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51Dissemination Corner: One True LogicThe Reasoner 16 (1): 3-4. 2022.A brief article introducing *One True Logic*. The book argues that there is one correct foundational logic and that it is highly infinitary.
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100Focussed Issue of The Reasoner on Infinitary Reasoning (edited book). 2022.A focussed issue of The Reasoner on the topic of 'Infinitary Reasoning'. Owen Griffiths and A.C. Paseau were the guest editors.
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64Introducing IdentityJournal of Philosophical Logic 50 (6): 1449-1469. 2021.The best-known syntactic account of the logical constants is inferentialism. Following Wittgenstein’s thought that meaning is use, inferentialists argue that meanings of expressions are given by introduction and elimination rules. This is especially plausible for the logical constants, where standard presentations divide inference rules in just this way. But not just any rules will do, as we’ve learnt from Prior’s famous example of tonk, and the usual extra constraint is harmony. Where does this…Read more
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126Ways of Being and LogicalityJournal of Philosophy 120 (2): 94-116. 2023.Ontological monists hold that there is only one way of being, while ontological pluralists hold that there are many; for example, concrete objects like tables and chairs exist in a different way from abstract objects like numbers and sets. Correspondingly, the monist will want the familiar existential quantifier as a primitive logical constant, whereas the pluralist will want distinct ones, such as for abstract and concrete existence. In this paper, we consider how the debate between the monist …Read more
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Propositional logics of logical truthIn Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning, Cambridge University Press. 2021.
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48Is English consequence compact?Thought: A Journal of Philosophy 10 (3): 188-198. 2021.Thought: A Journal of Philosophy, Volume 10, Issue 3, Page 188-198, September 2021.
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16Reinflating Logical ConsequenceJournal of Philosophical Logic 43 (1): 171-179. 2014.Shapiro (Philos Q 61:320–342, 2011) argues that, if we are deflationists about truth, we should be deflationists about logical consequence. Like the truth predicate, he claims, the logical consequence predicate is merely a device of generalisation and more substantial characterisation, e.g. proof- or model-theoretic, is mistaken. I reject his analogy between truth and logical consequence and argue that, by appreciating how the logical consequence predicate is used as well as the goals of proof t…Read more
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47Isomorphism invariance and overgeneration – corrigendumBulletin of Symbolic Logic 23 (4): 546-546. 2017.
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83Isomorphism invariance and overgenerationBulletin of Symbolic Logic 22 (4): 482-503. 2016.The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrec…Read more
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110Formal and informal consequenceThought: A Journal of Philosophy 3 (1): 9-20. 2014.The now standard definition of logical consequence is model-theoretic. Many writers have tried to justify, or to criticise, the model-theoretic definition by arguing that it extensionally captures, or fails to capture, our intuitions about logical consequence, such as its modal character or its being truth-preservation in virtue of form. One popular means of comparing the extension of model-theoretic consequence with some intuitive notion proceeds by adapting Kreisel's squeezing argument. But th…Read more
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126Problems for Logical PluralismHistory and Philosophy of Logic 34 (2): 170-182. 2013.I argue that Beall and Restall's logical pluralism fails. Beall–Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ‘settled core’ of consequence: they believe that truth-preservation, necessity, formality and normativity are ‘settled’ features of logical consequence and that any relation satisfying these criteria is a logic…Read more
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94Reinflating Logical ConsequenceJournal of Philosophical Logic (1): 1-9. 2012.Shapiro (Philos Q 61:320–342, 2011) argues that, if we are deflationists about truth, we should be deflationists about logical consequence. Like the truth predicate, he claims, the logical consequence predicate is merely a device of generalisation and more substantial characterisation, e.g. proof- or model-theoretic, is mistaken. I reject his analogy between truth and logical consequence and argue that, by appreciating how the logical consequence predicate is used as well as the goals of proof t…Read more
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78Inferentialism and QuantificationNotre Dame Journal of Formal Logic 58 (1): 107-113. 2017.Logical inferentialists contend that the meanings of the logical constants are given by their inference rules. Not just any rules are acceptable, however: inferentialists should demand that inference rules must reflect reasoning in natural language. By this standard, I argue, the inferentialist treatment of quantification fails. In particular, the inference rules for the universal quantifier contain free variables, which find no answer in natural language. I consider the most plausible natural l…Read more
Areas of Interest
Philosophy of Language |
Logic and Philosophy of Logic |