PAGE BEING RECONSTRUCTED! The blog here started in March 2006, and since then there have been — rather astonishingly — 1,634 posts. Of course, many of these were of merely temporary relevance. But over the years, there have been some posts, or series of posts, of perhaps less ephemeral interest. So this page will have links [TO COME] to a selection.
I also link to a few papers, book reviews, and other pieces which I think might be still be worth reading, and also link to a page of logical snippets I’ve posted elsewhere, and to some old but perhaps useful advice on writing for graduate students.
Papers
These old pieces 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.
- 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)
- 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
- Critical Notice of Volker Halbach Axiomatic Theories of Truth and Leon Horsten The Tarskian Turn in Analysis 2013
- Review of Baaz et al. Kurt Gödel and the Foundations of Mathematics: Horizons of Truth in Philosophia Mathematica 2012.
- Review of Penelope Maddy Defending the Axioms (with Luca Incurvati) in Mind 2012
- Is ‘no’ a force-indicator? Sometimes, possibly (with Luca Incurvati) Analysis 2012
- The philosophical significance of Tennenbaum’s Theorem (with Tim Button) Philosophia Mathematica 201
- Review of Alan Weir Truth Through Proof in Mind 2011.
- Four lectures on the First Theorem given to maths students, Easter 2011.
- 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.
- The MRDP Theorem (introduction to what it says and why it matters)
- 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.)
- On chs 5 & 6 of Mary Leng’s Mathematics and Reality (concerning naturalism about mathematics)
- 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]’).
- Field on truth: how complex is too complex? (worries sceptically about the conceptual significance of Field’s intricate constructions).
- Curry’s paradox, Lukasiewicz and Field (some cheerfully naive notes introducing Ch. 4 of Field’s Saving Truth from Paradox, for a reading group).
- Kleene’s Normal Form Theorem entails Gödel’s Incomplete Theorem (explained in just two pages).
- 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!)
- Induction and predicativity (another talk given in New Zealand, for a non-expert audience)
- 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!)
- Back to basics: revisiting the Incompleteness Theorems (46 page handout for three lectures aimed at graduates)
- Rejection and valuations (with Luca Incurvati, draft of Analysis paper published in Jan 2010)
- Critical Notice of Charles Parsons’s Mathematical Thought and Its Objects (published in Analysis Reviews, 2009; excerpted from postings on the blog)
- Wittgenstein on mathematics and games (discussing §108 of the Big Typescript)
- Review of Rayo and Uzquiano (eds), Absolute Generality (short review in BSL, excerpted from postings on the blog)
- 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”)
- Ancestral arithmetic and Isaacson’s thesis (stand-alone paper published in Analysis, reworking ideas in my Gödel book)
- Induction, more or less (expanded version of talk given at Dan Isaacson’s seminar in Oxford in 2007, mostly on ACA0)
- Review discussion of Adam Olszewski et al. Church’s Thesis after 70 Years (originally written, paper by paper, for my blog).
Logical snippets
- Over 100 links to short notes giving advice/info answering student questions first posted on the forum math.stackexchange. Many of these are aimed at beginners or near beginners in logic.
General advice about writing
- Developing a writing style. (First written for beginning graduate students, but no doubt undergraduates could use the advice too!)