[FOM] "Mathematician in the street" on AC

Sara L. Uckelman S.L.Uckelman at uva.nl
Wed Aug 12 05:57:23 EDT 2009

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.
Since this thread began, I've started quizzing some of my non-logician-
but-still-mathematician friends about their knowledge and beliefs of AC,
to get some informal data of my own.  Most of them can state AC or one
of its equivalents (usually Zorn's Lemma) without having to look it
up (or feel guilty that they can't because they think they should be
able to), but when asked whether they think it's true, they take a much
more pragamatic approach, saying things like "I'm not sure that it even
makes sense to ask whether it's true or false, but I have no qualms
about using it in a proof" and "I'm not sure that "true" is the right
term.  I think it's useful, and that doing without it would be
frustrating and annoying (unless you were making a career of doing

Did the mathematicians you spoke with who think AC is true say anything
about what grounds their belief that it is?


Sara L. Uckelman
Institute for Logic, Language, & Computation
Universiteit van Amsterdam

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