Re: Alan Turing's Halting Problem is incorrectly formed (PART-TWO)

From: George Greene (greeneg_at_greeneg-cs.cs.unc.edu)
Date: 06/29/04 

Date: 29 Jun 2004 16:38:31 -0400

 : > >> Perhaps technically incorrect in the sense that the problem statement
 : > >> seems to presume that a solution must exist, but the problem can easily
 : > >> be restated in the form, "Does a ________ exist such that
 : ___________?".
 : > >> If the halting problem is restated in that way, do you still consider
 : it
 : > >> an incorrect problem?

"Peter Olcott" <olcott@worldnet.att.net> writes:

 : > > Then it would not be incorrect.

Oh, *** you, bitch.

 : > > Congratulations you are the third person to completely understand
 : > > what I have been saying.

Bull***. You have NOT been saying ANYthing REMOTELY LIKE this.

 : > I didn't really expect you to agree to that. It just didn't occur to me
 : > that what you were saying at great length could be as trivial as that.

And it is indeed trivial.

 : > Mathematicians just implicitly understand questions of the form
 : >
 : > Find a ________ that satisfies __________.
 : >
 : > to mean:
 : >
 : > Find a ________ that satisfies __________, or prove that
 : > none exists.

Even if we don't understand it that way, it would STILL go
without saying that IF you had proved that none exists, that
would HAVE to be counted as AN ANSWER to the question!

 : Its not really trivial.

Yes, it is. It's worse than trivial.

 : If as one respondent has stated the Halting Problem
 : is analogous to the incompletess theorem,

It is.

 : then the great refutation of the
 : logical positivists was incorrect,

No, it wasn't.

 : and they were right all along.

No, they weren't, and more to the point, you personally
have at least 1 fewer degrees in philosophy than I do, and
you don't have the faintest clue what "the logical positivists"
OR "the great refutation of them" even said (if such a thing
even exists).

 : The only things that are impossible are those things that are impossible
 : by the very meaning of the words.

By virtue of the meaning of the words "possible" and "impossible",
it is impossible for that sentence to be true.

 : Logical positivists refer to this as analytical truth.

EVERYbody refers to that as analytical truth, dumbass.

 : The inability to do the analytically impossible could
 : not be reasonably construed to be required to form a complete set
 : of capabilities.

"Complete" has a rather subjective meaning there.
First-order logic has both an incompleteness theorem AND
a completeness theorem. You are here trying to allege that
the fact that the class of all TMs is not "complete" enough to
include one implementing Halt(,) should not be held to mean
that it is "incomplete" in any important sense. But that is
just ridiculous. There are lots of well-defined things that
no TM can do. The class of TMs IS "incomplete" in that sense. 

-- 
 --- The history of our nation has demonstrated that separate is seldom, if ever, equal.
 --- (Feb.3,2004) Supreme Judicial Court of Massachusetts (4-3), adv.Sen.#2175
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