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}.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.

http://LiarParadox.org/Provability_with_Minimal_Type_Theory.pdf

--

(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)

(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)