On 11/20/23 7:32 PM, olcott wrote:
> On 11/20/2023 3:39 PM, olcott wrote:
>> ...14 Every epistemological antinomy can likewise be
>> used for a similar undecidability proof...(Gödel 1931:43-44)
>>
>> An epistemological antinomy is a self-contradictory expression.
>>
>> ∀L ∈ Formal_System
>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> The only possible place to insert Gödel's above reference
>> to an epistemological antinomy in the above definition of
>> Incompleteness is x.
>>
>> So Gödel's quote is saying that a formal system <is> incomplete
>> when it cannot prove or refute a self-contradictory expression.
>>
>> He says this even though the actual reason that self-contradictory
>> expressions cannot be proven or refuted is that there is something
>> wrong with them.
>
> I am only referring to the above Gödel quote and stipulating that
> anything else that he ever said or did is an dishonest dodge
> way from the point.
So, since that statement doesn't mention incompleteness, your arguement
is just incoherent.
And, if you widen the context that it is in his incompleteness proof, he
doesn't say that the epistemological antinomy has anything to do
directly with the sentence that shows the Formal System to be incomplete.
Only by you applying your strawman INCORRECT presumptions can you
attempt to link them.
Thus, you are shown to just be a ignorant pathological lying troll
>
> I am also only referring to the above definition of incompleteness
> thus not any naive paraphrase.
And since the statement didn't mention incompeteness, the definition
doesn't apply.
>
> The first incompleteness theorem states that in any consistent formal
> system F within which a certain amount of arithmetic can be carried out,
> there are statements of the language of F which can neither be proved
> nor disproved in F.
>
https://plato.stanford.edu/entries/goedel-incompleteness/
>
So, you are LYING that you are only using that first quote?
Note, by bringing in the theorem, and are talking about the proof, you
have brought into the discussion the WHOLE proof.
And yes, he claims that there is a statement in F which can neither be
proven nor disproven in F, and comes up with that statement, which is
commonly called G, and can be expressed appoximately in the words:
G: There does not exist a Natural Number g that satisfies a particular
Primitive Recursive Relationship (which is developed in detail in the proof)
Note, this G, is NOT an epistemologal antinomy, as it is simple to show
that such a statment MUST be either True or False.
Thus, it is shown that you claim that he is some how referencing the
"sentence" that shows the system to be incomplete when he talks about
the epistemological antinomy used in the proof is incorrect, and you
attempts to try to limit it to that is just a deception.
Thus, your whole arguement is shown to be incorrect due to a total lack
of understanding by yourself of what is being done.