These are the answers by computer scientist Jacques Carette 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 depends on your underlying theory.

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

    No.

    It depends on your underlying theory.

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

    No.

    There are as many infinite cardinalities as you want!

  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?

    Mu.

    It is a meaningful statement of some theories. In some theories, it even has a definite truth value.

  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?

    Mu.

    It is a meaningful statement of some theories. In some theories, it even has a definite truth value.

  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?

    Mu.

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

    Mu.

    I believe that for any two defined statements this is true, it is false for non-denoting statements.

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

    No.

    It may or may not, depending on the theorem!

  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.