### 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). - Gödel Without (too many) Tears (an 88 page handout for eleven lectures given at Christchurch in March and April 2010), revised for a Cambridge course later in the year.
- 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 ACA
_{0}) - 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!)