Category: Mathematics
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By Catarina Dutilh Novaes As readers will have noticed, since yesterday there has been an outpour of expressions of sorrow for the passing of Patrick Suppes everywhere on the internet. He was without a doubt one of the most influential philosophers of science in the 20th century, and so all the love and appreciation is…
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By Catarina Dutilh Novaes Alexander Grothendieck, who is viewed by many as the greatest mathematician of the 20th century, has passed away yesterday after years of living in total reclusion. (To be honest, I did not even know he was still alive!) He was a key figure in the development of the modern theory of…
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By Catarina Dutilh Novaes Today my research group in Groningen (with the illustrious online participation of Tony Booth, beaming in from the UK) held a seminar session where we discussed Fabienne Peter’s 2013 paper ‘The procedural epistemic value of deliberation’. It is a very interesting paper, which defends the view that deliberation has not only…
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By Catarina Dutilh Novaes (Cross-posted at M-Phi) In December, I will be presenting at the Aesthetics in Mathematics conference in Norwich. The title of my talk is Beauty, explanation, and persuasion in mathematical proofs, and to be honest at this point there is not much more to it than the title… However, the idea…
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(Cross-posted at M-Phi) Mathematics has been much in the news recently, especially with the announcement of the latest four Fields medalists (I am particularly pleased to see the first woman, and the first Latin-American, receiving the highest recognition in mathematics). But there was another remarkable recent event in the world of mathematics: Thomas Hales has…
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Eric Schwitzgebel recently took up the question of whether an infinitely extended life must be boring. The discussion ended (when I looked at it) with Eric’s fruitfully suggesting that we look at various cognitive architectures and their capacities for boredom over the long run. No doubt there are many kinds of minds. Let’s radically simplify…
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Hitler does not like Gödel's theorem one bit. Perhaps surprisingly, he displays a sophisticated understanding of the implications and presuppositions of the theorem. (In other words, there's some very solid philosophy of logic in the background — I think I could teach a whole course only on the material presupposed here.) (Courtesy of Diego Tajer,…
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A few weeks ago I had a post on different ways of counting infinities; the main point was that two of the basic principles that hold for counting finite collections cannot be both transferred over to the case of measuring infinite collections. Now, as a matter of fact I am equally (if not more) interested…
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(Cross-posted at M-Phi) In his Two New Sciences (1638), Galileo presents a puzzle about infinite collections of numbers that became known as ‘Galileo’s paradox’. Written in the form of a dialogue, the interlocutors in the text observe that there are many more positive integers than there are perfect squares, but that every positive integer is the root…
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I'm currently running a series of posts at M-Phi with sections of a paper I'm working on, 'Axiomatizations of arithmetic and the first-order/second-order divide', which may be of interest to at least some of the NewAPPS readership. It focuses on the idea that, when it comes to axiomatizing arithmetic, descriptive power and deductive power cannot…
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