On 9/7/2024 8:19 AM, Richard Damon wrote:
> On 9/7/24 9:06 AM, olcott wrote:
>> On 9/7/2024 3:35 AM, Mikko wrote:
>>> On 2024-09-06 12:22:04 +0000, olcott said:
>>>
>>>> On 9/6/2024 6:55 AM, Mikko wrote:
>>>>> On 2024-09-03 12:44:00 +0000, olcott said:
>>>>>
>>>>>> On 9/3/2024 5:38 AM, Mikko wrote:
>>>>>>> On 2024-09-02 13:01:23 +0000, olcott said:
>>>>>>>
>>>>>>>> On 9/2/2024 2:54 AM, Mikko wrote:
>>>>>>>>> On 2024-09-01 13:47:00 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 9/1/2024 7:52 AM, Mikko wrote:
>>>>>>>>>>> On 2024-08-31 18:48:18 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> *This is how I overturn the Tarski Undefinability theorem*
>>>>>>>>>>>> An analytic expression of language is any expression of
>>>>>>>>>>>> formal or natural language that can be proven true or false
>>>>>>>>>>>> entirely on the basis of a connection to its semantic
>>>>>>>>>>>> meaning in this same language.
>>>>>>>>>>>>
>>>>>>>>>>>> This connection must be through a sequence of truth
>>>>>>>>>>>> preserving operations from expression x of language L to
>>>>>>>>>>>> meaning M in L. A lack of such connection from x or ~x in L
>>>>>>>>>>>> is construed as x is not a truth bearer in L.
>>>>>>>>>>>>
>>>>>>>>>>>> Tarski's Liar Paradox from page 248
>>>>>>>>>>>> It would then be possible to reconstruct the antinomy of
>>>>>>>>>>>> the liar
>>>>>>>>>>>> in the metalanguage, by forming in the language itself a
>>>>>>>>>>>> sentence
>>>>>>>>>>>> x such that the sentence of the metalanguage which is
>>>>>>>>>>>> correlated
>>>>>>>>>>>> with x asserts that x is not a true sentence.
>>>>>>>>>>>> https://liarparadox.org/Tarski_247_248.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> Formalized as:
>>>>>>>>>>>> x ∉ True if and only if p
>>>>>>>>>>>> where the symbol 'p' represents the whole sentence x
>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> *Formalized as Prolog*
>>>>>>>>>>>> ?- LP = not(true(LP)).
>>>>>>>>>>>> LP = not(true(LP)).
>>>>>>>>>>>
>>>>>>>>>>> According to Prolog semantics "false" would also be a correct
>>>>>>>>>>> response.
>>>>>>>>>>>
>>>>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>>>>>> false.
>>>>>>>>>>>
>>>>>>>>>>> To the extend Prolog formalizes anything, that only formalizes
>>>>>>>>>>> the condept of self-reference. I does not say anything about
>>>>>>>>>>> int.
>>>>>>>>>>>
>>>>>>>>>>>> When formalized as Prolog unify_with_occurs_check()
>>>>>>>>>>>> detects a cycle in the directed graph of the evaluation
>>>>>>>>>>>> sequence proving the LP is not a truth bearer.
>>>>>>>>>>>
>>>>>>>>>>> Prolog does not say anything about truth-bearers.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It may seem that way if you have no idea what
>>>>>>>>>> (a) a directed is
>>>>>>>>>> (b) what cycles in a directed graph are
>>>>>>>>>> (c) What an evaluation sequence is
>>>>>>>>>
>>>>>>>>> More relevanto would be what a "truth-maker" is.
>>>>>>>>> Anyway, it seems that Prolog does not say anything about
>>>>>>>>> truth-bearers because Prolog does not say anything about
>>>>>>>>> truth-bearers.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When Prolog derives expression x from Facts and Rules
>>>>>>>> by applying the truth preserving operations of Rules to
>>>>>>>> Facts is the truthmaker for truth-bearer x.
>>>>>>>
>>>>>>> A Prolog impementation applies Prolog operations.
>>>>>>
>>>>>> Which are (like logic) for the most part truth preserving.
>>>>>> If (A & B) then A
>>>>>
>>>>> Logic where the infoerence rules are for the most part truth prserving
>>>>> is not useful. They all must be.
>>>>>
>>>>>>> For some cases
>>>>>>> Prolog offers several operations letting the implementation to
>>>>>>> choose which one to apply.
>>>>>>
>>>>>> I don't thing so. Once the Facts and Rules are specified
>>>>>> Prolog chooses whatever Facts and Rules to prove x or not.
>>>>>> It is back-chained inference.
>>>>>
>>>>> Standard Prolog is what the Prolog standard says. Conforming
>>>>> implementations
>>>>> may vary if the standard allows. If you think otherwise you are wrong.
>>>>> There are also non-starndard Prlongs that vary even more.
>>>>>
>>>>
>>>> The fundamental architectural overview of all Prolog implementations
>>>> is the same True(x) means X is derived by applying Rules (AKA truth
>>>> preserving operations) to Facts.
>>>
>>> The details are permitted to differ.
>>>
>>
>> Instead of using any single order of logic we simultaneously
>> represent an arbitrary number of orders of logic in a type
>> hierarchy knowledge ontology.
>>
>
> Doesn't work, and just shows that you don't understand what you are
> talking about.
This already implemented in conventional type theory.
Objects of thought at differing orders of logic are different types.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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