Four lectures, online

1st – 10th December (7-9 pm on Wednesdays and Fridays, 1st, 3rd, 8th, 10th)  

Hosted by the Department of Philosophy and Religious Studies at Peking University and the Chinese Institute of Foreign Philosophy

Live Stream links for the four lectures

Bilibili:    https://live.bilibili.com/22229481     

Youtube: Lecture 1 https://youtu.be/iGC4DQXB6A8

Lecture 2 https://youtu.be/Zu-2CdYgRC0

Lecture 3 https://youtu.be/vs4S_n3hH1U

Lecture 4 https://youtu.be/9GQkm4Z-D5U

About the speaker

A. W. Moore is Professor of Philosophy and Lecturer in Philosophy at the University of Oxford, and Tutorial Fellow of St Hugh’s College Oxford. He studied philosophy as an undergraduate at King’s College Cambridge, and did postgraduate work at Balliol College Oxford, where he obtained his doctorate under the supervision of Michael Dummett. He has held teaching and research positions at University College Oxford and King’s College Cambridge. Since 2003 he has been Bernard Williams’ literary executor. From 2014 to 2015 he was President of the Aristotelian Society. Since 2014 he has been philosophy delegate of Oxford University Press, and since 2015 he has been joint editor, with Lucy O’Brien, of MIND. He has published five books, and edited or co-edited four more. The most recent of these are, in a third edition, The Infinite (Routledge, 2019) and Language, World, and Limits: Essays in the Philosophy of Language and Metaphysics (Oxford University Press, 2019).

Career highlights

2014-15 President of the Aristotelian Society  

2014-24 Philosophy Delegate of Oxford University Press

2015 - Joint Editor, with Lucy O’Brien, of MIND

2016 Presenter of the BBC Radio 4 series A History of the Infinite

2017-20 Vice-Principal of St Hugh’s College Oxford

Monographs

1990 The Infinite, Routledge (revised, expanded third edition, 2019)  

1997 Points of View, Oxford University Press

2003 Noble in Reason, Infinite in Faculty: Themes and Variations in Kant’s Moral and Religious Philosophy, Routledge

2012 The Evolution of Modern Metaphysics: Making Sense of Things, Cambridge University Press

2019 Language, World, and Limits: Essays in the Philosophy of Language and Metaphysics, Oxford University Press

A full CV is available at https://users.ox.ac.uk/~shug0255/pdf_files/cv-pdf.pdf

Abstract

These lectures will trace the history of thought about the infinite during the last two and a half thousand years. I shall look at the infinite in philosophical terms, in theological terms, in scientific terms, and in mathematical terms. As I hope to demonstrate, part of the importance of the topic is that, in trying to make sense of the infinite, we are also trying to make sense of ourselves. We are trying to make sense of our own experiences and our own limitations, and what these tell us about our place in the world. Always, in the background of these lectures, there will be a sense of our own finitude. Always the question will come back to how we, in our finitude, relate to what surpasses that finitude. In whatever way the history of the infinite develops, it is sure to be, as it has always been, a vital part of our own history.  

LECTURE ONE: The Infinite in Ancient and Medieval Thought

I shall begin by exploring the old adage that ‘the Greeks abhorred the infinite’, and show why and how they did so.  I shall focus in particular on Pythagoras and his followers, who divided the world into two fundamental cosmic principles: what they called Peras (the Limited) and Apeiron (the Unlimited, or the Infinite).  The former subsumed everything that was good, and the latter everything that was bad.  The Pythagoreans thought they could explain the world around them in terms of the natural numbers 1, 2, 3, 4, et cetera—the numbers that we use to count finite collections of things—and they were dismayed when they discovered that that this was not so.  According to legend one of them was shipwrecked at sea for revealing this discovery to their enemies!  I shall also consider Zeno of Elea, who, after wrestling with the notion of infinity and discovering various associated paradoxes involving motion, came to the conclusion that motion itself was impossible.  But the primary focus of this lecture will be Aristotle, who sought a reconciliation between the idea that things can go on for ever and the Greeks’ abhorrence of any such idea.  Aristotle famously distinguished between the potential infinite and the actual infinite, and argued that the former, and the former alone, was the acceptable face of infinity.  This enabled him to revisit Zeno’s paradoxes and to provide his own solution to them without denying the very possibility of motion.  Aristotle’s views held sway for thousands of years.  In particular, they had a very significant impact on medieval thought.  This was largely through the intermediary St Thomas Aquinas, who attempted to reconcile Aristotle’s teachings on the infinite with the doctrines of the Catholic church.  He enjoyed some success in this endeavour, and, once the church had embraced Aristotle’s teachings as the new orthodoxy, philosophers stepped out of line at their peril.  I shall signal in particular Galilei Galileo, who did just that.  He dared to add some new paradoxes of his own to discussion of the infinite: these foreshadowed later thinking on the infinite (as I shall discuss in Lecture Three) and showed that Aristotle’s views were not as straightforward as they had come to seem.

LECTURE TWO: The Infinite in Science and Technology

In this lecture I shall consider ways in which the concept of the infinite has been applied in science and technology.  I shall begin by considering the invention of the calculus, which makes precise some of the ideas that people have had when trying to reckon with the infinitely small and without which science and technology these days would be literally unthinkable.  From the design of aircraft to the design of irrigation channels; from the prediction of birth rates to the computation of marginal costs and revenues; from the calculation of an optimal projection angle for putting a shot to the estimation of how much a tumour will shrink in a given time with effective chemotherapy: the calculus is at work throughout our lives.  I shall explain some of the basic ideas of the calculus, and I shall discuss the dispute between the two seventeenth-century mathematicians Isaac Newton and Gottfried Leibniz concerning which of them could claim the credit for its invention.  I shall also discuss the disagreements that dogged the calculus’s early days, in which the church too got involved.  I shall then turn attention from the infinitely small to the infinitely big.  Do space and time go on for ever?  Are there infinitely many stars?  I shall look at the various considerations that have been advanced over the centuries for answering these questions, culminating in the contemporary orthodoxy that space is finite, albeit unbounded, and that time too may be finite—with many cosmologists arguing, by appeal to the expansion of the universe, that everything started with a big bang and may all end with a big crunch.  I shall explain why scientists are generally wary of the infinite, just as the ancient Greeks were, and that whenever it appears in any of their calculations this forces them back to the drawing  board to reconsider what has led them there.

LECTURE THREE: The Infinite in Mathematics

This lecture will be concerned with the mathematics of the infinite, most of which has developed relatively recently.  I shall outline the principal ideas of the brilliant German mathematician, Georg Cantor, who not only showed that we can distinguish between different infinite sizes, but who devised infinitely big numbers to measure them and who showed how to perform calculations with these numbers.  Cantor’s work was both revolutionary and profound.  But it greatly polarized opinion amongst his late nineteenth- and early twentieth-century contemporaries, contributing to a complete breakdown in Cantor’s mental health.  His work also gave rise to several new paradoxes that also contributed to a breakdown of sorts—a breakdown in work on the foundations of mathematics.  I shall expound some of these paradoxes, including Bertrand Russell’s famous paradox of the set of all and only those sets that do not belong to themselves, and I shall discuss how mathematicians reacted to them.  In particular, I shall talk about Gottlob Frege’s reaction, which was exacerbated by the fact that Russell’s paradox looked as though it had completely destroyed his life’s work, namely his attempt to provide mathematics with rigorous and secure foundations.  I shall also discuss subsequent developments in mathematics that exploit some of these paradoxes, including some of Kurt Gödel’s work.  I shall conclude that, by subjecting the infinite to formal scrutiny, mathematicians have ended up creating more problems for themselves than they have been able to solve and have found themselves having to reckon with some extraordinarily deep puzzles at the very heart of their discipline.

LECTURE FOUR: Human Finitude

In this lecture I shall begin by looking back at the early modern period in the history of thought about the infinite, the period of enlightenment that began with the work of René Descartes.  Descartes was a paradigmatic enlightenment philosopher, who sought to establish what understanding we can have of the infinite using our own finite resources.  He was keen to address the question of how we can so much as have an idea of the infinite, given that we have no direct experience of it.  Descartes’ answer to this question was that the idea must have originated in something that was itself infinite; indeed this was one of his basic arguments for the existence of God.  But more empirically minded philosophers took issue with this and were prepared to infer from the fact that we had no direct experience of the infinite meant that we did not really have any idea of it at all.  Immanuel Kant played his quintessential rôle of arbiter.  He agreed with Descartes that we do have an idea of the infinite which is not derived from experience, but he also agreed with the empiricists that this idea could not furnish us with any substantive knowledge and certainly could not be used to prove the existence of God in the way in which Descartes had thought.  Rather, Kant argued, our idea of the infinite had various practical uses, including enabling us to have faith in the existence of an infinite God and to treat one another as beings of infinite worth.  I shall pass from these historical reflections to broader considerations of our own finitude.  I shall look in particular at the question of whether, if we could, we would want to live for ever.  Some philosophers find solace in the fact that we are mortal; others lament it.   But there is, I shall suggest, consensus on one point: the sheer fact that one day our life will come to an end does not rob it of meaning.  Indeed it is arguably our very sense of our own finitude that produces  what has been called ‘the restlessness of the human heart’: our constant desire to reach out for more.  I shall conclude the lecture by asking where this all leaves us, and what grasp we really have of the infinite.  I shall argue that it is our grasp of our own finitude that is fundamental to whatever grasp we have of the infinite.  But there is a final paradox here with which we must reckon: our grasp of our own finitude not only gives us whatever grasp we have of the infinite, but also makes us think that we cannot have any real grasp of the infinite at all.  I shall sketch a way of coming to terms with this paradox.

Chair

Sebastian Sunday Grève (王小塞), Peking University

Panellists

Chen Bo 陈波, Wuhan University

Han Linhe 韩林合, Peking University

Li Qilin 李麒麟, Peking University

Mei Jianhua 梅剑华, Shanxi University

Nan Xing 南星, Peking University

Sun Yongping 孙永平, Peking University

Wang Wei 王纬, Fudan University

Wang Yanjing 王彦晶, Peking University

Wu Tianyue 吴天岳, Peking University

Yan Chunling 颜春玲, Chinese Academy of Sciences

Ye Feng 叶峰, Capital Normal University

Zhao You 赵悠, Peking University