These are the answers by logician Jesper Carlström to the ten questions about intuitionism:

I must object a little. You use the principle of excluded middle too much in the questions. For instance: if intuitionists doubt the principle "there are discontinuous functions", they need not agree that "there are no discontinuous functions", because they don't hold that there either are or not.

So it would have been more proper to formulate the questions in the positive way. Instead of asking

Do you agree that it is impossible to define a total function from the reals to the reals which is not continuous?

one should ask

Do you agree that it is possible to define a total function from the reals to the reals which is not continuous?

For the next time, perhaps.

  1. Do you agree that it is impossible to define a total function from the reals to the reals which is not continuous?

    No.

    (But I have seen no such definition and I don't expect one; nor do I expect a proof that it is impossible.)

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

    No.

    Only that we have no proof of it, nor a disproof.

  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.

    This is two questions. CH is meaningful, but I don't know that it "has a definite truth value, even if we do not know what it is".

  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.

    Same answer as for CH.

  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.

    (Only for mathematical questions whose answers are yes or no.)

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

    No.

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

    Yes.

  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.

    (Isn't this the opinion of every mathematician?)

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

    No.