Re: Why does Cantor a target for cranks?


Larry Hammick wrote:
On Dec 9, 9:32 pm, "Andrew Usher"
<k_over_hb...@xxxxxxxxx> wrote:
Why are there so many on this groups whose
mathematical goal is to
disprove uncountability? I can't imagine, really,
why it would be a
crank target.
Well, when Cantor himself was around, it wasn't
just the cranks who had
their doubts about his stuff. Remember Kronecker
and Poincaré, who
were far from cranks. Set theory, axioms of choice,
cardinals, and all
that stuff, were hotly disputed for quite a few
years.
A survey of this branch of crankology:

http://www.crank.net/cantor.html

Wilfrid Hodges's paper "An Editor Recalls Some
Hopeless Papers" at this
website (
http://www.crank.net/cgi-bin/redirect.cgi?http://www.m
ath.ucla.edu/~asl/bsl/0401/0401-001.ps
) is especially telling; on page 3, he states: "It's
nothing more than
a guess, but I do guess that the problem with
Can­tor's argument is as
follows. This argument is often the first
mathematical argument that
people meet in which the conclusion bears no relation
to any­thing in
their practical experience or their visual
imagination."

I'll add a minor detail: Nowadays many people work
on computers and
software and they acquire a variety of bad habits
of thought in the
process. One example (putting it informally) is the
notion that if no
amount of RAM will ever be enough to distinguish
one infinite ordinal
from another, then there must be something
objectionable about
comparing infinite ordinals. That's just an
example.

N. J. Wildberger's rant about Set Theory (I think
it's "Set Theory:
Should You Believe?") also springs to mind. He states
that we should
never consider big numbers, because we have no way to
represent them in
the Universe. My reaction was the question of why we
should abandon
something just because it's beyond the grasp of one
particular
individual (Wildberger). The fact that that
particular individual
should know better just reinforces my "beliefs".

--- Christopher Heckman


Wildberger's hyperbole of speech notwithstanding, his
argument is not particularly cranky.

http://web.maths.unsw.edu.au/~norman/views2.htm

There were and are many mathematicians before and
since, who have sought to render personal belief
entirely irrelevant to the art of mathematics, which
is requisite to converting math to a true science.
The giveaway to this goal is in Wildberger's subtitle,
"Does mathematics require axioms?" It's a poignant
question -- science does not require axioms.

Tom
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... most of the standard axioms would get scrapped ... you claim that set theory is ... theory in which to express virtually all of mathematics. ... S (call this function 'omega pre S'). ...
    (sci.math)
  • Re: Skolems Paradox and why is math the way it is?
    ... > This is not a job the axioms were ever meant to do. ... other person's interpretation require a winning strategy, no more, no ... I'm pretty sure than any model of set theory is intuitively ... figuring out how I tell what is real in mathematics. ...
    (sci.math)
  • Re: Set Theory: Should You Believe
    ... Why, in your opinion, is the orthodoxy in set theory ... mathematics, ignoring the misgivings of geniuses like Poincare, Weyl, ... When NW said that "You don't need axioms", ... NAFL theories (but infinite proper classes, ...
    (sci.logic)
  • Re: Set Theory: Should You Believe
    ... questioning of the status quo. ... the foundations of logic and mathematics as exists today. ... Why, in your opinion, is the orthodoxy in set theory ... and proofs do require axioms as starting points. ...
    (sci.logic)
  • Re: Uncountable sets in CZF?
    ... When I first heard about uncountable sets, ... but these axioms and definitions have a certain intuitive appeal. ... This is mathematics. ... Imagine if a set theory had a set of all sets. ...
    (sci.math)