These are the answers by logician Leon Horsten to the ten questions about intuitionism:

  1. Do you agree that it is impossible to define a total function from the reals to the reals which is not continuous?

    No.

    It has been done.

  2. Do you agree that the intermediate value theorem does not hold the way that it is normally stated?

    No.

    It has been proved.

  3. Do you agree that there are only three infinite cardinalities?

    No.

    There are infinitely many.

  4. 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?

    Yes.

  5. 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?

    Yes.

  6. 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?

    Yes.

    But it may be very very very hard to know whether your "machine" does the job. I think this is not fair at all. Many readers are going to read this question in a way that is different from what it literally says, and it is intended by the questioner that readers misread this question: it is formulated in such a way that misinterpretation is encouraged (by the word "machine", of course).

  7. Do you agree that for any two statements the first implies the second or the second implies the first?

    No.

    (And classical mathematics is by no means committed to it.)

  8. Do you agree that a constructive proof of a theorem gives more insight than a classical proof?

    No.

    It gives a different kind of insight.

  9. 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?

    No.

    Classical logic is applicable to all mathematical problems.

  10. Do you agree that all mathematical truths are true, but that some mathematical truths are more true than other mathematical truths?

    No.