These are the answers by mathematician Doron Zeilberger 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?

    Yes.

    (Because it is meaningless.)

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

    Yes.

    (Because it is meaningless.)

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

    No.

    (There are 0 infinite cardinalities.)

  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?

    No.

  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?

    No.

  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?

    No.

    (But it should be possible to build a machine that decides meaningfulness.)

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

    No.

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

    Usually.

    Sometimes constructions are artificial.

  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?

    Yes.

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

    No.

    A statement is either true, false, or (most often) meaningless.