Re: A modern view of the halting problem

On 22 Oct 2006 08:49:56 -0700
"randyhyde@xxxxxxxxxxxxx" <randyhyde@xxxxxxxxxxxxx> wrote:

:The generalized proof of undecideability (the generic problem posed by
:the halting problem) does *not* apply to humans. It applies to *Turing
:Machines* [. . .]

Rewriting history again, are we? The generalized proof of undecidability
is contained in Godel's First Incompleteness Theorem, which was published
in 1931, a full five years before Turning published his paper on Turing
machines, and therefore could not possibly have been developed with Turing
machines in mind.

You really should try reading it sometime. I would type it here,
except that some of the symbols which it uses do not come across correctly
in news groups. However, the net of it, in plain language, is that a
proposition is said to be undecidable in a logic system if neither it, nor
its negation can be proven within that system.

For example, the statement "This statement is true." Is undecidable,
because, although it is consistent with being either true or false, it is
not possible to prove either case.

There is nothing, other than the requirement that the logic system be
consistent and stable, which excludes it from applying to human beings. In
fact, the concept that it does, indeed, apply to humans is supported by
your own citation that "it has been taken to imply that you'll never
entirely understand yourself, since your mind, like any other closed
system, can only be sure of what it knows about itself by relying on what
it knows about itself".

:"Turing Machines (an abstract model which models all real computers, as
:far as :we know).

As far as YOU know, perhaps, but those of us who live in the real world
know better. As a trivial example, like many others, I have a display on
my desktop which constantly informs of the current time and date,
customized for my local time zone. And, of course, it does this without
interfering with whatever other computing functions are going on. How would
you propose modeling this function on a Turing machine?

-- Chuck







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