[FOM] "Mathematician in the street" on AC

[Timothy Y. Chow]

"Sara L. Uckelman" <S.L.Uckelman at uva.nl> wrote:
> Henrik Nordmark wrote:
>  > A very large majority claimed that AC was generally accepted as true.
> 
> Do you mean by this that a large majority claim that they themselves
> think it is true, or that a large majority claim that they think most
> other people think it's true, though they themselves may have a
> different opinion?  If the former, I find this result pretty amazing.

Beware of a potential confounding factor here, namely the word "true."  It 
sounds like you definitely used the word "true" explicitly when quizzing 
your friends.  It's not clear to me from Henrik Nordmark's offhand comment 
whether the word "true" was explicitly used when they posed the question.

In an unguarded state, when they're absorbed in doing mathematics,
mathematicians will freely use the word "true."  However, if you pose a 
philosophical-sounding question to them using the word true, then often
their guard goes up and they may some things that seem to contradict their 
unguarded usage of the word "true."

For a concrete example, if a student asks a professor, "My classmate said 
that there exist non-measurable sets.  Is that true?"  Almost surely, the 
professor will say yes without hesitation.  However, if a philosopher 
approaches the same professor and asks, "Do you believe that 
non-measurable sets truly exist?" then it is likely that the response 
will be completely different.

Tim