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“... As you’ve probably begun to see,’ David Foster Wallace writes in Everything and More, ‘Aristotle manages to be sort of grandly and breathtakingly wrong, always and everywhere, when it comes to infinity.’ A much milder version of this antagonism towards Aristotle appears in both Brian Clegg’s Brief History of Infinity and Robert and Ellen Kaplan’s The Art of the Infinite ...”

“... In May 2000 the Clay Mathematics Institute announced that it was offering seven prizes, worth $1 million each, for the solutions to seven mathematical problems, which had been identified by a group of internationally acclaimed mathematicians as the seven most difficult and most important unsolved mathematical problems of the day. They became known as the Millennium Problems ...”

“... The world, according to Ted Sider, has a basic structure. An optimal description of the world must capture this structure. It must also consist of truths. But these are two distinct requirements. We can produce more and more truths about the world and still not come any closer to capturing its structure. To do the latter we need to produce not just truths, but truths of the right sort ...”

“... Ludwig Wittgenstein’​s Tractatus Logico-Philosophicus, the only book he published during his lifetime, is one of the greatest philosophical works of the 20th century. It might have been expected, when it first appeared in 1921, to have limited appeal. It is very much the work of a philosophers’ philosopher, forbiddingly technical in places and esoteric throughout ...”

“... that makes any sense. They are thus worried about ‘the possibility of objectivity’. A.W. Moore’s book is a sort of defence of the possibility of objectivity (what he often calls the possibility of ‘absolute representations’). He doesn’t argue that objectivity is ever attained or ever likely to be; perhaps not even in our most scrupulous ...”

“... Bernard Williams had a very large mind. To read these three posthumously published collections of essays (there will be a fourth, on opera) is an overwhelming reminder of his incandescent and all-consuming intelligence. He brought philosophical reflection to an opulent array of subjects, with more imagination and with greater cultural and historical understanding than anyone else of his time ...”

“... the many poems inserted in the text; the verse is sub-Shelleyan, with some influence from Thomas Moore. When the element which Bulwer has in common with Becker is abstracted, we are left with a romantic novelette of melodramatic character, spiced with a particularly mawkish kind of Evangelical Christianity. A rich young Greek, Glaucus, ‘an Alcibiades ...”