It is Sunday, the 7th of September 1930. The place is Konigsberg
and the occasion is a small conference on the foundations of
mathematics. Arend Heyting, the foremost disciple of L. E. J.
Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna
Circle has expounded on logicism; Johann (formerly Janos and in a
few years to be Johnny) von Neumann has explained Hilbert's proof
theory-- the so-called formalism; and Hans Hahn has just propounded
his own empiricist views of mathematics. The floor is open for
general discussion, in the midst of which Heyting announces his
satisfaction with the meeting. For him, the relationship between
formalism and intuitionism has been clarified: There need be no war
between the intuitionist and the formalist. Once the formalist has
successfully completed Hilbert's programme and shown "finitely"
that the "idealised" mathematics objected to by Brouwer proves no
new "meaningful" statements, even the intuitionist will fondly
embrace the infinite. To this euphoric revelation, a shy young man
cautions "According to the formalist conception one adjoins to the
meaningful statements of mathematics transfinite
(pseudo-')statements which in themselves have no meaning but only
serve to make the system a well-rounded one just as in geometry one
achieves a well rounded system by the introduction of points at
infinity."
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