem merely an ill-formed question?



On Oct 22, 7:09 pm, "Peter Olcott" <NoS...@xxxxxxxxxxxxx> wrote:
An ill-formed question is any question that requires an answer from a solution
set where no correct answer exists within this solution set. One example of an
ill-formed question is the following: "How tall are you green or blue?".


At the instant the question is asked, neither YES nor NO is a correct
answer that can be made accessible. But *later*, it turns out that
there will be an answer that is either YES or NO. Classical logic
prescribes that the answer always was either YES or NO-- classically
truths are time-independent. So that is your problem - if the answer
was always either YES or NO, why isn't it possible to at least guess
which one and make a correct guess available in advance? I agree with
you that this is a paradoxical situation which strongly suggests that
the clasical philosophy of eternal, time-independent truth is
unsatisfactory in many scenarios. This is well-known from ancient times
-- e.g. does Aristotle's "There will be a sea-battle tomorrow" have a
definite truth value *today*?

What you need to understand, however, is that in order to challenge
this you need to challenge classical logic itself. You are really
asking for a temporal logic in which truths are time-dependent. NAFL is
one of these -- self-reference is indeed unacceptable in NAFL and
Turing's argument will not go through. Biut you have to understand both
the classical and NAFL concepts of truth very clearly and in full depth
to really have an appreciation for why Turing's argument fails in NAFL
and in general, why NAFL rejects self-reference.

Regards, RS

.

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