intuitsionistliku

Intuitionism is a philosophy of mathematics that was developed primarily by L.E.J. Brouwer in the early 20th century. It stands in contrast to classical mathematics, particularly in its approach to existence proofs and the law of the excluded middle. Intuitionists hold that a mathematical statement is true only if it can be constructively proven. This means that a proof must provide a method for constructing the object whose existence is asserted.

A key principle in intuitionism is the rejection of the law of the excluded middle, which states that for any proposition P, either P is true or its negation (not P) is true. Intuitionists argue that this law cannot be applied to all mathematical statements, especially those involving infinite sets, unless a constructive proof for either P or not P can be provided. For example, proving the existence of a prime number greater than a certain value doesn't require proving that such a number must exist; it requires finding one.

This constructive approach leads to certain theorems in classical mathematics not being accepted as valid in intuitionistic mathematics. For instance, the principle of indirect proof (reductio ad absurdum) is viewed with suspicion. While intuitionism has a different logical framework, it is not a rejection of mathematics itself, but rather a different perspective on what constitutes a valid mathematical truth and proof. It emphasizes the mental construction of mathematical objects.