These are the answers by computer scientist Michelangelo Lonardi to the ten questions about intuitionism:
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).
Yes.
(see above)
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.
No.
If HC is independent of the axiom system, HC has no definite truth value; however continuum hypothesis is a meaningful statement.
No.
(see above)
Yes.
Brouwer should answer no (middle excluded), but I answer yes, because I like classical logic.
Yes.
I like classical logic.
No.
Perhaps it's true the inverse: classical proof gives more insight.
Yes.
Different logics exist because different kinds of reasoning exist.
No.
No, because the mathematical truths are statement like P → Q where P is a logic and Q is a theorem in P.