These are the answers by mathematician Maxim Hendriks 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?

    Mu.

    I do not like the metaphysical implications of the words "meaningful" and "true" here.

  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.

    I do not like the metaphysical implications of the words "meaningful" and "true" here.

  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.

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

    Mu.

    This depends on the context, specifically on what mean by the word "implication". Within the calculus of propositional logic, I would answer "yes". Within constructive logic, "no". And within the context of everyday language "no" as well, because implication has a causal meaning in that setting (causality being a primitive notion of the model of the world a speaker has at a given moment).

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

    No.

    (A very definite "no".) One gains information by a constructive proof. But one also gains a lot of information from a non-constructive proof, albeit different information.

  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.

    When doing mathematics per se, different methods give different (interesting) results. When applying mathematics to real-world problems, some methods might be useless at a given moment, although theoretically very interesting.

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

    No.

    The concept of "truth" is very expedient, but when thinking about the connection between thought and the world, we might prefer to work without it, since it presupposes a "picture view" of what perceiving is, and thereby a metaphysical structure of the world. Is that structure present?

    Maybe we better take a pragmatist view, cf. Richard Rorty, "Objectivism, relativism and truth".