I don't understand what you mean by cavalier, I've always though of intuitionistic logic as having a more stringent requirement for things to be true. Thanks f

I don't understand what you mean by cavalier, I've always though of intuitionistic logic as having a more stringent requirement for things to be true. Thanks for mentioning Nelson's Internal Set Theory, I didn't know about it before. I will point out that the logic in IST is also classical, unlike in synthetic differential geometry were it is intuitionistic.