FOM: simultaneous truth of consistent statements

Vladimir Sazonov sazonov at
Thu Feb 24 10:46:12 EST 2000

Andrian-Richard-David Mathias wrote:

> Thus although Hilbert's dream of a universe in which all possible objects
> simultaneously exist was impossible, fascinating approximations to it exist.

Was it really Hilbert's dream on *simultaneous* existence in the same
universe? It seems that Consistency => Existece means only that any
consistent theory has intuitively imaginable model. (Without any
reference to any universe or to ZFC or RCA0+WKL0, etc. G"odel's
theorem is only a possible mathematical version of this principle.)
Do you (did Hilbert) mean that the conglomerate of all our ideas,
illusions, imaginations constitutes a mathematical universe?

Vladimir Sazonov

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