WRONG. Again you conflate Analytic truth with truth.
The Collatz conjecture, that there exist no number N such that the
sequence of progreesing to 3N+1 for N odd, and N/2 for N even doesn't
eventually reach 1, MUST be either True of False. There is no possible
"non-answer", as math doesn't allow for such things.
Thus either the statement "Collatz is True", or "Collatz is False", must
be true, and there is no known proof or refutation for either, While
this doesn't prove that no proof exists, it does point out a flaw with
your statement, until you have actually proved or refuted a statement,
you don't even know if it could be a truth bearer.
Thus we have a, at least possible, counter-example when you claim none
exist. You can only refute this as a possible counter-example by actualy
proving that a proof or refutation actually exists.
>
>> If needs to be taken as an assumption, it is not something that IS
>> unconditionally true.
>>
>>>
>>> There are only two possible ways that any ANALYTICALLY expression of
>>> language can possibly be true:
>>> (1) It is stipulated to be true. // like an axiom
>>> (2) It is derived by applying only truth preserving operations to (1)
>>> or the consequences of (2). // like sound deduction
>>
>> WRONG.
>>
>> There are only two possible ways that they can be ANALYTICALLY true.
>>
>
> Should I capitalize my use of ANALYTICALLY too so that you can see that
> I already specified this? (I capitalized it, above)
Except then it points out that you erroeous omit it in your other
statements.
>
>>>
>>> Analytic truth includes every expression of language that can be
>>> completely verified as totally true entirely on the basis of its
>>> meaning without requiring any sense data from the sense organs.
>>
>> And there are other truths besides Analytic Truth. That is implied by
>> the need of the adjective.
>
> All of math and logic is exclusively ANALYTICAL.
That is part of your error. Math and Logic use analytical methods to
prove its ideas, but not all Truth in math and logic is Analytical.
>
>>>
>>> Empirical expressions of language also require sense data from the
>>> sense organs to verify their truth.
>>
>> Nope, things can be empirically true even without the sense data.
>> Without the sense data they are not KNOWN to be true, but might be.
>>
>
> to verify their truth.
> to verify their truth.
> to verify their truth.
Truth doesn't need to be "Verified" to be True. It only needs to be
verified before its Truth can be used to create other Truths in a Proof.
>
>>>
>>> This means that if there are no connected set of semantics meanings
>>> (sound deduction) that make an analytical expression of language true
>>> then then it cannot possibly be true unless it was stipulated as true.
>>
>> WRONG. You are again confalating KNOWLEDGE with TRUTH.
>
> Counter-examples are categorically impossible because ALL ANALYTIC
> expressions of language ONLY derive their truth value from semantic
> connections to other ANALYTIC expressions of language that are known to
> be true, AKA sound deduction.
>
Thus, the circular definition.
You only show that ANALYTIC Truth must be proven, not Truth.
Analytics accept that not all Truth is Analytically proven. You make a
category error assuming all Truth must be Analytically True.
Note, An Analytical Statement might be True but not Analytically ture.
>
>>>
>>> The conclusion of Wittgenstein's analysis and mind is that if G is
>>> unprovable in F then G is simply untrue in F.
>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)).
>>
>> WRONG.
>>
>> Makes the erroneous assumption that Truth requires proof, and becomes
>> a circular argument.
>
> It is not a circle it is a tree of sound deduction.
> The conclusion is linked backwards (sound deduction in reverse) to every
> expression of language that derives it.
Nope. Give the NON-CIRCULAR proof.
Your failure to show what you claim is evidence that you don't actually
have a real proof.
Your statement that "Something is True only if it is Provable" is itself
a contradiction unless you can ACTUALLY prove it, and until you do, you
can not use it.
Without such a proof, the statement says it can not be true, so you can
not use it.
>
>>
>>>
>>> Even though F does meet the erroneous mathematical definition of
>>> Incomplete(F) that F was ever construed as incomplete is simply
>>> incorrect because it does not screen out expressions of language that
>>> are simply not truth bearers.
>>
>> Except that the expression of language WAS a Truth Bearer, as a given
>> statement MUST be either Provable or not. This comes because you of
>> course can't prove an statement that can't be true, like a non-sense
>> sentence.
>>
>
> As recently as 1974, people were still clueless about the issue of the
> liar paradox.It is the simplest of all self-reference paradoxes so I
> bought the domain name
liarparadox.org for my work.
>
> Tarski based his whole proof on the liar paradox and proved in his
> metatheory that it is not provable in his theory, same result as Godel.
>
>> Unless you are willing to define that Provability isn't a Truth
>> Bearer, which since you are then defining Truth as Provable, the Truth
>> of a statement isn't a Truth Bearer, you have a problem. You whole
>> logic system collapses as it can no longer talk about itself.
>>
>
> True(F, x) is implemented as Provable(F, x) through sound deduction on
> the basis of premises known to be true. In a reverse sound deduction
> (same thing as Prolog back-chaining inference) know truths (AKA Prolog
> facts) are sought on the basis of Prolog rules.
>
>
https://www.google.com/search?q=prolog+back+chainikng&rlz=1C1GCEJ_enUS813US813&oq=prolog+back+chainikng&aqs=chrome..69i57j33i10i160.4658j0j15&sourceid=chrome&ie=UTF-8
>
>
And Prolog doesn't define logic, but is just a programming languge to
handle simple rule sets.
Note, Prolog doesn't provide a well implemented "Not" operator, in part
BECAUSE it defines a statement that is unprovable as false.
If you want to limit your logic to what Prolog can handle, be my guess,
but then stay out of things beyond its capability, like Compuation Theory.
I don't think you are smart enough to understand the limitation of
Prolog (or even simple logic) and thus make enormous errors not
understanding the limited domain of your tools.
You just don't see that you logic system has become horribly
inconsistent because you close your eyes to those errors and say that
logic must be wrong, but you can't actually define WHAT is wrong with
the logic, because it actually does follow the rules you propose.