Notes for a talk I gave on constructivism
Constructivism is the philosophy that the existence of mathematical objects must be proven by demonstrating how to find them. Proof by contradiction is a non-constructive technique, and the law of excluded middle (that every statement is either true or false) cannot be taken as a universal truth in constructive logics. In this talk, we examine common non-constructive proofs, and show how they can be made constructive. These constructive proofs have aesthetic value in a classical setting. We see that some basic propositions of classical logic cannot be made constructive.