Foundations explores the logical and philosophical basis of mathematical logic. Encountered by both Philosophy and Mathematics majors, students are introduced to the history and rigorous analysis of abstract, self-referencing systems.
What is a formal system? What are proofs and axioms? Is mathematics self evident?
Spoiler alert : Gödel’s incompleteness theorem shows that if axioms don’t contradict each other and are “listable”, then there are some statements which are true but can never be proved. Additionally, a system of axioms cannot show its own consistency.
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