These are the answers by computer scientist Michelangelo Lonardi 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.

    I suppose you talking about reals according to Brouwer, but at this moment, I don't remember well; I think that it's possible define in a way constructive reals according to Cantor (Cauchy series must be defined in a way constructive). So the Dirichlet function is definable (1 to rationals 0 otherwise), because it is definable in a analytic way (Peano).

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

    Yes.

    (see above)

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

    No.

    I think me too that the power set (of a infinite set) not exists, so according to me only potential infinite exists. However, in classical logic, everyone can play with infinite as everyone liked (surreal numbers, ordinal numbers, iperreal numbers, ZFC, ecc...), but without contradictions, if possible.

  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.

    If HC is independent of the axiom system, HC has no definite truth value; however continuum hypothesis is a meaningful statement.

  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.

    (see above)

  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.

    Brouwer should answer no (middle excluded), but I answer yes, because I like classical logic.

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

    Yes.

    I like classical logic.

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

    No.

    Perhaps it's true the inverse: classical proof gives more insight.

  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.

    Different logics exist because different kinds of reasoning exist.

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

    No.

    No, because the mathematical truths are statement like P → Q where P is a logic and Q is a theorem in P.