Logical notes and papers

Some logical blog pieces

  1. Philosophy of maths: a reading list
  2. Does mathematics need a philosophy?
  3. Philosophical logic: five books from the back catalogue
  4. On Frege seeing what is in front of his nose.
  5. Begriffsschrift and absolutely unrestricted quantification
  6. What Frege didn’t tell you
  7. Tarski on Truth, a thumbnail sketch
  8. Partial functions and free logic
  9. Revisiting an old result of Hintikka’s
  10. A query about countability
  11. Negative type theory
  12. [More to be added]

A few papers and handouts

These old pieces written round about the time I retired are of very varying levels of sophistication, difficulty and interest: but I haven’t tried to impose any more order on the list other than a rough (reverse) chronological order.

  1. Notes on ‘the contemporary conception of logic’ gives evidence against a claim by Goldfarb (endorsed by some others) about the supposedly dominant conception of logic as dealing in schemata. (2013)
  2. Tennenbaum’s Theorem (a rewritten version of a reasonably accessible proof, with the old short discussion of its sometimes supposed conceptual significance which fed into the joint paper with Tim Button). 2013, revised 2014.
  3. Is ‘no’ a force-indicator? Sometimes, possibly (with Luca Incurvati) Analysis 2012.
  4. The philosophical significance of Tennenbaum’s Theorem (with Tim Button)  Philosophia Mathematica 2011
  5. Squeezing arguments (on Kreisel’s argument — what it does and doesn’t show: expanding a bit on part of the Squeezing Church’s Thesis talk). Draft of paper in Analysis 2011.
  6. The MRDP Theorem (introduction to what it says and why it matters)
  7. Cuts, consistency and axiomatized theories (A short and naive introduction to the chapter in Negri and von Plato’s Structural Proof Theory on cut-elimination for certain kinds of theories — though you don’t have to have read the book to follow the story.)
  8. On chs 5 & 6 of Mary Leng’s Mathematics and Reality (concerning naturalism about mathematics).
  9. The Galois connection between syntax and semantics (explains Lawvere’s remark about ‘the familiar Galois connection between sets of axioms and classes of models, for a fixed [signature]’).
  10. Field on truth: how complex is too complex? (worries sceptically about the conceptual significance of Field’s intricate constructions).
  11. Curry’s paradox, Lukasiewicz and Field (some cheerfully naive notes introducing Ch. 4 of Field’s Saving Truth from Paradox, for a reading group).
  12. Kleene’s Normal Form Theorem entails Gödel’s Incomplete Theorem (explained in just two pages).
  13. Squeezing Church’s Thesis again (a talk given a few times in New Zealand, explaining what I was up to at the end of my Gödel book, but a little better!)
  14. Induction and predicativity (another talk given in New Zealand, for a non-expert audience).
  15. Entailment, with nods to Lewy and Smiley (an introductory talk to a seminar, something of an exercise in Cambridge piety: the promised next talk on Tennant wasn’t given though for reasons I can’t recall!).
  16. Rejection and valuations (with Luca Incurvati, draft of Analysis paper published in Jan 2010).
  17. Wittgenstein on mathematics and games (discussing §108 of the Big Typescript).
  18. There are sea-serpents, Jim, but not as we know them (talk given to a metaphysics group in Cambridge, commenting on Zoltan Szabo’s “Believing in things”).
  19. Ancestral arithmetic and Isaacson’s thesis (stand-alone paper published in Analysis, reworking ideas in my Gödel book).
  20. Induction, more or less (expanded version of talk given at Dan Isaacson’s seminar in Oxford in 2007, mostly on ACA0).
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