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Re: Matheology § 051
Posted:
Jun 28, 2012 6:25 AM
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On Jun 27, 3:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> Matheology § 051
>
> Herren Geheimrat Hilbert und Prof. Dr. Cantor, I'd like to be Excused
> from your "Paradise": It is a Paradise of Fools, and besides feels
> more like Hell
>
> David Hilbert famously said: "No one shall expel us from the paradise
> that Cantor has created for us."
>
> Don't worry, dear David and dear Georg, I am not trying to kick you
> out. But, it won't be quite as much fun, since you won't have the
> pleasure of my company. I am leaving on my own volition.
>
> For many years I was sitting on the fence. I knew that it was a
> paradise of fools, but so what? We humans are silly creatures, and it
> does not harm anyone if we make believe that ? zero, ? one , etc. have
> independent existence. Granted, some of the greatest minds, like
> Gödel, were fanatical platonists and believed that infinite sets
> existed independently of us. But if one uses the name-dropping
> rhetorics, then one would have to accept the veracity of Astrology and
> Alchemy, on the grounds that Newton and Kepler endorsed them. An
> equally great set theorist, Paul Cohen, knew that it was only a game
> with axioms. In other words, Cohen is a sincere formalist, while
> Hilbert was just using formalism as a rhetoric sword against
> intuitionism, and deep in his heart he genuinely believed that
> Paradise was real.
>
> My mind was made up about a month ago, during a wonderful talk (in the
> INTEGERS 2005 conference in honor of Ron Graham's 70th birthday) by
> MIT (undergrad!) Jacob Fox (whom I am sure you would have a chance to
> hear about in years to come), that meta-proved that the answer to an
> extremely concrete question about coloring the points in the plane,
> has two completely different answers (I think it was 3 and 4)
> depending on the axiom system for Set Theory one uses. What is the
> right answer?, 3 or 4? Neither, of course! The question was
> meaningless to begin with, since it talked about the infinite plane,
> and infinite is just as fictional (in fact, much more so) than white
> unicorns. Many times, it works out, and one gets seemingly reasonable
> answers, but Jacob Fox's example shows that these are flukes.
>
> It is true that the Hilbert-Cantor Paradise was a practical necessity
> for many years, since humans did not have computers to help them,
> hence lots of combinatorics was out of reach, and so they had to cheat
> and use abstract nonsense, that Paul Gordan rightly criticized as
> theology. But, hooray!, now we have computers and combinatorics has
> advanced so much. There are lots of challenging finitary problems that
> are just as much fun (and to my eyes, much more fun!) to keep us
> busy.
>
> Now, don't worry all you infinitarians out there! You are welcome to
> stay in your Paradise of fools. Also, lots of what you do is
> interesting, because if you cut-the-semantics-nonsense, then you have
> beautiful combinatorial structures, like John Conway's surreal numbers
> that can "handle" "infinite" ordinals (and much more beyond). But as
> Conway showed so well (literally!) it is "only" a (finite!) game.
>
> While you are welcome to stay in your Cantorian Paradise, you may want
> to consider switching to my kind of Paradise, that of finite
> combinatorics. No offense, but most of the infinitarian lore is sooo
> boring and the Bourbakian abstract nonsense leaves you with such a
> bitter taste that it feels more like Hell.
>
> But, if you decide to stick with Cantor and Hilbert, I will still talk
> to you. After all, eating meat is even more ridiculous than believing
> in the (actual) infinity, yet I still talk to carnivores, (and even am
> married to one).
>
> [Doron Zeilberger: "Opinion 68" (2005)]http://www.math.rutgers.edu/~zeilberg/Opinion68.html
>
> Regards, WM
A fool quoting another one...ain't that beautiful!
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