FOM: simultaneous truth of consistent statements

Andrian-Richard-David Mathias Andrian-Richard-David.Mathias at
Thu Feb 24 10:52:51 EST 2000

The passage from Hilbert's letter to Frege that I quoted suggests to my eye that 
Hilbert was thinking of mathematics as a complete theory which is being revealed 
piecemeal to us; we add to our axioms whenever it becomes known that a possible 
addition is consistent with the axioms that are already accepted. I find no 
suggestion in his letter of an awareness that one might have to choose between 
mutually conflicting but individually consistent additions. 

A R D Mathias 

ardm at

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