[FOM] Should mathematicians be explicit about what they are assuming?

Martin Davis martin at eipye.com
Tue Feb 26 11:40:37 EST 2013

The discussion of this matter has been ignoring the social and 
historical context in which mathematical work takes place.

You will rarely see a contemporary paper noting dependence of a 
particular theorem on the axiom of choice. As late as the 1940s it 
was standard practice to do so. Once in calculations that used 
complex numbers, it would be noted that these are "fictitious".

The statement that "ZF+ some large cardinal" is consistent is Pi-0-1. 
Hence if that system is inconsistent, there will be a numerical 
counterexample which in turn would imply that a specific polynomial 
equation has an integer root.


Martin Davis
Professor Emeritus, Courant-NYU
Visiting Scholar, UC Berkeley
eipye + 1 = 0

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