38 | Can We Understand Infinity? ~ Adrian Moore

Infinity is a puzzling idea. Even young children are fascinated by its various manifestations: What is the biggest number? Does the universe have an edge? Does time have a beginning?

Philosophers have tried to answer these questions since time immemorial. More recently, they have been joined by scientists and mathematicians. Indeed, a whole branch of mathematics has become dedicated to the study of infinity. 

So what have we learned? Can we finally understand infinity? And what has this quest taught us about ourselves? 

To explore this topic, I am joined by philosopher Adrian W. Moore. 

Professor Moore is a special guest for two reasons. First, he is a world expert on infinity, known for an excellent BBC series, "History of the Infinite". More personally, he is the head tutor of Philosophy at St Hugh’s College, Oxford, where I studied my BA in Philosophy and Psychology. It has now been ten years since Prof Moore interviewed me and, for whatever reason, accepted me as a student. I feel honoured to mark the occasion with this episode.

In this episode, we discuss:

(02:35) Why infinity fascinates

(12:20) Greeks on infinity

(20:05) A finite cosmos? 

(25:00) Zeno’s paradoxes

(32:35) Answering Zeno

(42:35) Measuring infinities? Georg Cantor

(54:05) Infinity vs human understanding

(66:20) Mystics on infinity

As always, we finish with Prof Moore’s reflections on humanity.

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MENTIONS

Names: Aristotle; Zeno; Archytus; Ludwig Wittgenstein; Kurt Gödel; Alan Turing; Georg Cantor; William Blake; Immanuel Kant 

Terms: Pythagoreans; Zeno’s paradoxes; calculus; transfinite arithmetic; counting numbers, i.e. positive integers; absolute infinities, or inconsistent totalities

Books: The Infinite (Moore)

Other scholarship: For games on infinite boards, see e.g. the work of Davide Leonessi: https://leonessi.org/