Re: Set Theory: Should You Believe


"Rupert" <rupertmccallum@xxxxxxxxx> wrote in message
news:1151447464.769423.254170@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Norman Wildberger, an Associate Professor at my university (the
University of New South Wales), has written a discussion of the
foundations of mathematics called "Set Theory: Should You Believe"
which is current available on his website at
http://web.maths.unsw.edu.au/~norman/

I am sure he would appreciate any feedback. He can be reached at
n.wildberger@xxxxxxxxxxx


The more I read about this guy, the more I think he is a crank that somehow
scored an Associate Professorship.

His "rational geometry" appears to be based only defing a rational angle as
the sine of an "normal" angle. This makes some calculations easier (because
it eliminates a "sine" term) but makes common operations - like adding two
angles - far more complex. It adds absolutely zero mathematically - his
underlying structure is still Euclidean geometry - and as a practical
technique for surveying, physics, building etc it is way more cumbersome
than normal trig.

I couldn't find the paper you mention, but the closest was on multi-sets.
His summary states "For more than a century, mathematicians have been
hypnotized by the allure of set theory. Unfortunately, the theory has at
least two crucial failings. First of all, infinite set theory doesn't make
proper logical sense. Secondly, the fundamental data structures in
mathematics ought to be the same ones that are the most important in
computer science, science and ordinary life". Pure crank territory.

The four new structures he proposes to replace set theory are presented
without axioms, and indeed just use set theory machinery to prove his
"theorems". The whole thing could be formalised quite easily, in much the
same way as n-tuples can be defined in terms of sets (indeed, n-tuples are
one of the new "basic structures" he proposes). Maybe he didn't do this
because it would destroy his basic premise that these four "new" structures
(known for a 100 years) are more fundamental than set theory.

Strip away his title, and the guy looks like a "b-grade" internet crank to
me. My advice is to avoid his classes entirely.

Peter Webb


.

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: Cantorian pseudomathematics
    ... What I mean is set theory was not born just by the great thought of Cantor. ... of mathematics behind, which help greatly, and which even where necessary for the theory to be imagined. ... formalization, at a level up, for meta-theory. ... scientists and engineers doesn't have to be used by engineers. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... What I mean is set theory was not ... >> prove only the mathematics we set out to prove and not statements about ... >> formalization that does not compromise the other criteria. ... >> or show a formalization that does not compromise the other criteria. ...
    (sci.math)
  • Re: Kuratowski Ordered Pair
    ... notions of temporality and things like that, ... operation and mathematics seems to do just fine with the Kuratowski ... definitions are offered by detractors of the Kuratowski definition? ... Fromout set theory ...
    (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)