### Turing and Wittgenstein on Logic and Mathematics

### PROFESSOR RAY MONK

November 6th, 2017

@ 6:15 pm - 8:00 pm

Bloomsbury, 50 Bedford Square

London WC1B 3DP

About the Speaker

Speaker Bibliography

Abstract

Video

Report

About the Reporter

### About the Speaker

Ray Monk FRSL is Professor of Philosophy at the University of Southampton, where he has taught since 1992.

He won the John Llewellyn Rhys Prize and the 1991 Duff Cooper Prize for his biography of Wittgenstein, *Ludwig Wittgenstein: The Duty of Genius*. His interests lie in the philosophy of mathematics, the history of analytic philosophy, and philosophical aspects of biographical writing. His biography of Robert Oppenheimer was published in 2012.

In 2015 he was awarded a Fellowship by the Royal Society of Literature

### SELECTED Bibliography

### Abstract

In this lecture I want to discuss the relations, personal and intellectual, between Alan Turing and Ludwig Wittgenstein, concentrating in particular on their exchange during Wittgenstein’s lectures in 1939. In recent times, the person who has written at greatest length on this topic is the philosopher Juliet Floyd, but, in my view, what is especially interesting in the exchanges between Turing and Wittgenstein, namely their very divergent ways of looking at mathematics and logic, is in danger of being obscured by Floyd’s determination to stress the similarities between the two. In contrast, my lecture will highlight the profound and fundamental differences between them and thus try to get better in focus the issues at stake in this fascinating clash between two of the greatest figures in the history of twentieth century thought.

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### Report

Ray Monk has form. He has written splendid biographies — of Ludwig Wittgenstein, Bertrand Russell and Robert Oppenheimer — in which the fascinating life of the subject has been woven with intellectual development, significance and criticisms. Ray’s lecture manifested more of that fine form — informative, thought-provoking and entertaining — in this case, regarding the intertwining of the lives and thoughts of Wittgenstein and Alan Turing at Cambridge. The lecture centred on their thinking and disagreements regarding perplexities in logic and mathematics, perplexities raised by other major figures such as Russell, Hilbert and another outstanding thinker, Frank Ramsey.

Turing, twenty-three years Wittgenstein’s junior, was an undergraduate who later attended some of Wittgenstein’s lectures. In 1939, Alistair Watson, another mathematician (Turing was primarily a mathematician), brought them together, sometimes wandering through Cambridge’s Botanic Garden, arguing about mathematics’ foundations. Turing worried about them; Wittgenstein dismissed them as illusion. Turing wanted to resolve contradictions in logic and mathematics (for example, Russell’s Paradox); Wittgenstein was once troubled by the Paradox — it led him to Cambridge to intrude upon Russell — but later argued it was no matter.

Ray brought forth our two protagonists discussing ‘The Bridge’. How could a contradiction in mathematics have consequences? A bridge may fall down because we misunderstand the laws of nature; it may fall down because we erred in our calculations. It may fall down because we have not made the foundations sturdy enough — but could it fall down because the foundations of mathematics were not sufficiently sturdy?

Although Turing and Wittgenstein both rejected Russell’s logicism (where mathematics reduces to logic), Turing still required a place for logic in mathematics’ foundations. Wittgenstein saw no place and saw no foundations, no ‘leading problems’. Contradictions arise, according to Wittgenstein, through everyday language: for example, philosophers play with The Liar, with an individual who says ‘I am lying’; but, asks Wittgenstein, what use is there in such assertions? We may add: if such assertions trouble us, don’t make them. After all, why should they matter?

Ray’s lecture matters for it shows the importance of, and disagreements within, Turing and Wittgenstein’s understandings of mathematics. The topic, being somewhat arcane, has lacked the popular appeal of Turing’s cracking the Enigma code; and mainstream philosophy has focused far more on the Turing Machine and Wittgenstein’s transformative approach to mind and language. As Ray told us, though, Wittgenstein thought his work in the philosophy of mathematics was his most important work — perhaps explained by the fact that it was Russell’s Paradox that first engaged Wittgenstein with philosophy.

Peter Cave

### About the Reporter

For Peter Cave’s lively takes on many philosophical perplexities, try his latest:

*The Big Think Book: Discover Philosophy Through 99 Perplexing Puzzles. *For video extracts – and look out for Farmer McDonald’s stilettos in Humpty Dumpty and Ms Turkey – try: http://www.philosophycave.com