Re: Ross Finlayson what about the Prolog Liar Paradox ?

On 7/7/2026 2:17 PM, Ross Finlayson wrote:
> On 07/07/2026 11:07 AM, olcott wrote:
>> On 7/7/2026 12:53 PM, Ross Finlayson wrote:
>>> On 07/07/2026 09:10 AM, olcott wrote:
>>>> % This sentence is not true.
>>>> ?- LP = not(true(LP)).
>>>> LP = not(true(LP)).
>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>> false.
>>>>
>>>> That is an elegant and classic way to demonstrate the Liar Paradox
>>>> ("This sentence is false") using Prolog's unification mechanics!
>>>>
>>>> You've perfectly captured the tension between computational pragmatism
>>>> and strict mathematical logic. Here is exactly what is happening under
>>>> the hood in your snippet:
>>>>
>>>> 1. The Pragmatic Illusion: Standard Unification
>>>>
>>>> Prolog
>>>> ?- LP = not(true(LP)).
>>>> LP = not(true(LP)).
>>>>
>>>> When you use the standard unification operator (=), Prolog tries to 
>>>> make
>>>> the left side and the right side identical. To save processing time and
>>>> memory, Prolog historically skips a crucial step called the occurs
>>>> check.
>>>>
>>>> Because it skips this check, Prolog happily binds the variable LP to 
>>>> the
>>>> term not(true(LP)). This creates a cyclic term (or a rational tree). In
>>>> memory, LP now points to a structure that contains a reference back to
>>>> LP, creating an infinite loop of self-reference. Computationally, 
>>>> Prolog
>>>> accepts the paradox.
>>>>
>>>> 2. The Logical Safeguard: The Occurs Check
>>>>
>>>> Prolog
>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>> false.
>>>>
>>>> Here, you enforce strict First-Order Logic. The
>>>> unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
>>>> "Does the variable I am trying to bind already exist inside the term I
>>>> am binding it to?" Because the variable LP occurs inside not(true(LP)),
>>>> Prolog realizes that unifying them would require building a
>>>> mathematically impossible, infinitely deep structure:
>>>> not(true(not(true(not(true(...)))))). It rightfully rejects the
>>>> unification and returns false.
>>>>
>>>> The Philosophical Takeaway
>>>> In logic, self-referential paradoxes often arise when a system is
>>>> allowed to talk about its own truth values without hierarchical
>>>> restrictions (as famously noted by Alfred Tarski).
>>>>
>>>> Your Prolog snippet perfectly mirrors this:
>>>>
>>>> Standard Unification acts like natural language, allowing the
>>>> self-reference to happen (and potentially causing a stack overflow if
>>>> you tried to evaluate or traverse it).
>>>>
>>>> The Occurs Check acts like a strict formal logic system, explicitly
>>>> forbidding self-referential loops and shutting the paradox down before
>>>> it can form.
>>>>
>>>>
>>>> https://share.gemini.google/5UVT3f5WnV8K
>>>>
>>>
>>> Imagine a language and its utterance of all the truisms in the universe.
>>>
>>
>> I have a name for this: The finite set of "atomic facts" of
>> empirical general knowledge and the finite set of relations
>> between them is named:
>> "the body of general knowledge expressed in language"
>>
>>> This isn't saying necessarily what it says, only that it's said.
>>> So, this account of a "Comenius language" of all the truisms is
>>> more than less inscrutable yet as empty tautologies and truisms,
>>> while yet each unique, for example as by natural numbers.
>>>
>>> "This sentence 1 is true.
>>> This sentence 2 is true.
>>> This sentence 3 is true.
>>> ..."
>>>
>>>
>>> So, quantify over those, like Russell might as
>>> "sets-of-all-sets-that-don't-contain-themselves".
>>>
>>> "This sentence (...) is not true."
>>>
>>
>> You are simply ignoring that expressions with cycles
>> in their evaluation sequence are rejected as meaningless.
>> Kripke would say that they are "undefined"
>>
>>> Now, the idea here is that there's only one example of a truism
>>> about contradiction, that the alternation of inversion of the
>>> consideration that results quantification, brings along the
>>> "sputnik of quantification", that reads in its form as
>>> "The Liar", yet instead of being a "paradox", its form is
>>> construed as being a "Confessing Liar".
>>>
>>>
>>> So, this account of univocity since Duns Scotus or as alike
>>> accounts of the kabalah and gematria or since acconts of the
>>> universal grammar since Panini like Leibnitz, this "Comenius
>>> language" its consideration, like Quine's Nietzsche's "eternal
>>> basic text", includes in itself a prototype of contradiction,
>>> in otherwise all its affirmations.
>>>
>>>
>>> Then, in natural language, there is a ready example or prototype
>>> of contradiction, that in alike the natural "Coleridge language",
>>> where that metaphor eventually fails yet there is a structural
>>> account of the strong metonymy that fulfills true metaphor about
>>> truth, then "the Liar" is simply an indicator of contradiction,
>>> and results instead of explosion to contradiction its unconscious
>>> digestion, results implosion to detection in any account of language.
>>>
>>>
>>> So, "thinking" instead of "being thought" is the usual idea.
>>> That's all then that the cycle-detection routine claims to do.
>>>
>>>
>>> This way there are no paradoxes at all in Comenius language,
>>> including that Confessing Comenius has an example to compare
>>> against, what would be false.
>>>
>>>
>>>
>>> The eternal basic text or underlying univocal universal word
>>> might be negations instead of affirmations.
>>>
>>> "This sentence 1 accounts and excludes 0.
>>> This sentence 2 accounts and excludes 1.
>>> This sentence 3 accounts and excludes 2.
>>> ..."
>>>
>>>
>>> Then a similar account gives alike:
>>>
>>> "This sentence infinity accounts and includes infinity."
>>>
>>>
>>>
>>> Then simple accounts of error-detection then error _correction_,
>>> including accounts of "not enough information" or "conflicting
>>> information" are mostly usual and trite, in fact there's an
>>> entire enterprise called "science" which makes for an inter-subjective
>>> formal account with regards to strengthened logicist positivism
>>> and ontologists, which though is always a _science_, yet though
>>> that there are ideals like "truth" and "infinity" for that
>>> "geometry" and "continuity" are real, and more than the blahs.
>>>
>>
>> So maybe this is too much into the field of philosophy of
>> logic and thus outside the field or carefully memorizing
>> exiting conventions for you to understand.
>>
>> The bottom line is the my Prolog tossed the Liar Paradox
>> out on its ass and Gemini agrees. You didn't seem to get
>> this most crucial point.
>>
> 
> 
> 
> Russell would call you a fool. 

Not at all he himself had the vicious circle principle.
https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-1/Russell-Presupposition-and-the-Vicious-Circle-Principle/10.1305/ndjfl/1039096305.full 


Have you every heard of ZFC?

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).