FOM: simultaneous truth of consistent statements

[Andrian-Richard-David Mathias]

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 univ-reunion.fr