These are the answers by owner Freek Wiedijk 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.

    The function f defined by f(x) = if(x ≥ 0, 1, 0) is total and not continuous. The fact that you cannot effectively compute it has nothing to do with that.

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

    No.

    The non-computational version of the intermediate value theorem, which is what people mean with the term "intermediate value theorem", holds.

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

    No.

    If you do not allow reasoning about the power set, you lose the whole mathematical universe.

  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, but it depends on which kind of sets you talk about whether it is true or not.

  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, but it depends on which kind of sets you talk about whether it is true or not.

  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.

    I buy the argument with the two machines.

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

    Yes.

    For the "mathematical" meaning of implication this holds.

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

    No.

    It might have more computational content, but it does not necessarily give more insight. On the contrary, I would guess.

  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.

    Reasoning is reasoning. If you work in a different logic, you give the logical terms different meanings, but the reasoning process stays the same.

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

    No.

    True is true. If someone does not recognise the truth or mistakenly believes falsehoods to be true, that's a property of that someone, not of those truths.