Discussion:
Halting Problem Final Conclusion
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Pete Olcott
2017-06-08 14:44:45 UTC
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The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
Compared to my prior claims, this one seem trivial and
obvious. Possibly this claim adds a slight nuance to the
problem that has not been widely discussed before.
If we construe pathological self-reference as another
error condition, then this does remove the impossibility
of creating a useful tool.
Now (thirteen years later) I have created a branch of mathematics called [Minimal Type Theory] (MTT) to formalize the notion of {Pathological Self Reference}.

http://LiarParadox.org/Provability_with_Minimal_Type_Theory.pdf
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Peter Percival
2017-06-08 14:46:41 UTC
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Post by Pete Olcott
The Liar Paradox can be shown to be nothing more than a incorrectly
formed statement because of its pathological self-reference. The
Halting Problem can only exist because of this same sort of
pathological self-reference.
The primary benefit of solving the Halting Problem was to detect
programs that failed to halt, thus were incorrect. Pathological
self-reference can also be viewed as a form of error. If the
Halting Problem is redefined (which does not refute anyone), then
this redefined problem can be easily solved.
Now we have three possible correct results: (a) Halts (b) Does Not
Halt (c) Pathological Self Reference to Halt
Compared to my prior claims, this one seem trivial and obvious.
Possibly this claim adds a slight nuance to the problem that has
not been widely discussed before. If we construe pathological
self-reference as another error condition, then this does remove
the impossibility of creating a useful tool.
Now (thirteen years later) I have created a branch of mathematics
That's "created" as in "fantasized about". Peer Olcott is unwilling,
and indeed unable, to answer any questions about MTT.
Post by Pete Olcott
called [Minimal Type Theory] (MTT) to formalize the notion of
{Pathological Self Reference}.
http://LiarParadox.org/Provability_with_Minimal_Type_Theory.pdf
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Kaz Kylheku
2017-06-08 15:04:57 UTC
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Post by Pete Olcott
Now (thirteen years later) I have created a branch of mathematics
called [Minimal Type Theory] (MTT) to formalize the notion of
{Pathological Self Reference}.
http://LiarParadox.org/Provability_with_Minimal_Type_Theory.pdf
Maybe you should take a break from this and take a crack at
trisecting angles with a straightedge and compass.
Pete Olcott
2017-06-08 15:24:37 UTC
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Post by Kaz Kylheku
Post by Pete Olcott
Now (thirteen years later) I have created a branch of mathematics
called [Minimal Type Theory] (MTT) to formalize the notion of
{Pathological Self Reference}.
http://LiarParadox.org/Provability_with_Minimal_Type_Theory.pdf
Maybe you should take a break from this and take a crack at
trisecting angles with a straightedge and compass.
http://www.cyc.com/documentation/ontologists-handbook/
My single-minded focus is to provide the mathematical foundation for the above system.

Once the Cyc Project has a complete mathematical foundation reverse-engineering the design of the automated process to complete the population of the Cyc knowledge ontology will be possible.

The foundations of this design are:
(1) The mathematics of sub atomic semantic compositionality. (Exactly and precisely how do all of the tiniest pieces of meaning fit together?).
(2) Minimal bootstrap knowledge ontology. (The minimum meta-knowledge (knowledge about knowledge) required as the initial basis).

We need to find the definition of the absolute minimum bootstrap knowledge ontology because the criterion measure derived for this absolute minimum will provide deep insight into the design of the process:

It will provide a list of the types of elements required and exactly how these elements fit together, basically a further elaboration of sub atomic semantic compositionality.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Arnaud Fournet
2017-06-08 18:19:59 UTC
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Post by Pete Olcott
Post by Kaz Kylheku
Post by Pete Olcott
Now (thirteen years later) I have created a branch of mathematics
called [Minimal Type Theory] (MTT) to formalize the notion of
{Pathological Self Reference}.
http://LiarParadox.org/Provability_with_Minimal_Type_Theory.pdf
Maybe you should take a break from this and take a crack at
trisecting angles with a straightedge and compass.
http://www.cyc.com/documentation/ontologists-handbook/
My single-minded focus is to provide the mathematical foundation for the above system.
Once the Cyc Project has a complete mathematical foundation reverse-engineering the design of the automated process to complete the population of the Cyc knowledge ontology will be possible.
(1) The mathematics of sub atomic semantic compositionality. (Exactly and precisely how do all of the tiniest pieces of meaning fit together?).
(2) Minimal bootstrap knowledge ontology. (The minimum meta-knowledge (knowledge about knowledge) required as the initial basis).
It will provide a list of the types of elements required and exactly how these elements fit together, basically a further elaboration of sub atomic semantic compositionality.
On behalf of Franz, I would like to protest against Franz's threads being hijacked by loonies like Pete Olcott.
A.

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