Aristotle and the Explosive Vegetable: Exploring Classical Thought in Modern Logic

Schimmel/Conrades Science Center Atrium

When we argue, we often invoke the three classical laws of thought: the law of identity, the law of excluded middle and the law of non-contradiction, without thinking too much about it. However, do these laws still apply in our modern treatment of logic? We establish that many popular systems of propositional and first-order logic, such as that proposed in the Principia Mathematica, still obey these laws, but there are still many others that do not. We discuss what happens to the consistency and completeness of those systems which reject such laws, relating to the principle of explosion and Gödel’s incompleteness theorem.