moderate intuitionism

Moderate intuitionism is a school of mathematical thought introduced by L.E.J. Brouwer in the early 20th century. It challenges classical logic by questioning the principle of the excluded third, especially when dealing with infinite sets. This principle states that for any proposition, either it is true or its negation is true.12

Intuitionists believe that mathematical truths must be knowable through mental constructions. They argue that for infinite sets, it's not always possible to definitively prove or disprove a statement by examining every element. Moderate intuitionism accepts constructivism but not extreme finitism, suggesting infinite sets exist only potentially. This approach emphasizes provability as a basis for truth in mathematics.213