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Topic: Matheology § 204
Replies: 2   Last Post: Jan 31, 2013 12:49 PM

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Posts: 18,076
Registered: 1/29/05
Matheology § 204
Posted: Jan 30, 2013 2:56 AM
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Matheology § 204

Of today's literature on the foundations of mathematics, the
doctrine that Brouwer advanced and called intuitionism forms the
greater part. Not because of any inclination for polemics, but in
order to express my views clearly and to prevent misleading,
conceptions of my own theory, I must look more closely into certain of
Brouwer's assertions.
Brouwer declares (just as Kronecker did in his day) that existence
statements, one and all, are meaningless in themselves unless they
also contain the construction of the object asserted to exist; for him
they are worthless scrip, and their use causes mathematics to
degenerate into a game. [...]
What, now, is the real state of affairs with respect to the
reproach that mathematics would degenerate into a game? [...] The
formula game that Brouwer so depreciates has, besides its mathematical
value {{matheology à la Banach-Tarski-paradox contains no value at all
- the mathematical value of the proofs that Hilbert believs in can at
most be measured in small fractions of lira which not even a single
cent will be paid for}}, an important general philosophical
significance. For this formula game is carried out according to
certain definite rules, in which the technique of our thinking is
expressed. These rules form a closed system that can be discovered and
definitively stated {{like other religious systems too: Buddhism,
Christianity, Hinduism, Islam, Judaism, ... In Islam they enjoy
apostasy-punishment by death. Heretics are usually killed. In
matheology heretics are called cranks and attempts are made to remove
them from their academic poitions. So matheology is not quite as
intolerant as Islam but less tolerant than Buddhism and Hinduism.
There is another parallel: Moslems are not allowed to contact God in
any other language than the Arabic. Allah seems to be less educated
than Jahwe or God who accept prayers in every language. In matheology
every important prayer must be uttered in a certain formal language.
The God of matheology and his disciples seem to be very limited too.}}
[E. Artin et al. (ed.): "D. Hilbert: Die Grundlagen der
Mathematik" (1927). Abh. Math. Seminar Univ. Hamburg, Bd. 6, Teubner,
Leipzig (1928) 65-85. English translation in J. van Heijenoort: "From
Frege to Gödel", Harvard Univ. Press, Cambridge, Mass. (1967)

Regards, WM

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