On Monday, October 16, 2023 at 1:42:18 PM UTC-7, Ross Finlayson wrote:
On Wednesday, October 4, 2023 at 7:22:38 PM UTC-7, Ross Finlayson wrote:
On Saturday, September 23, 2023 at 10:45:35 AM UTC-7, Ross Finlayson wrote:
On Wednesday, September 20, 2023 at 2:11:40 AM UTC-7, Mild Shock wrote:
I want to make a fruit cake top ten list, who is the most
creative head on sci.logic and sci.math. But I don't know
how to order it. I ended up with, but I am not sure:
1. Ross Finlayson
2. Dan Christensen (questions are indeterminate)
3. ChatGPT (very good in halucination sometimes)
4. Steve Spiros
Man Goes Crazy Rips off Shirt [Steve Spiros] https://www.youtube.com/watch?v=uXwRgnZ990I
Ross Finlayson schrieb am Dienstag, 8. August 2023 um 05:15:44 UTC+2:
On Monday, August 7, 2023 at 6:46:23 AM UTC-7, Mild Shock wrote:
We are doomed, R.I.P.:
Peter Aczel (31 October 1941 – 1 August 2023). https://en.wikipedia.org/wiki/Peter_Aczel
Now we are subject to the extraordinary set gibberish
of Rossy Boy even more. But isn't Category Theory more "conscientious" in this respect. Instead of having set theory
that struggles with extraordinary sets, but then can nevertheless integrate them through some clumsy extended graph
construction, so as to construct models,
Maybe we shall be more concerned with situating both the mathematics and the underlying intuitions in a broader picture, one derived from work in coalgebra,
which might be a call for Category Theory.
Ross Finlayson schrieb am Montag, 7. August 2023 um 03:06:16 UTC+2:
set theories were sort of the "camp of Aczel", but there was Finsler and Boffa,
Category theory and the arrow functor is kind of similar to set theory and elt, i.e., it's a theory with a fundamental relation, like other theories like class theories with mem, part theories
with part, mereology with boundaries, about whether there
are one or two kinds of fundamental objects and one of two
kinds of fundamental relations.
When Homotopy Type Theory came up with "Homotopy Type
Theory, now with Univalency, strong as ZFC plus two large cardinal axioms", the point of equi-interpretability is that their paradoxes are resolved rather together, or, they're not.
... Aczel, and Finsler and Boffa, and Dana Scott.
Yeah, twenty years ago, the Internet was pretty great, but it was pretty difficult to find anything about the non-standard except "Robinso(h)n's hyperreals, yet another conservative extension of ZF, this is our infinitesimals", yet Skolem and Aczel stuck out for their
extra-ordinary along with Hausdorff and Poincare for their full ordinary.
Nobody even bothered to point out Aristotle's continuum to go along with Zeno's arguments, or Peano's or Veronese's or Stolz' or Dodgson's
or, well there was Bell's, or Brouwer's, infinitesimals, sort of along with
Conway's "surreal numbers", those are all different kinds.
Yeah pretty much all there was was Robinson's useless halos and Conway's extension of an Archimedean field, all conservative.
These days though there have been some revivals of the camps of
the extra-ordinary, so it's easier to find the closest ones to approbity.
"Re-Vitali-ization: rather like signal-reals."
I.e., it's fixed in an extra-ordinary set theory, or, it's not.
Model theory is just sort of a ready grounds for equi-interpretability,
but objectively abstractly is abstractly is abstractly.
But, what if then I just start like so:
Plato
Duns Scotus
The Eliatics
Euclid including Bourbaki
G. Priest and D. Scott
Kant's "sublime", DesCartes "riddles"
De Morgan into Frege
De Morgan into Russell
Zermelo and Fraenkel and Vitali and Hausdorff
the regular and the uncountable
delta-epsilonics and measure theory
algebraic GEOMETRY versus ALGEBRAIC geometry
the silver thread of antiquarian reflection on reason
Heraclitus, first theorist, followed by the above
Ross ...
paleo-classical non-standard
extra-ordinary and super-standard
rulial, regular, ordinary
replete continuity
true theories
"square Cantor space"
"language of a Comenius language"
"paradox: none"
"Of the _logos_ being forever do men prove to be uncomprehending,
both before they hear and once they have heard it. For although all things happen according to this Word they are like the unexperienced experiencing words and deeds such as I explain when I distinguish each thing according to its nature and declare how it is. Other men are unaware
of what they do when they are awake just as they are forgetful of what they do when they are asleep. " -- Heraclitus
"Geometry is motion", ha, it isn't. I suppose it "is", "thinking" about it.
There's always room in a monist's theory for the insuperable.
In fact, there isn't for much else.
So, yeah, anyways, if you get through the rest of those before you get to me,
mostly I only refer to the ones there already are, and in fact I do.
Truth is discovered / lies are invented / when a lie's discovered / that's a truth.
-- Platonism
Picked up a copy of Langer's "An Introduction to Symbolic Logic", '67, it's not bad reading after something like Quine, mentions Quine.
I don't know if it's "modern and 21'st century foundations",
though at least "obviously these peculiarities [of material implication] do not belong to the ''ordinary'' concept of implication."
"Is there any sense in calling this relation ''implication'' at all?"
"... where p _materially implies_ q holds and ''real implication'' does not,
inference is irrelevant anyway."
There isn't an index entry for "model theory" but "connexity" is found in "abstraction and interpretation". I enjoy it.
Yeah, Langer's "An Introduction To" Symbolic Logic is about authoritative.
Of course whatever is "meta theory" and "theory" is model theory and proof theory.
("The theory")
Reading Kepler "Epitome...", Norman Davidson's astronomy and Lindsay's energy, Courant's textbook, Langer's logic, ....
All good according to model theory and a science of it, to me.
Of course I have one, though, ....
"A Theory"
Of course set theory is very good for making regular models of regular things.
There's plenty of model theory of it, ....
--- SoupGate-Win32 v1.05
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