These are the answers by philosopher Robert Black 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.

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

    No.

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

    No.

  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?

    Mu.

    It's (hopefully) true in some models and false in others. It might be false in all models, but nobody thinks this.

  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.

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

    Mu.

    (True if "implies" means truth of the material conditional and the statements have truth values.)

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

    Mu.

    (Obviously sometimes yes, but nonconstructive proofs can generalize when constructive proofs don't.)

  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.

    (Let a hundred flowers bloom!)

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

    No.

    (Just silly.)