A History of the Infinite

BBC Radio 4•www.bbc.co.uk

Science

Adrian Moore journeys through philosophical thought on infinity over the last two and a half thousand years.

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Episodes

10. Where does this leave us?

Adrian Moore reaches the end of his journey through two and half millennia of philosophical thought about the infinite. In this final episode, with the help of writers and philosophers as diverse as Rene Descartes, Ludwig Wittgenstein and Iris Murdoch, Adrian returns to the theme of our finite nature and how that is fundamental to our sense of what is infinite. He considers the relation between the infinite and the transcendent and examines where the desire to look for something beyond ourselves...

Sep 30, 2016•14 min

9. Death and Immortality

In his series on thought about infinity through the centuries, Adrian Moore has considered the topic through the lenses of philosophy, theology and mathematics. Now, in this penultimate episode, the focus is firmly on us. Adrian ponders our finite nature and confronts the question of whether, if we could, we really would want to live for ever. He brings us the Czech composer Janacek’s opera, with its eponymous heroine Elina Makropulos. Her father, the court physician, has procured an elixir of l...

Sep 29, 2016•14 min

8. The Cosmos

Does space go on for ever? Are there infinitely many stars? These are some of the questions Adrian Moore explores in this episode in his series about philosophical thought concerning the infinite. With the help of the theories of the Ancient Greeks through to those of modern cosmologists, Adrian examines the central question of whether our universe is finite or infinite. For most of us, looking up at the stars gives us a sense of infinity but, as Adrian discovers, there is a strong body of opini...

Sep 28, 2016•14 min

7. Crisis and Uncertainty

Adrian Moore’s series on philosophical thought on infinity finds him mired in a near meltdown in mathematics. Adrian tells the story of the controversy caused by the work of the German mathematician, Georg Cantor, on the infinite. In a world of paradoxes, we meet the nun who can't decide whether to pray for herself. Her dilemma is beautifully explained by Marcus Giaquinto, Emeritus Professor of Philosophy at UCL, in conversation with Adrian. And we find out how an associated paradox, first posed...

Sep 27, 2016•14 min

6. The Mathematics of the Infinitely Big

Adrian Moore continues his exploration of two and a half millennia of philosophical thought on infinity. Discover the brilliant but tortured German mathematician, Georg Cantor, who devised a way of distinguishing between infinitely big numbers and of performing calculations with them. His work was revolutionary but, as Adrian discovers, it greatly polarised opinion amongst his late 19th and early 20th century contemporaries. We hear how Cantor himself suffered a complete breakdown in his mental ...

Sep 26, 2016•14 min

5. The Mathematics of the Infinitely Small

Having looked at the infinite in philosophical and theological terms, it’s time to view it through the lens of mathematics. Adrian Moore introduces us to the pivotal role mathematics has played in the quest to understand the infinite. He begins by enlisting the help of very modern technology and considering the real question put by an 11 year old boy - what is zero divided by zero? That’s the trigger for Adrian’s investigation of the calculus – the tool we use to reckon with very small quantitie...

Sep 23, 2016•14 min

4. The Infinite and Human Experience

Adrian Moore continues his journey through philosophical thought on infinity over the last two and a half thousand years. He brings us to the verge of the modern world and the way we think now. He leaves the arguments of the medieval church and renaissance thinkers behind and steps into the world of enlightenment philosophy, as heralded by Rene Descartes. Adrian tells us that Descartes was a typical enlightenment philosopher, seeking to establish what understanding we can have of the infinite us...

Sep 22, 2016•14 min

3. The Infinite and the Divine

Adrian Moore continues his journey through philosophical thought on infinity over the last two and a half thousand years. He explains how the church attempted to stamp its authority on the debate and how that led to some explosive disagreements amongst medieval thinkers. With the help of Cecilia Trifogli, Lecturer in Medieval Philosophy at Oxford University, Adrian finds out about the life of St Thomas Aquinas. Aquinas defied his mother to become a Dominican friar – she had hoped for a career in...

Sep 20, 2016•14 min

2. Aristotle’s Rapprochement

Adrian Moore continues his journey through philosophical thought on infinity over the last two and a half thousand years. He introduces us to the Greek philosopher, Aristotle, who attempted a reconciliation between the idea of things going on for ever and ever and the Greeks’ abhorrence of the very notion. We hear how he came up with the idea of two different types of infinite - the potential and the actual - and how it was the potential infinite that he presented as the acceptable face of infin...

Sep 20, 2016•14 min

1. Horror of the Infinite

Adrian Moore starts his journey through philosophical thought on infinity over the last two and a half thousand years. For starters, he finds out why the idea made the Greeks so uncomfortable and introduces us to some of the first great thinkers on infinity. We meet Pythagoras and his followers who divided the world into two fundamental cosmic principles. On one side was everything they thought of as limited or finite, and therefore good, and on the other everything they considered unlimited or ...

Sep 19, 2016•14 min

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