Intuitionistic logic

Intuitionistic Logic is the logical branch of Mathematical intuitionism. Roughly speaking, 'intuitionism' holds that logic and math are 'constructive' mental activities. That is, they are not analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and math are the application of internally consistent methods to realize more complex mental constructs (really, a kind of game). In a stricter sense, intuitionistic logic can be investigated as a very concrete and formal kind of symbolic logic. While it may be argued whether such a formal calculus really captures the philosophical aspects of intuitionism, it has properties which are also quite useful from a practical point of view.