This page lists various notes, handouts, papers, and so on from the last few years. Many of these pieces are also linked to from other pages here or from old blog postings. They 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).

Dear prof. Smith,

I am reading your book on Goedel’s Theorems: I have not yet finished to study it, but it’s already apparent that it is beautifully clear: I will go through the book in the next weeks. Thank you!

You wrote “there’ s a sequel planned for enthusiasts”(p. xiii): I am surely among them. So what about the sequel? I will be looking forward to reading it.

Well, I hope there will first be one not-quite-a-sequel, on the significance of Gentzen’s consistency proofs for arithmetic. And I have another plan too for a short book comparing ten different ways of proving Gödel’s first theorem …