Topic summary
Constructive mathematics
Extracted from the Wikipedia article Constructivism (philosophy of mathematics).
Constructive mathematics
Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle. This law states that, for any proposition, either that proposition is true or its negation is. This is not to say that the law of the excluded middle is denied entirely; special cases of the law will be provable. It is just that the general law is not assumed as an axiom. The law of non-contradiction (which states that contradictory statements cannot both be true at the same time) is still valid.