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Special Issue: Williamson on Modality

Volume 46 - Issue 4-5 - August 2016
Canadian Journal of Philosophy Volume 46 - Issue 4-5 - Special Issue: Williamson on Modality
Contents

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Articles

  • Modal science

  • Timothy Williamson
  • Published online by Cambridge University Press: 01 January 2020, pp. 453-492

  • This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions arguably include some necessitist principles.

  • Higher-order free logic and the Prior-Kaplan paradox

  • Andrew Bacon, John Hawthorne, Gabriel Uzquiano
  • Published online by Cambridge University Press: 01 January 2020, pp. 493-541

  • The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior's paradox and Kaplan's paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior's and Kaplan's derivations at face value.

  • First-order modal logic in the necessary framework of objects

  • Peter Fritz
  • Published online by Cambridge University Press: 01 January 2020, pp. 584-609

  • I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson's argument.

  • Williamson on necessitism

  • Jeremy Goodman
  • Published online by Cambridge University Press: 01 January 2020, pp. 613-639

  • I critically discuss some of the main arguments of Modal Logic as Metaphysics, present a different way of thinking about the issues raised by those arguments, and briefly discuss some broader issues about the role of higher-order logic in metaphysics.

  • Plurals and modals

  • Øystein Linnebo
  • Published online by Cambridge University Press: 01 January 2020, pp. 654-676

  • Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.

  • On Williamson and simplicity in modal logic

  • Theodore Sider
  • Published online by Cambridge University Press: 01 January 2020, pp. 683-698

  • According to Timothy Williamson, we should accept the simplest and most powerful second-order modal logic, and as a result accept an ontology of "bare possibilia". This general method for extracting ontology from logic is salutary, but its application in this case depends on a questionable assumption: that modality is a fundamental feature of the world.

  • Models and reality*

  • Robert Stalnaker
  • Published online by Cambridge University Press: 01 January 2020, pp. 709-726

  • Kripke models, interpreted realistically, have difficulty making sense of the thesis that there might have existed things that do not in fact exist, since a Kripke model in which this thesis is true requires a model structure in which there are possible worlds with domains that contain things that do not exist. This paper argues that we can use Kripke models as representational devices that allow us to give a realistic interpretation of a modal language. The method of doing this is sketched, with the help of an analogy with a Galilean relativist theory of spatial properties and relations.

  • An A-theory without tense operators

  • Meghan Sullivan
  • Published online by Cambridge University Press: 01 January 2020, pp. 735-758

  • A-theorists think there is a fundamental difference between the present and other times. This concern shows up in what kinds of properties they take to be instantiated, what objects they think exist and how they formalize their views. Nearly every contemporary A-theorist assumes that her metaphysics requires a tense logic – a logic with operators like (‘it was the case that...’) and (‘it will be the case that...’). In this paper, I show that there is at least one viable A-theory that does not require a logic with tense operators. And I will argue that three common indispensability arguments for tense operators are unsound.

  • Williamsonian modal epistemology, possibility-based

  • Barbara Vetter
  • Published online by Cambridge University Press: 01 January 2020, pp. 766-795

  • Williamsonian modal epistemology (WME) is characterized by two commitments: realism about modality, and anti-exceptionalism about our modal knowledge. Williamson's own counterfactual-based modal epistemology is the best known implementation of WME, but not the only option that is available. I sketch and defend an alternative implementation which takes our knowledge of metaphysical modality to arise, not from knowledge of counterfactuals, but from our knowledge of ordinary possibility statements of the form ‘x can F’. I defend this view against a criticism indicated in Williamson's own work, and argue that it is better connected to the semantics of modal language.

  • Epistemicism and modality

  • Juhani Yli-Vakkuri
  • Published online by Cambridge University Press: 01 January 2020, pp. 803-835

  • 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 ways of extracting an epistemicist semantics from that model theory, one of which I will find to be more plausible than the other.

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