These are the answers by physicist Marni Sheppeard 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.

    Brouwer was right.

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

    Yes.

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

    Mu.

    Depends on the topos you live in.

  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.

    It is an independent axiom outside of an internal notion of truth.

  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.

    Certainly not!

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

    No.

    Certainly not.

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

    Mu.

    Classical proofs are often much more elegant, but there is the possibility of deeper insight with constructivism, and then it depends on the case....

  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?

    Yes.

    Truth is contextual, and some kinds of truth have a higher level of truth (in a category theoretic sense) than others.