Do you agree...
Ten Questions about Intuitionism
This website has as its goal to investigate the opinions
of the mathematical community on intuitionism. To this end
it presents ten slightly provocative questions and collects
answers to these questions from as many people as possible.
If you want to participate in this investigation, send your
answers to the ten questions to firstname.lastname@example.org.
The web site also contains an annotated version of
these questions which for each question presents a short
explanation of how you might look at it.
Each question should be answered by yes or no or mu
(= "the question is meaningless", or "it depends", or maybe, as Bas put it:
"explaining how you should look at this question takes so
much text that there is no point in doing so"; also use this
if you do not know your answer to a question,
or do not want to think about it), together with a possibly
empty motivation. Try to have as little mus as possible.
For each person the answers will be summarized on the main
page as a string of +s, -s or #s.
Do you agree that it is impossible to define a total
function from the reals to the reals which is not
Do you agree that the intermediate value theorem does not
hold the way that it is normally stated?
Do you agree that there are only three infinite
Do you agree that the continuum hypothesis is a
meaningful statement that has a definite truth value,
even if we do not know what it is?
Do you agree that the axiom which states the existence
of an inaccessible cardinal is a meaningful statement
that has a definite truth value, even if we do not know
what it is?
Do you agree that for any mathematical question it is
easy to build a machine with two lights, yes and no,
where the light marked yes will be on if it is true
and the light marked no will be on if it is false?
Do you agree that for any two statements the first
implies the second or the second implies the first?
Do you agree that a constructive proof of a theorem
gives more insight than a classical proof?
Do you agree that mathematics can be done using different
kinds of reasoning, and that depending on the situation
different kinds of reasoning are appropriate?
Do you agree that all mathematical truths are true,
but that some mathematical truths are more true than
other mathematical truths?
(last modification 2008-01-07)