- On Moore's notion of proof, forthcoming in the Canadian Journal of Philosophy
- Presentism and modal realism, forthcoming in Analytic Philosophy
**Abstract**: David Lewis sells modal realism as a package that includes an eternalist view of time. There is, of course, nothing that ties together the thesis that modality should be analyzed in terms of "concrete" possibilia with the view that non-present things exist. In this paper I develop a theory I call*modal realist presentism*that is a combination of modal realism and presentism, and argue that is has compelling answers to some of the main objections to presentism, including the arguments from (i) singular propositions, (ii) cross-temporal relations, and (iii) truthmaking. Toward the end, I compare modal realist presentism favorably to some similar theories, including Bigelow's modal theory of time, Williamson's theory of the ex-concrete, and Dainton's theory of many-worlds presentism. - Possible worlds, forthcoming in the Routledge Handbook of Modality (Otávio Bueno and Scott Shalkowski, eds.)
- There is more to negation than modality (with Hitoshi Omori), Journal of Philosophical Logic, Volume 47, Issue 2, 2018, pp 281-299
**Abstract**: There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the consequence that negation is a modal operator, a claim Francesco Berto (2015) defends in a recent paper. According to one such modal account, the negation of a sentence is true at a world*x*just in case all the worlds at which the sentence is true are*incompatible*with*x*. Incompatibility is taken to be the key notion in the account, and what minimal properties a negation has comes down to which minimal conditions incompatibility satisfies.Our aims in this paper are twofold. First, we wish to point out problems for the modal account that make us question its tenability on a fundamental level. Second, in its place we propose an alternative, non-modal, account of negation as a contradictory-forming operator that we argue is superior to, and more natural than, the modal account.

- On the Humphrey objection to modal realism, Grazer Philosophische Studien, Vol. 95, Issue 2, 2018, pp. 159-179
**Abstract**: An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one's modal properties without being concerned about the properties one's other-worldly counterparts have. I assess this objection in a variety of forms, and then provide my own formulation that does not beg the question against the modal realist. Finally, I consider two potential answers to the objection so understood and conclude that only one of them has a chance of succeeding. - Classical and empirical negation in subintuitionistic logic (with Hitoshi Omori), Advances in Modal Logic Vol. 11, College Publications, 2016, pp. 217-235
**Abstract**: Giovanna Corsi (1987) and Greg Restall (1994) investigate propositional subintuitionistic logics that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. Both Corsi and Restall confine their attention to the standard intuitionistic language. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other with by what has been dubbed "empirical" negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research. - Intrinsicality and counterpart theory, Synthese, Vol. 193, No. 8, 2016, pp. 2353-2365
**Abstract**: It is shown that counterpart theory and the duplication account of intrinsicality—two key pieces of the Lewisian package—are incompatible. In particular, the duplication account yields the result that certain intuitively extrinsic modal properties are intrinsic. Along the way I consider a potentially more general worry concerning certain existential closures of internal relations. One conclusion is that, unless the Lewisian provides an adequate alternative to the duplication account, the reductive nature of their total theory is in jeopardy. - Classical Negation and Expansions of Belnap-Dunn Logic (with Hitoshi Omori), Studia Logica, Vol. 103, No. 4, 2015, pp. 825-851
**Abstract**: We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion**BD+**of four-valued Belnap-Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare**BD+**to some related systems found in the literature, specifically a four-valued modal logic of Béziau and the logic of classical implication and a paraconsistent de Morgan negation of Zaitsev. - More on Empirical Negation (with Hitoshi Omori), Advances in Modal Logic Vol. 10, College Publications, Rajeev Goré, Barteld Kooi, and Agi Kurucz (editors), 2014, pp. 114-133 [open access]
**Abstract**: Intuitionism can be seen as a verificationism restricted to mathematical discourse. An attempt to generalize intuitionism to empirical discourse presents various challenges. One of those concerns the logical and semantical behavior of what has been called 'empirical negation'. An extension of intuitionistic logic with empirical negation was given by Michael De (2013) and a labelled tableaux system was there shown sound and complete. However, a Hilbert-style axiom system that is sound and complete was missing. In this paper we provide the missing axiom system which is shown sound and complete with respect to its intended semantics. Along the way we consider some further applications of empirical negation. - Empirical Negation, Acta Analytica, Vol. 28, No. 1, 2013, pp. 49-69 [open access]
**Abstract**: An extension of intuitionism to empirical discourse, a project most seriously taken up by Dummett and Tennant, requires an empirical negation whose strength lies somewhere between classical negation ('It is unwarranted that...') and intuitionistic negation ('It is refutable that...'). I put forward one plausible candidate that compares favorably to some others that have been propounded in the literature. A tableau calculus is presented and shown to be strongly complete. - Can Logical Consequence be Deflated?, in
*Insolubles and Consequences : essays in honour of Stephen Read*, Catarina Dutilh Novaes and Ole Hjortland (eds.), College Publications, 2012, pp. 23-33**Abstract**: An interesting question is whether deflationism about truth (and falsity) extends to related properties and relations on truthbearers. Lionel Shapiro (2011) answers affirmatively by arguing that a certain deflationism about truth is as plausible as an analogous version of deflationism about logical consequence. I argue that the argument fails on two counts. First, it trivializes to any relation between truthbearers, including substantive ones; in other words, his argument can be used to establish that deflationism about truth is as plausible as deflationism about an arbitrary sentential relation. Second, the alleged analogy between the arguments for deflationism about truth and deflationism about consequence fails. Along the way I consider what implications the failure of the equiplausibility thesis has for deflationism about falsity. - Negation in Context, PhD thesis, University of St Andrews, 2011
**Abstract**: The present essay includes six thematically connected papers on negation in the areas of the philosophy of logic, philosophical logic and metaphysics.

**Abstract**: Much has been said about Moore's proof of the external world, but the notion of proof that Moore employs has been largely overlooked. I suspect that most have either found nothing wrong with it, or they have thought it somehow irrelevant to whether the proof serves its anti-skeptical purpose. I show, however, that Moore's notion of proof is highly problematic. For instance, it trivializes in the sense that any known proposition is provable. This undermines Moore's proof as he conceives it since it introduces a skeptical regress that he goes at length to resist. I go on to consider various revisions of Moore's notion of proof and finally settle on one that I think is adequate for Moore's purposes and faithful to what he says concerning immediate knowledge.