
19Forall x: Calgary RemixCreateSpace. 2018.Introduction to truthfunctional and firstorder logic.

18Wittgenstein on Solipsism in the 1930s: Private Pains, Private Languages, and Two Uses of ‘I’Royal Institute of Philosophy Supplement 82 205229. 2018.

21Grades of Discrimination: Indiscernibility, Symmetry, and RelativityNotre Dame Journal of Formal Logic 58 (4): 527553. 2017.There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain firstorder formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discr…Read more

3Philosophy and Model TheoryOxford University Press. 2018.Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike.

53Knot and Tonk: Nasty Connectives on ManyValued TruthTables for Classical Sentential LogicAnalysis 76 (1): 719. 2016.Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use manyvalued truthtables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the problem of ma…Read more

25Hyperloops do not threaten the notion of an effective procedureLecture Notes in Computer Science 5635 6878. 2009.This paper develops my (BJPS 2009) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that "effectively computable" is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.

110Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of MathematicsPhilosophia Mathematica 24 (3): 283307. 2016.This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

125Dadaism: Restrictivism as Militant QuietismProceedings of the Aristotelian Society 110 (3pt3): 387398. 2010.Can we quantify over everything: absolutely, positively, definitely, totally, every thing? Some philosophers have claimed that we must be able to do so, since the doctrine that we cannot is selfstultifying. But this treats restrictivism as a positive doctrine. Restrictivism is much better viewed as a kind of militant quietism, which I call dadaism. Dadaists advance a hostile challenge, with the aim of silencing everyone who holds a positive position about ‘absolute generality’

183The Metamathematics of Putnam's ModelTheoretic ArgumentsErkenntnis 74 (3): 321349. 2011.Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three modeltheoretic arguments, and I argue against Bays (2001…Read more

36Naturalism, Realism, and Normativity By Hilary Putnam, edited by Mario de Caro Harvard University Press, 2016, 248pp., £39.95 ISBN: 9780674659698 (review)Philosophy 92 (2): 305315. 2017.

36The chair that is used to sit in. Review of: The American Pragmatists by Cheryl Misak (review)Times Literary Supplement. 2013.In The American Pragmatists (2013), Cheryl Misak casts Peirce and Lewis as the heroes of American pragmatism. She establishes an impressive continuity between pragmatism and both logical empiricism and contemporary analytic philosophy. However, in casting James and Dewey as the villains of American pragmatism, she underplays the pragmatists' interest in action.

173SAD computers and two versions of the Church–Turing thesisBritish Journal for the Philosophy of Science 60 (4): 765792. 2009.Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between nonTuring computability and nonEuclidean geometry, showing t…Read more

166Every now and then, nofuturism faces no sceptical problemsAnalysis 67 (4). 2007.Tallant (2007) has challenged my recent defence of nofuturism (Button 2006), but he does not discuss the key to that defence: that nofuturism's primitive relation 'x is realasof y' is not symmetric. I therefore answer Tallant's challenge in the same way as I originally defended nofuturism. I also clarify nofuturism by rejecting a common mischaracterisation of the growingblock theorist. By supplying a semantics for nofuturists, I demonstrate that nofuturism faces no sceptical challenges…Read more

253There's no time like the presentAnalysis 66 (2). 2006.Nofuturists ('growing block theorists') hold that that the past and the present are real, but that the future is not. The present moment is therefore privileged: it is the last moment of time. Craig Bourne (2002) and David BraddonMitchell (2004) have argued that this position is unmotivated, since the privilege of presentness comes apart from the indexicality of 'this moment'. I respond that nofuturists should treat 'x is realasof y' as a nonsymmetric relation. Then different moments are re…Read more

315Truth by Analysis: Games, Names, and Philosophy By Colin McGinn (review)Analysis 73 (3): 577580. 2013.In Truth by Analysis (2012), Colin McGinn aims to breathe new life into conceptual analysis. Sadly, he fails to defend conceptual analysis, either in principle or by example.

93Brains in vats and model theoryIn Sanford Goldberg (ed.), The Brain in a Vat, Cambridge University Press. forthcoming.Hilary Putnam’s BIV argument first occurred to him when ‘thinking about a theorem in modern logic, the “Skolem–Löwenheim Theorem”’ (Putnam 1981: 7). One of my aims in this paper is to explore the connection between the argument and the Theorem. But I also want to draw some further connections. In particular, I think that Putnam’s BIV argument provides us with an impressively versatile template for dealing with sceptical challenges. Indeed, this template allows us to unify some of Putnam’s most e…Read more

114Spotty Scope and Our Relation to FictionsNoûs 46 (2): 24358. 2012.Whatever the attractions of Tolkein's world, irrealists about fictions do not believe literally that Bilbo Baggins is a hobbit. Instead, irrealists believe that, according to The Lord of the Rings {Bilbo is a hobbit}. But when irrealists want to say something like “I am taller than Bilbo”, there is nowhere good for them to insert the operator “according to The Lord of the Rings”. This is an instance of the operator problem. In this paper, I outline and criticise Sainsbury's (2006) spotty scope a…Read more

43Exclusion Problems and the Cardinality of Logical SpaceJournal of Philosophical Logic 46 (6): 611623. 2017.Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colourexclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The condition is: logi…Read more

75The Weight of Truth: Lessons for Minimalists from Russell's Gray's Elegy ArgumentProceedings of the Aristotelian Society 114 (3pt3): 261289. 2014.Minimalists, such as Paul Horwich, claim that the notions of truth, reference and satisfaction are exhausted by some very simple schemes. Unfortunately, there are subtle difficulties with treating these as schemes, in the ordinary sense. So instead, minimalists regard them as illustrating oneplace functions, into which we can input propositions (when considering truth) or propositional constituents (when considering reference and satisfaction). However, Bertrand Russell's Gray's Elegy argument …Read more

147Realistic structuralism's identity crisis: A hybrid solutionAnalysis 66 (3). 2006.Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a nontrivial automorphism, distinct indiscernible positions within the structure cannot be shown to be nonidentical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive twoplace relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positio…Read more

94Deflationary metaphysics and ordinary languageSynthese 125. forthcoming.Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a…Read more

368The Limits of RealismOxford University Press UK. 2015.Tim Button explores the relationship between minds, words, and world. He argues that the two main strands of scepticism are deeply related and can be overcome, but that there is a limit to how much we can show. We must position ourselves somewhere between internal realism and external realism, and we cannot hope to say exactly where.
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