On 12/21/22 10:17 AM, olcott wrote:
> On 12/20/2022 10:56 AM, Richard Damon wrote:
>> On 12/20/22 11:44 AM, olcott wrote:
>>> On 12/18/2022 6:03 PM, Richard Damon wrote:
>>>> On 12/18/22 10:28 AM, olcott wrote:
>>>>
>>>>> It may be the case "there is no finite proof of Goldbach's conjecture"
>>>>> is true and unknowable because the answer requires an infinite proof.
>>>>>
>>>>
>>>> Which means you accept that there may exist a statement (which
>>>> actually allows for statements) that is actually TRUE but which can
>>>> not be actually PROVEN and thus is unknowable.
>>>>
>>>> This is because proofs, by definition, are finite.
>>>>
>>>> Thus, you admit that your logic system might be incomplete.
>>>>
>>>
>>> I never said that tracing through semantic connects had to be finite.
>>> I only stipulated that when they do not exist then the expression of
>>> language is not a truth bearer.
>>
>> So you accept that there is a diffence between something True and
>> something Provable.
>>
>
> Unless and until an expression of language has been proven it is not an
> element of the set of knowledge.

Right, but that doesn't keep it out of the set of Truth.

That is what I keep on pointing out and you keep on forgetting.

There is a DIFFERENCE between what is TRUE, and what is KNOWN TO BE TRUE.

>
>>>
>>> Every element of the body of analytic truth is only true on the basis of
>>> its semantic connections to other elements of the body of analytic
>>> truth. Tracing through these connections is the proof of this truth.
>>>
>>>> In faxt, because of Godel's proof, which is similar, it is shown
>>>> that it MUST be incomplete.
>>>>
>>>> How does it feel to admit that you whole work is proven wrong by
>>>> your own words.
>>>
>>> "This sentence is not provable." Is not provable because it is
>>> self-contradictory and has a vacuous truth object.
>>
>> But it is true, since no proof exists, something very demonstrable.
>> The only issue is that the "proof" of the statement can only be done
>> with a infintite search, or logic in a "meta-field" about the field.
>
> G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))
> G is true if and only if G is unprovable and irrefutable in F
> ∃G ∈ F (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G))) is simply false

Nope,

>
> within this foundational theorem
> ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

Which is false in the logic system of F that is able to express G.

>
>> This just shows you don't understand your own logic, or the definition
>> of what a PROOF is.
>>
>
> To distinguish my ideas from the somewhat erroneous ideas of others my
> system is called correct reasoning rather than any form of logic.
>

So, you admit it has nothing to do with what everyone else calls logic.

Thus can NOT be just applied to things like the Halting Problem,
Incompleteness, of even Tarski's undefinable paradox.

Those are all statements in "Logic", not in your "Correct Reasoning".

Until you can provide the framework that extends your first principles
of "Correct Reasoning" to develop your equivalent expressions you can't
talk about them.

Until you can provide enough framework that extends your first
principles of "Correct Reasoning" to show that they can handle at least
some significant part of what we use the existing logical framework,
people aren't going to be interested in you system.

Go ahead, you only have a whole history of logic to re-derive based on
your new foundation.