•  276
    This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of LF, lays out…Read more
  •  662
    Modal Epistemology
    with John Hawthorne
    Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.
  •  157
    In general, a given object could have been different in certain respects. For example, the Great Pyramid could have been somewhat shorter or taller; the Mona Lisa could have had a somewhat different pattern of colours; an ordinary table could have been made of a somewhat different quantity of wood. But there seem to be limits. It would be odd to suppose that the Great Pyramid could have been thimble-sized; that the Mona Lisa could have had the pattern of colours that actually characterizes T…Read more
  •  13
    Reply to Bourget and Mendelovici
    Inquiry: An Interdisciplinary Journal of Philosophy. forthcoming.
    We detect three main critical ideas in Bourget and Mendelovici's (2022; henceforth BM) discussion of Narrow Content (Yli-Vakkuri and Hawthorne 2018). We will discuss each in this reply.
  •  123
    Being in a position to know
    Philosophical Studies 179 (4): 1323-1339. 2022.
    The concept of being in a position to know is an increasingly popular member of the epistemologist’s toolkit. Some have used it as a basis for an account of propositional justification. Others, following Timothy Williamson, have used it as a vehicle for articulating interesting luminosity and anti-luminosity theses. It is tempting to think that while knowledge itself does not obey any closure principles, being in a position to know does. For example, if one knows both p and ‘If p then q’, but on…Read more
  •  103
    The Necessity of Mathematics
    Noûs 54 (3): 549-577. 2020.
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
  •  25
    Précis of narrow content
    Philosophical Studies 178 (9): 3013-3016. 2020.
  •  20
    Reply to Pietroski
    Philosophical Studies 178 (9): 3055-3059. 2020.
    In this reply to Paul Pietroski’s comment on our book Narrow Content, we address his concern that we assume too tight a connection between sentences and contents and thus ignore polysemy. We argue that we were not relying on problematic disquotational assumptions and that our arguments are fully compatible with rampant polysemy. We also argue that Pietroski’s strategy of making room for a theoretically interesting kind of narrow content by giving up the idea that contents determine extensions at…Read more
  •  27
    Reply to Speaks
    Philosophical Studies 178 (9): 3061-3065. 2020.
  •  135
    Reply to Byrne
    Philosophical Studies 178 (9): 3049-3054. 2020.
    In this reply to Alex Byrne’s comment on our book Narrow Content, we address Byrne’s claim that internalism is best framed as a thesis about properties of agents rather than properties of thoughts, arguing that a thought-based framework is better suited to standard internalist ambitions. We also discuss whether there is any prospect for a view in the internalist spirit that prescinds from multiplying indices beyond worlds, address Byrne’s ordinary language considerations against an ontology of t…Read more
  •  735
    Vagueness & Modality—An Ecumenical Approach
    Philosophical Perspectives 30 (1): 229-269. 2016.
    How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness…Read more
  •  1383
    Knowledge of objective modality
    Philosophical Studies 176 (5): 1155-1175. 2019.
    The epistemology of modality has focused on metaphysical modality and, more recently, counterfactual conditionals. Knowledge of kinds of modality that are not metaphysical has so far gone largely unexplored. Yet other theoretically interesting kinds of modality, such as nomic, practical, and ‘easy’ possibility, are no less puzzling epistemologically. Could Clinton easily have won the 2016 presidential election—was it an easy possibility? Given that she didn’t in fact win the election, how, if at…Read more
  •  311
    Narrow Content
    Oxford University Press. 2018.
    Can there be 'narrow' mental content, that is entirely determined by the goings-on inside the head of the thinker? This book argues not, and defends instead a thoroughgoing externalism: the entanglement of our minds with the external world runs so deep that no internal component of mentality can easily be cordoned off.
  •  830
    The Necessity of Mathematics
    Noûs 52 (3): 549-577. 2018.
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
  •  1112
    The idea that the epistemology of modality is in some sense a priori is a popular one, but it has turned out to be difficult to precisify in a way that does not expose it to decisive counterexamples. The most common precisifications follow Kripke’s suggestion that cases of necessary a posteriori truth that can be known a priori to be necessary if true ‘may give a clue to a general characterization of a posteriori knowledge of necessary truths’. The idea is that whether it is contingent whether p…Read more
  •  797
    Modal skepticism and counterfactual knowledge
    Philosophical Studies 162 (3): 605-623. 2013.
    Abstract   Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic ( Reducibility ). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference ( counterfactual development , or CD ) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays …Read more
  •  992
    Externalism is the thesis that the contents of intentional states and speech acts are not determined by the way the subjects of those states or acts are internally. It is a widely accepted but not entirely uncontroversial thesis. Among such theses in philosophy, externalism is notable for owing the assent it commands almost entirely to thought experiments, especially to variants of Hilary Putnam's famous Twin Earth scenario. This paper presents a thought experiment-free argument for externalism.…Read more
  •  1330
    Moderate Modal Skepticism
    In Matthew A. Benton, John Hawthorne & Dani Rabinowitz (eds.), Knowledge, Belief, and God: New Insights in Religious Epistemology, Oxford University Press. pp. 302-321. 2018.
    This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal sk…Read more
  •  1075
    Operator arguments revisited
    Philosophical Studies 176 (11): 2933-2959. 2019.
    Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims …Read more
  •  774
    Conditional and habitual analyses of disposition ascriptions
    Philosophical Quarterly 60 (240): 624-630. 2010.
    Michael Fara's ‘habitual analysis’ of disposition ascriptions is equivalent to a kind of ceteris paribus conditional analysis which has no evident advantage over Martin's well known and simpler analysis. I describe an unsatisfactory hypothetical response to Martin's challenge, which is lacking in just the same respect as the analysis considered by Martin; Fara's habitual analysis is equivalent to this hypothetical analysis. The feature of the habitual analysis that is responsible for this cannot…Read more
  •  405
    Williamson on Modality
    Canadian Journal of Philosophy 46 (4-5): 453-851. 2016.
    This special issue of the Canadian Journal of Philosophy is dedicated to Timothy Williamson's work on modality. It consists of a new paper by Williamson followed by papers on Williamson's work on modality, with each followed by a reply by Williamson. Contributors: Andrew Bacon, Kit Fine, Peter Fritz, Jeremy Goodman, John Hawthorne, Øystein Linnebo, Ted Sider, Robert Stalnaker, Meghan Sullivan, Gabriel Uzquiano, Barbara Vetter, Timothy Williamson, Juhani Yli-Vakkuri
  •  842
    Epistemicism and modality
    Canadian Journal of Philosophy 46 (4-5). 2016.
    What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two…Read more
  •  34
    Williamson on Modality (edited book)
    Routledge. 2017.
    Timothy Williamson is one of the most influential living philosophers working in the areas of logic and metaphysics. His work in these areas has been particularly influential in shaping debates about metaphysical modality, which is the topic of his recent provocative and closely-argued book *Modal Logic as Metaphysics* (2013). The present book comprises ten essays by metaphysicians and logicians responding to Williamson’s work on metaphysical modality. The authors include some of the most distin…Read more