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WILDBERGER_MATH

                                                              October 18, 2019
Looking at some of Wildberger's
lectures on Math History:

    "Sets, Logic and Computability"
    "Computability and Problems with Set Theory"


These lectures fill in a little of my gross
ignorance of the field I was (trying) to             MATHISM
criticize:

There was an "Intuitionist" school that rose up
in reaction to Russell's push for "Logicism"--          Kronecker
I think I was trying to re-invent Intuitionism.         Borel
                                                        Poincare
It could be that the sniping at intuition I've          Weyl
seen in some of Russell's popular writings were         Brouwer
reactions against this rebellion.

Wildberger informs about the general consensus
view of modern mathematicians, who regard ZFC as
the foundation of set theory and further, set        ZFC just rules out
theory is the foundations of all of mathematics.     self-reference:
                                                     no set can be a
  ZFC = Zermello-Fraenkel plus the Axiom of Choice   member of itself.

0ne of the things that's interesting                   As expected, the solution
about these Wildberger lectures is that                to Russell's Paradox is
he periodically makes an aside to the                  "don't do that".
effect that he's giving us the standard,
consensus view of this material but he
doesn't really believe any of this crap
himself.

         (A man after my own heart.)
                                               There are other places where
He keeps his objections vague, at one          he goes into more detail,
point mentioning that you might want to        taking aim at the post-Cantor
put quotations around all of the terms,        proliferation of the idea of
because it's not clear they've really          infinity throughout math.
thought through what they mean.
                                                       INFINITE_WILDBERGER

When he presents the conclusion that ZFC underlies
set theory which underlines math, he states
that very few working mathematicians seem to have
any trouble with any of this, which he regards as
rather remarkable.  He also comments that they
don't seem to think about it very much, they just
accept it and (very occasionally) use it.

    Goedel was a blow against
    "Formalism" but it recovered,       (What the difference is between
    and ZFC is where it ended up--      "Formalism" and "Logicism" is unclear
                                        to me...  At a guess, that Russell
                                        and Whitehead stuff seemed too
                                        much-- an interjection from an
                                        outsider?-- so the Formalists wanted
                                        another label for themselves.)


The "Axiom of Choice": Wildberger remarks that
it originally wasn't an accepted principle of       His thumbnail description
Zermelo-Frankel (which is why the C gets tacked     of Choice is that for any
on to the name), and that it's the only             family of sets you can
principle of ZFC which working mathematicians       create a new set composed
use with any frequency.                             of an item choosen from
                                                    each set.
        (Doesn't it seem funny that it's
        "C" for Choice and not "Z" for                 When Wildberger mentions
        "Zungo-Schrietskraten-Mueller"                 the term "family" he
        or some such?  Someone let a key               interjects "whatever
        part of mathematics out into the               that means".
        wild without slapping their name
        on it.)                                        Elsewhere, he complains
                                                       of mathematicians using
                                                       verbal circumlocutions
  The name of the band "Axiom of Choice"               to avoid saying "set"
  suddenly seems clear: they're a middle               when it might seem
  eastern band with respect for arabic                 problematic.
  traditions, and yet they also embrace the
  modern world-- Arabic mathematicians were
  leading the way when the West was still                   INFINITE_WILDBERGER
  busy with "the dark ages"-- and for their
  name they've adopted a mathematical
  phrase, but it's a decidedly modern one.

          (And I just thought they
          figured it sounded cool.)





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