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Matheology § 204
Posted:
Jan 30, 2013 2:56 AM


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 BanachTarskiparadox 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 apostasypunishment 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) 6585. English translation in J. van Heijenoort: "From Frege to Gödel", Harvard Univ. Press, Cambridge, Mass. (1967) 464479.] http://www.marxists.org/reference/subject/philosophy/works/ge/hilbert.htm
Regards, WM



