Re: The Circles

On 07/19/2025 08:17 AM, Ross Finlayson wrote:

On 07/08/2025 09:32 PM, Ross Finlayson wrote:

On 07/06/2025 06:10 AM, Ross Finlayson wrote:

On 06/29/2025 09:40 PM, Ross Finlayson wrote:

On 06/28/2025 09:24 PM, Ross Finlayson wrote:

On 06/28/2025 08:38 PM, Ross Finlayson wrote:

Oh, been a while, figure I'll post.
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Watching a speech of Dr. Woodin the other day, sort of like,
"well Scott keeps generalizing his theorem and our closed
bounded universes if you don't mind me calling the cumulative
hierarchy that, sort of make that large cardinals sort of reiterate
and I'm not sure whether a large supercompact cardinal is going
to read right when the ordinary inductive set has neither compactness
nor is it extra-ordinarily super, while we're calling Cohen's method
blueprints now and really that's Skolem when in model relativization
we're pretty sure we can't add any axioms without them confounding
each other".
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And it's like, try less axioms, arrive at the extra-ordinary
immediately
and resolve the paradoxes up front, since there are at least three
different rulial regularities the foundness, ordering, and
dispersion,
otherwise you're not going to have a good time, and yes that's
provable.
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Watching some Dr. Tao, "me and my mental collaborators are really
pretty happy about being able to divide-and-conquer proofs, though
one may aver that the implicits in the derivation aren't included in
the usual sort of dimensionless analysis, as that with regards to the
general awe of Breen-Deligne, we've sort of neglected quadratic
reciprocity".
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So, "foundations", on the one hand, and "number theorems", on the
other,
both sort of seem needing some ways to look at them, a little
different,
to help that otherwise there's "the circles" and "the going around in
the circles".
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Pretty good from Mark van Atten on Brouwer and models of continua.
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When it comes to foundations it's me who I trust.  It's gratifying
that sufficient mental reasoners find it quite thorough.
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Been enjoying some of this Yufei Zhou,
at least he knows there's a difference
between the ergodic and combinatoric,
sort of like "Borel vs. Combinatorics",
and when he mentions Ramsey theory
he knows there's a difference between 2 and 3,
and mentions Bergelson and Liebman or Oprocha,
about the quasi-invariant measure theory,
and differences between finitary and infinitary, and
when discussing Roth and Rusza, at least
entertains the various conjectures, and mentions
when things aren't done yet, then though as with
regards to various recently "decided" conjectures,
there's yet for various "independent" features of
number theory, in the infinitary, about things like
quadratic reciprocity and higher geometry.
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So, my foundations is pretty much great for all that,
descriptive set theory and all.
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Of course it's know since antiquity that merely-inductive accounts
aren't their own grounds, and the other day ten years ago at a
festival for Charles Parsons, Van Atta quotes even Dummett
as something like "inductive set defines the integers, integers
define the inductive set: it's circular", in a speech about the
intuitionism of LEJ Brouwer.
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There Brauwer, Linebbo, and Shapiro, they got a thing getting
figured out, "free choice sequences" or ubiquitous ordinals,
"well our S4+ is sort of S4 though it's really S4 minus, ...".
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Then I learned from a talk of Menachem Magidor that these
days it's Paul Erdos who described this feature of that what
the independence theorems of CH are avoiding is Erdos'
"the Ugly Monster of Independence", since it allows one to
draw all sorts of contradictions.
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Then people are always looking for "the next axiom" when
they're going to have to do without some that already are,
and quite calling "the cumulative hierarchy" the "universes",
they're not, they're just scopes.
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Anyways "Foundations" knows there's stuff to figure out,
so something like my "Borel vis-a-vis Combinatorics" of
2003 is pretty great, when I discovered the super-standard
"Factorial/Exponential Identity".
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Yeah, there's it looks like Hindmann gets made a distinctness
instead of a uniqueness result, physics, heh, physics is all
over the place, category theory is relations again, then there's
whenever I see a professor joking about cheating mathematics,
it's like: Bertrand Russell: reality called and it's the truth.
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Been surveying the 'tube recently.
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About large cardinals, various ideas like potentialistic theories,
"well, when we run out, just say it takes a switch", sort of a
non-inductive account, while a comment of Lucke the other
day was along the lines of "I want to mention definitions
because they're going to change, and also that in large cardinals
often we'll find different things with the same structures yet
then different accounts and also different things doing again
what previous things intended to entail to have done", where
it may be kept in mind that large cardinals aren't cardinals nor sets,
they're just whatever aren't.
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To the Ramsey theory then, and about "ergodicity and unique ergodicity",
there's something like Masur in Hausdorff dimension, that's sort of a
way it should be, vis-a-vis the Erdossians, geometry's more than number
theory's, say, about the law(s), plural, of large numbers.
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Physics is just sort of having chewed its nails to the quick,
suddenly everyone's a "philosopher" again yet then they
still haven't read to the end of Einstein or Cohen.
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Enjoying something like Cyntia Pacchiano, and would sort
of read into James Fox among the Erdos-sians, oh and then
there were the "Aristotlean Realists", that's pretty good,
as philosophers sort of reasonable, then since there's
the Alain Aspect and Bell-type there's Bohm & deBroglie again,
this sort of pleases me since it's a continuum mechanics. Yet,
as many are sort of struggling with the concepts, I've encountered
these concepts also, so, I know there's a way to cope.
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"A" way, ....
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Yeah, that "Square Cantor Space" and my "Factorial/Exponential Identity"
of 2003 is sort of looking better all the time. Then this "identity
dimension" bit and an "original analysis" instead of an ever-more
"complex analysis", makes for a perspective on mathematics.
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And Berta Viteri, I sort of enjoy Berta Viteri, who I found from
reading from Cirlot.
Yeah it seems lots of people have never heard of Vitali or
for example Veronese and Stolz and then there's Vitali and
Hausdorff having already made Banach-Tarski the geometrical
way quite preceding Banach and Tarski or Mycelsky about
how to approach "the measure problem" when there are things
like the quasi-invariant with Bergelson and Oprocha, many of
the modern analysts they're sort of stuck with their quadratic
partial Laplacians and never looked into something like
Levi-Civita's discussion of indefinite forms and ds^2, or
Richardson about the "at least three things among the
electrical and magnetic fields and light that arrive at c",
that the usual quadratic partial semi-inductive half-accounts,
while being quite linear and tractable to numerical methods,
have they're traded their work getting done for their work.
You know, when I see the standard, serial, Oxford comma omitted,
I think it's illiterate, or from a particular archaic and backward
time and place, now, that might seem judgmental, yet,
there exist limits.