On 4/1/2023 2:40 PM, olcott wrote:
> On 4/1/2023 1:56 PM, olcott wrote:
>> On 4/1/2023 1:18 PM, olcott wrote:
>>> On 4/1/2023 12:46 PM, olcott wrote:
>>>> On 4/1/2023 12:15 PM, olcott wrote:
>>>>> On 4/1/2023 11:42 AM, olcott wrote:
>>>>>> On 4/1/2023 11:19 AM, olcott wrote:
>>>>>>> On 4/1/2023 10:17 AM, olcott wrote:
>>>>>>>> On 4/1/2023 9:34 AM, olcott wrote:
>>>>>>>>> On 4/1/2023 12:16 AM, olcott wrote:
>>>>>>>>>> When G asserts that it is unprovable in F this cannot be
>>>>>>>>>> proven in F because it would be a proof in F that no such
>>>>>>>>>> proof exists in F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> No self-contradictory expressions can ever be proven in any formal
>>>>>>>>> system because they are self-contradictory not because the
>>>>>>>>> formal system
>>>>>>>>> is incomplete.
>>>>>>>>>
>>>>>>>>> This sentence is not true: "This sentence is not true" is true
>>>>>>>>> because
>>>>>>>>> the outer sentence refers to a self-contradictory sentence that
>>>>>>>>> cannot
>>>>>>>>> possibly be true under any circumstance.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> "This sentence is not true" is indeed not true yet that does not
>>>>>>>> make it true.
>>>>>>>>
>>>>>>>> When we drop Gödel numbers thus have G directly asserting that
>>>>>>>> itself is
>>>>>>>> unprovable in F this cannot be proven in F because it would be a
>>>>>>>> proof
>>>>>>>> in F that no such proof exists in F.
>>>>>>>>
>>>>>>>> Thus G is unprovable in F because G is self-contradictory in F not
>>>>>>>> because F is incomplete.
>>>>>>>
>>>>>>> Unless we drop Gödel numbers it is impossible to see WHY G is
>>>>>>> unprovable
>>>>>>> in F, diagonalization only shows THAT G is unprovable in F, thus
>>>>>>> leaving
>>>>>>> us free to simply guess WHY.
>>>>>>>
>>>>>>> When we see that G is unprovable in F because it would be a proof
>>>>>>> in F
>>>>>>> that no such proof exists in F, then we know that it is not
>>>>>>> unprovable
>>>>>>> in F because F is incomplete.
>>>>>>>
>>>>>>
>>>>>> When we see that G is unprovable in F because it would be a proof
>>>>>> in F
>>>>>> that no such proof exists in F, this is all that we need to know.
>>>>>>
>>>>>> Any reference to meta-F is not a proof in F that G is unprovable in F
>>>>>> thus merely an example of the strawman deception dishonest dodge away
>>>>>> from the point at hand.
>>>>>
>>>>> When we make a G in F that does assert its own unprovability in F then
>>>>> this F right here that we just made is unprovable in F because it
>>>>> would
>>>>> be a proof in F that no such proof exists in F.
>>>>>
>>>>> The only [fake] "rebuttal" to this requires the dishonest dodge of the
>>>>> strawman deception to change the subject to a different F than the one
>>>>> that we just specified. *There are no legitimate rebuttals to this*
>>>>>
>>>>
>>>> Even though it is not precisely Gödel's G
>>>>
>>>> 14 Every epistemological antinomy can likewise be used for a similar
>>>> undecidability proof. (Gödel 1931:39-41)
>>>>
>>>> the above shows that Gödel did know that self-contradiction is the key
>>>> element of every equivalent proof.
>>>>
>>>> Because epistemological antinomies are semantically ill-formed
>>>> expressions that are unprovable ONLY because they are
>>>> self-contradictory
>>>> we know that they are not unprovable for any other reason.
>>>>
>>>> Thus when the whole concept of mathematical incompleteness is debunked
>>>> then every use of mathematical incompleteness by each and every
>>>> proof is
>>>> invalidated.
>>>>
>>>
>>> When G asserts that it is unprovable in F this cannot be proven in F
>>> because it would be a proof in F that no such proof exists in F.
>>>
>>> Every rebuttal of this is one kind of a lie or another.
>>>
>>> If the above G is unprovable in F only because it is self-contradictory
>>> in F then it is not unprovable in F because F is incomplete.
>>>
>>> Every rebuttal of this is one kind of a lie or another.
>>>
>>
>>
>> When G
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>> asserts that
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>> is unprovable in F
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>>   THIS G RIGHT HERE
>> cannot be proven in F
>> because it would be a proof in F that no such proof exists in F.
>>
>> 14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof. (Gödel 1931:39-41)
>>
>> Thus every equivalent proof that Gödel refers to does not prove that its
>> formal system is incomplete, thus universally nullifying the notion of
>> mathematical incompleteness for all of these equivalent proofs.
>>
>
> When I show that the generic notion of mathematical incompleteness is
> bogus by showing that it is bogus for every equivalent proof that Gödel
> just referred to this is not any kind of fallacy.
>
> Because I just proved that I do know what epistemological antinomies
> are by providing an epistemological antinomy proves that I know what
> they are:
>
> > When G
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> > asserts that
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> > is unprovable in F
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> >   THIS G RIGHT HERE
> > cannot be proven in F
> > because it would be a proof in F that no such proof exists in F.
>
> Antinomy
> ...term often used in logic and epistemology, when describing a paradox
> or unresolvable contradiction.
> https://www.newworldencyclopedia.org/entry/Antinomy
>
> An empty unsupported claim that I am incorrect about this is the same as
> claims of election fraud without any evidence of election fraud, the
> tactic used by liars in an attempt to fool the gullible.
>

Incompleteness just requires that there exist SOME statement that it
True but not provable.

The only reason that Gödel has been able to get away with this is
because he is misconstruing provable in meta-F as true in F.

This is the way that analytical truth really works thus disagreeing with
it is the same as disagreeing that a baby kitten is not a type of ten
story office building.

*This system abolishes Gödel incompleteness and Tarski undefinability*
*Introducing the foundation of correct reasoning*

Just like with syllogisms conclusions a semantically necessary
consequence of their premises

Semantic Necessity operator: ⊨□

(a) Some expressions of language L are stipulated to have the property
of Boolean true.
(b) Some expressions of language L are a semantically necessary
consequence of others.
P is a subset of expressions of language L
T is a subset of (a)

Provable(P,X) means P ⊨□ ~X
True(T,X) means X ∈ (a) or T ⊨□ X
False(T,X) means T ⊨□ ~X

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer