Re: Undecidability based on epistemological antinomies V2 --Mendelson--

On 04/26/2024 12:01 PM, Richard Damon wrote:

On 4/26/24 2:40 PM, olcott wrote:
>

Mathematical incompleteness and decision problem undecidability
have a totally vacuous philosophical foundation.
>

>
Nope, THAT STATEMENT has an incorrect philosophical foundation, because
you just don't understand the meaning of the words you are using.
>
>
Even the most grand philosophical foundations admit that fundamentally,
there can be truths that are not knowable in sufficiently complicated
logical systems.
>
That you don't understand that is YOUR limitation, not the limitation of
philosophy.

So, that's your theory of the logic of it?
There is one, then, what it is?
Is there, logic, at all?
Truth?
That the integers do not have a standard model, i.e.,
that there are infinite members,
or at least one, or maybe half, or most,
and about whether it's composite or prime,
or among triple, quadruple, and infinite primes,
in the arithmetic with the fundamental theorem of arithmetic,
and in algebra about the the indeterminate forms,
that are singularities yet multiplicities,
has that there are various truths knowable
about these system(s), what together comprise the
objects of arithmetic with regards to Goedel's
induction after non-constructive deduction,
the most usual sort of antidiagonal argument,
and furthermore, the objects of arithmetic.
Numbers, ....
That there's a difference between "vacuous" and "empty",
a difference between "trivial" and "profound",
sort of results after all, there isn't.
Foundation, here is a sole foundation that there's truth,
same for anybody.
So, most models of integers are fragments or extensions.
That there's a standard one is a usual conceit,
to that there isn't.
The "extra-ordinary", starting variously
in geometry and words
just like every other most usual
canon of technical philosophy,
is a sublime and transcendant thing,
as according to, for example, Kant and Hegel.
... And Aristotle and Hegel.
So, we look to Mirimanoff as for coining the word
"extra-ordinary", while the sublime and transcendant
has a bit longer prologue.
Which needn't result so much to have most it all, ....