Re: "Back to the Galilean Transformation and Newtonian Physics" - Moshe Eisenman c.2017

On 12/23/2024 01:18 PM, LaurenceClarkCrossen wrote:

About infinity, have your read Antonio Leon's papers? e.g.
https://www.academia.edu/keypass/TkJBMjhDeEhEUWxWWnNCMEd1Mmtodmd1SS95UkRJMHJtbUVpZXhSd25oQT0tLXFRQVNtNFVSL1pJS1ozM0NjaEFUb3c9PQ==--4df11fc561f63535dac714306c0fed14eaf01ec2/t/v7bK-SgAjFop-bn1pEm/resource/work/119656929/The_Axiom_of_Infinity_is_Inconsistent?email_work_card=title
>

Thanks, I hadn't heard of this, and it reflects upon some
usual problems that arrive when you put Henri Lebesgue and
Camille Jordan measure together like physics does.
I resolve these kinds of things a different way,
making them all work together instead of just
making paradoxes, so there aren't any paradoxes.
Then that Leon appears to arrive at "actual infinity
is inconsistent" I disagree, though it's agreeable
that "ordinary theory doesn't exist only fragments
and extensions" about the unbounded and extra-ordinary,
here it's considered that "retro-finitism" is backward.
One way to look at the Axiom of Infinity as it's usually
put forth in Zermelo Fraenkel set theory, is that it
says "there is an inductive set, and furthermore,
it's ordinary meaning well-founded". Well, that's not
necessarily so, it's called Russell's paradox, that
an infinite set in a theory of otherwise finite sets
would be extra-ordinary, which is how Russell sank Frege,
which is too bad since these days Frege is considered
good again, mathematics-wise, that "Russell's retro-thesis"
that there exists an "ordinary" infinity is disputable,
though comprehension arrives at that infinity doesn't not
exist, so, otherwise yeah there are quite brief accounts
that there are theories where ZF's Axiom of Infinity
is not a, "true", axiom, say.
In my recent podcast "Logos 2000: natural infinities"
this is outline, while at the same time I keep all
of ordinary set theory along with it, explaining how
there are three kinds of continuous domains and all,
that the standard linear curriculum carefully mums itself
about.