Proofs and the love of wisdom: what do we learn by proving a theorem in arithmetic?
Logic and Set Theory Seminar
15th November 2017, 5:15 pm – 6:30 pm
Physics, Powell Lecture Theatre
A public lecture bringing the Arts and Sciences together from InsideArts in collaboration with the Centre for Science and Philosophy.
Colin McLarty is Truman P. Handy Professor of Intellectual Philosophy and of Mathematics, Case Western Reserve University. His research explores the philosophical foundations of mathematics and he has published extensively on the history of science and of mathematics. His lecture asks whether there is a difference between knowing a mathematical result and understanding it. Why do mathematicians seek new proofs of theorems they already know? How do proof theorists study proofs themselves? How can there be anything more for mathematicians to learn about arithmetic?
This is the first John Mayberry Memorial Lecture. John was a lecturer in Mathematics at the University from the mid-1960s until 2005, when he became a research fellow in philosophy after his retirement. He was particularly interested in the Greek conception of number and in Kant’s philosophy of mathematics, as well as being an expert on mathematical logic and the foundations of Mathematics. He read Aristotle in Greek over many years with classicist Christopher Rowe. John argued that “the later nineteenth-century revolution in the foundations of mathematics was essentially a return to Greek arithmetic as Klein had described it in a new, non-Euclidean form.” After Aristotle, John’s intellectual hero was Richard Dedekind especially his “Was sind und was sollen die Zahlen”. Dedekind excised ideas of iteration or intuitions of time from the natural numbers basing them solely on the Axiom of Infinity. John’s work explored what happens to the supposedly fundamental mathematical notion of “natural number” if we adhere to Euclid’s common notion that “the whole is greater than the part”.