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Re: What formal logical systems resolve the Liar Paradox?

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On 1/13/26 1:43 PM, olcott wrote:
> On 1/13/2026 6:10 AM, Richard Damon wrote:
>> On 1/12/26 11:46 PM, olcott wrote:
>>> On 1/12/2026 9:16 PM, Richard Damon wrote:
>>>> On 1/12/26 4:41 PM, olcott wrote:
>>>>> How The Well-Founded Semantics for General Logic Programs
>>>>>
>>>>> of (Van Gelder, Ross & Schlipf, 1991)
>>>>> Journal of the Association for Computing Machinery,
>>>>> volume 38, number 3, pp. 620{650 (1991).
>>>>> https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf
>>>>>
>>>>> handle the Liar Paradox when we construe
>>>>> non-well-founded / undefined as not a truth-bearer?
>>>>>
>>>>> % This sentence is not true.
>>>>> ?- LP = not(true(LP)).
>>>>> LP = not(true(LP)).
>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>> false.
>>>>>
>>>>> WFS assigns undefined to self-referential paradoxes
>>>>> without external support.
>>>>>
>>>>> When we interpret undefined as lack of truth-bearer
>>>>> status the Liar sentence fails to be about anything
>>>>> that can bear truth values
>>>>>
>>>>> The paradox dissolves - there's no contradiction
>>>>> because there's no genuine proposition
>>>>>
>>>>> This is actually similar to how some philosophers
>>>>> (like the "gap theorists") handle the Liar: sentences
>>>>> that fail to achieve determinate truth conditions
>>>>> simply aren't truth-bearers. WFS's undefined value
>>>>> provides a formal mechanism for identifying exactly
>>>>> these cases.
>>>>>
>>>>> A Subtle Point The occurs-check failure in Prolog is
>>>>> slightly different from WFS's undefined assignment -
>>>>> it's a structural constraint on term formation. But
>>>>> both point to the same insight: circular, unsupported
>>>>> self-reference doesn't create genuine semantic content.
>>>>>
>>>>>
>>>>
>>>>
>>>> I thought you said that no one in the past handled the liar paradox?
>>>>
>>>
>>> That is no one in the past handling the Liar Paradox.
>>> That all happened today.
>>
>> So, today is 1991?
>>
> 
> The paper provides the basis for me to
> handle the Liar Paradox today. The Paper
> does not mention the Liar Paradox it
> only shows how to implement Proof Theoretic
> semantics in a logic programming system.
> 
>>>
>>>> I guess you are just admitting you are just a liar.
>>>>
>>>>
>>>> Note, since Prolog's logic is not sufficient to handle PA, 
>>>
>>> I never said it was. A formal system anchored in
>>> Proof Theoretic Semantics is powerful enough.
>>
>> Nope. It can't handle PA.
>>
> 
> It definitely can. I already showed you the details
> of how.

Nope,  you PRESUME that Godel is non-sense.

But, you can't show the step in his proof that he uses an incorrect 
logic step.

All you are doing is proving that you are just a pathological liar that 
can't cover his own lies.

And, your claim that it is just non-smese means that you claim of making 
truth computable CAN'T be true.

A fundamental of Godel's proof is showing that a proof checker is a 
computatble operation. That is the essense of what all of Godel's 
numbering and the relation he derives.

If you define that you can't even build a proof checker, how do you 
expect to be able to determine if a statement is actually true?

> 
>>>
>>>> your argument here doesn't affect the logic system that you are 
>>>> trying to argue about, and you are just showing that you don't 
>>>> understand that difference.
>>>>
>>>> Many system can handle some self-references, which Prolog, and 
>>>> yours, can't.
>>>
>>>
>>
> 
> 

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Thread

What formal logical systems resolve the Liar Paradox? olcott <polcott333@gmail.com> - 2026-01-12 15:41 -0600
  Re: What formal logical systems resolve the Liar Paradox? Richard Damon <Richard@Damon-Family.org> - 2026-01-12 22:16 -0500
    Re: What formal logical systems resolve the Liar Paradox? olcott <polcott333@gmail.com> - 2026-01-12 22:46 -0600
      Re: What formal logical systems resolve the Liar Paradox? Richard Damon <Richard@Damon-Family.org> - 2026-01-13 07:10 -0500
        Re: What formal logical systems resolve the Liar Paradox? olcott <polcott333@gmail.com> - 2026-01-13 12:43 -0600
          Re: What formal logical systems resolve the Liar Paradox? Richard Damon <Richard@Damon-Family.org> - 2026-01-14 21:57 -0500
            Re: What formal logical systems resolve the Liar Paradox? olcott <polcott333@gmail.com> - 2026-01-14 23:24 -0600
              Re: What formal logical systems resolve the Liar Paradox? Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-15 06:50 -0500
                Re: What formal logical systems resolve the Liar Paradox? olcott <polcott333@gmail.com> - 2026-01-15 17:40 -0600
                Re: What formal logical systems resolve the Liar Paradox? Richard Damon <Richard@Damon-Family.org> - 2026-01-15 22:27 -0500
                Re: What formal logical systems resolve the Liar Paradox? Mikko <mikko.levanto@iki.fi> - 2026-01-18 13:54 +0200
            Re: What formal logical systems resolve the Liar Paradox? Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-15 14:30 +0000
              Re: What formal logical systems resolve the Liar Paradox? Richard Damon <Richard@Damon-Family.org> - 2026-01-15 22:27 -0500

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