[FOM] "Mathematician in the street" on AC

[Timothy Y. Chow]

On Sat, 15 Aug 2009, A J Franco de Oliveira wrote:
> 1) is there a common understanding amongst FOMs of what "true" means
> when applied to AC, say?
> 2) If so, what exactly is it?

This seems to be a special case of the question schema, "Do all 
philosophers agree about X"?  Generically, the answer is no to all 
instances of this schema.

> 3-4) Same question for MISs, respectively.

When doing math, as opposed to when they have their guard up in a 
conversation that is perceived to be philosophical, I claim that 
mathematicians' use of the word "true" is roughly Tarskian.  That is, they 
will assert that "X" is true under the same conditions that they will 
assert X.

Thus we're reduced to asking when mathematicians will assert X.  The most 
common case is that they'll assert X when they know how to prove X, or are 
confident that someone competent has proved X.  But they'll also sometimes 
assert X if X is conjectural but strongly supported---though only if it's 
clear from context that they're not claiming to know a proof of X.

Tim