I just keep tipping up the slate of paradox/no-paradox and
infinity/infinity-infinity, must be foundations.
I luxuried study in the types and so when there is inspection
and reflection on the mathematical objects, there are all the
paradoxes of the mathematics and logic which results in objects
what so confirm for example for geometry all their truth besides
how it's possibly comprehensible, if at all.
I.e., the paradoxes like Zeno's, or the paradox of motion,
are simply laws either way with respect to what must be time.
Still, motion in geometry is for the usual _objective_, i.e. that
geometry the theory allows theory is objective. (If not "my theory",
subjective, "the theory sublime to any other theory including mine",
So it's a luxury when "for my theory what is actually sublime to
this formalism where paradox means stop not build a bridge to
the other side of complete objective formality", it's what foundations
is relevant or not for the applied, that these total questions in theory
are just mindless inference.
Then for countability/uncountability or "infinity / no, infinity",
I already had a clock hypothesis besides a lattice hypothesis,
so uncountability in finite domains is largely about combinatorics,
besides what the continuous is sublime to it. For "no paradox"
then is laws both ways, all real numbers.
Going from Cartesian what are the usual inner products about
that going from binary, 0-1, to any more values in the valency of
the logic from the multi-valued or multi-valent not being the
bi-valent Cartesian case, I define my functions regularly as
Cartesian about the Cantorian.
For example, where for function theory is defined for the
actual case in continuum mechanics about Descartes' lattice
in space and Cantor's lattice in space, each the same space
in ordinals, it's a usual result after primary function theory.
So, the slate for uncountability is a raft of results, what for
the usual conscientious formalist admit of course all sound
reason and that most outstanding questions, in mathematics,
often these days for example reflect questions about infinity
and continuum mechanics.
Thanks, I had enough time here to study foundations for its
own sake as much as usual for example matters what take
less time - that when people have issues or notice usual total
grand facts about things that I also found so profound and
of course for example confirming larger logic must be correct,
I mostly of course wrote immediately whatever possibly I could
use in a sentence that could possibly advance my "cause".
(What is to have written a foundations.)