Brouwerian system

The Brouwerian system, also known as intuitionism, is a school of mathematical thought founded by L.E.J. Brouwer. It posits that mathematics is based on mental constructions governed by self-evident laws. Intuitionists challenge traditional mathematical principles, deeming nonconstructive arguments as meaningless.

A key aspect of this system is its rejection of the law of excluded middle in classical logic. This law states that for any proposition, it must be either true or false. Brouwer argued that this principle may fail, particularly when dealing with infinite sets, as it's not always possible to definitively prove or disprove a statement about them. This leads to a focus on constructive proofs, where mathematical objects must be demonstrably built or constructed.