Monsters of Truth

Monsters of Truth, abandoned around 2019. The writing that sustained my philosophical thinking during most of my years teaching mathematics at Abingdon School. 1. Through the Looking Glass. 2. The Meaning of Probability. 3. Mathematical Recreations. 4. The Nature of Mathematics. 5. The Foundations of Mathematics. 6. Comparing Mathematics to a Game. 7. On Formally Undecidable Propositions. 8. Space, Time and Deity. 9. Our Knowledge of the External World. 10. The Mind and its Place in Nature. 11. Computing Machinery and Intelligence. 12. The Mysterious Universe. The original idea was for a book on philosophy as paradox, comparing philosophical paradoxes to paradoxes outside philosophy. And taking from Baltasar Gracián’s “Monsters of Truth” the idea that philosophical monsters, in a later sense, have an origin comparable to artistic monsters: centaurs, minotaurs, dragons, gryphons, and so on. But the Cambridge background to Wittgenstein’s thinking began to dominate and another idea entered, that of a “distant mirror”, borrowed from Freeman Dyson (1923-2020), in which we can see ourselves reflected, but only if we understand what Wittgenstein actually said. Hence Journeyings in Wittgenstein’s Cambridge became an alternative title. “Mirror reversal” is ultimately compared to and contrasted with the paradox of Achilles and the tortoise in its many historical manifestations. (The latter is itself a mirror, in which we see our own thinking reflected.) Included here is the final chapter “The Mysterious Universe”, research which would otherwise have been lost.