•  56
    In the context of classical (crisp, precise) sets, there is a familiar connection between the notions of counting, ordering and cardinality. When it comes to vague collections, the connection has not been kept in central focus: there have been numerous proposals regarding the cardinality of vague collections, but these proposals have tended to be discussed in isolation from issues of counting and ordering. My main concern in this paper is to draw focus back onto the connection between …Read more
  •  91
    Many-Valued Logics
    In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language, Routledge. pp. 636--51. 2012.
    A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have a many-valued semantics in the loose but…Read more
  •  78
    This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities assigned…Read more
  •  110
    Measuring and Modelling Truth
    American Philosophical Quarterly 49 (4): 345-356. 2012.
    Philosophers, linguists and others interested in problems concerning natural language frequently employ tools from logic and model theory. The question arises as to the proper interpretation of the formal methods employed—of the relationship between, on the one hand, the formal languages and their set-theoretic models and, on the other hand, the objects of ultimate interest: natural language and the meanings and truth conditions of its constituent words, phrases and sentences. Two familiar answe…Read more
  •  75
    Time Travel
    In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, . 2013.
    There is an extensive literature on time travel in both philosophy and physics. Part of the great interest of the topic stems from the fact that reasons have been given both for thinking that time travel is physically possible—and for thinking that it is logically impossible! This entry deals primarily with philosophical issues; issues related to the physics of time travel are covered in the separate entries on time travel and modern physics and time machines. We begin with the definitional ques…Read more
  •  10
    Reply to Francesco Paoli’s Comments on 'Fuzzy Logic and Higher-Order Vagueness'
    In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical, and Linguistic Perspectives, College Publications. pp. 37-40. 2011.
  •  9
    Reply to Libor Běhounek’s Comments on 'Fuzzy Logic and Higher-Order Vagueness'
    In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical, and Linguistic Perspectives, College Publications. pp. 29-32. 2011.
  •  164
    Fuzzy Logic and Higher-Order Vagueness
    In Petr Cintula, Chris Fermüller, Lluis Godo & Petr Hájek (eds.), Logical Models of Reasoning with Vague Information, . pp. 1--19. 2011.
    The major reason given in the philosophical literature for dissatisfaction with theories of vagueness based on fuzzy logic is that such theories give rise to a problem of higherorder vagueness or artificial precision. In this paper I first outline the problem and survey suggested solutions: fuzzy epistemicism; measuring truth on an ordinal scale; logic as modelling; fuzzy metalanguages; blurry sets; and fuzzy plurivaluationism. I then argue that in order to decide upon a solution, we need to und…Read more
  •  95
    If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is borderline hot, I will have some tendency to reach for a cup. Suppose that we take degrees of belief arising from uncertainty to…Read more
  •  379
    Orthodoxy has it that mereological composition can never be a vague matter, for if it were, then existence would sometimes be a vague matter too, and that's impossible. I accept that vague composition implies vague existence, but deny that either is impossible. In this paper I develop degree-theoretic versions of quantified modal logic and of mereology, and combine them in a framework that allows us to make clear sense of vague composition and vague existence, and the relationships between them
  •  95
    Semantic Regularity and the Liar Paradox
    The Monist 89 (1). 2006.
    My task here is the first one. I do present a consistent formal system and claim that it provides a perfect model of natural languages such as English, but this system involves no surprises. It is none other than the standard framework of classical logic and model theory. The real weight of the argument lies in the claim that the classical framework—without alteration or addition—contains the resources to model what happens when we say in English ‘This sentence is not true’.
  •  350
    Why Would Time Travelers Try to Kill Their Younger Selves?
    The Monist 88 (3): 388-395. 2005.
    In this note I raise a new problem for backwards time travel, and make some first suggestions as to how it might be solved. I call it the motivation problem. It is not a logical or a metaphysical problem, but a psychological one. It does not impact upon the possibility, or even the likelihood, of backwards time travel. Yet it is deeply puzzling, and we will have no idea what time travel would actually be like until we explore it. Thus, where other problems for backward time travel assume that we…Read more
  •  141
    Vagueness by numbers? No worries
    Mind 112 (446): 283-290. 2003.
    Rosanna Keefe (`Vagueness by Numbers' MIND 107 1998 565--79) argues that theories of vagueness based upon fuzzy logic and set theory rest on a confusion: once we have assigned a number to an object to represent (for example) its *height*, there is no distinct purpose left to be served by assigning a number to the object to represent its *degree of tallness*; she claims that ``any numbers assigned in an attempt to capture the vagueness of `tall' do no more than serve as another measure of h…Read more
  •  227
    Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..
  •  94
    Frege's judgement stroke
    Australasian Journal of Philosophy 78 (2). 2000.
    This paper brings to light a new puzzle for Frege interpretation, and offers a solution to that puzzle. The puzzle concerns Frege’s judgement-stroke (‘|’), and consists in a tension between three of Frege’s claims. First, Frege vehemently maintains that psychological considerations should have no place in logic. Second, Frege regards the judgementstroke—and the associated dissociation of assertoric force from content, of the act of judgement from the subject matter about which judgement is made—…Read more
  •  41
    The Problems of Backward Time Travel
    Endeavour 22 (4): 156--8. 1998.
    The so-called paradoxes of time travel have played a significant role in both the physics and philosophy literatures - but how much force do these alleged paradoxes really have?
  •  142
    Epiphenomenalism
    Routledge Encyclopedia of Philosophy. 1993.
    Epiphenomenalism is a theory concerning the relation between the mental and physical realms, regarded as radically different in nature. The theory holds that only physical states have causal power, and that mental states are completely dependent on them. The mental realm, for epiphenomenalists, is nothing more than a series of conscious states which signify the occurrence of states of the nervous system, but which play no causal role. For example, my feeling sleepy does not cause my yawning — ra…Read more
  •  633
    Bananas enough for time travel
    British Journal for the Philosophy of Science 48 (3): 363-389. 1997.
    This paper argues that the most famous objection to backward time travel can carry no weight. In its classic form, the objection is that backward time travel entails the occurrence of impossible things, such as auto-infanticide—and hence is itself impossible. David Lewis has rebutted the classic version of the objection: auto-infanticide is prevented by coincidences, such as time travellers slipping on banana peels as they attempt to murder their younger selves. I focus on Paul Horwich‘s more re…Read more
  •  148
    Vagueness and blurry sets
    Journal of Philosophical Logic 33 (2): 165-235. 2004.
    This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S₁ to the effect that 'Bob is bald' is x true, for x in [0, 1], there should be a further statement S₂ which tells us how true S₁ is, and so on - that is, it accommodates higher-order vagueness without resorting to the claim that the metalanguage in which the semanti…Read more
  •  157
    Vagueness as closeness
    Australasian Journal of Philosophy 83 (2). 2005.
    This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate 'F' is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then 'Fa' and 'Fb' are very close in respect of truth. The definition is extended to cover vaguene…Read more
  •  13
    Vagueness
    Dissertation, Princeton University. 2001.
    This dissertation is concerned with the problem of giving a correct account of the semantics of vague predicates such as '...is tall', '...is bald' and '...is near...'. ;In Chapter 1 I present a definition of vagueness that aims to capture, in a useful form, all our fundamental intuitions about the vagueness of predicates such as those mentioned above; such a definition is lacking in the literature. I also present an abstract characterisation of the Sorites paradox: one that is independent of th…Read more
  •  280
    Inconsistency in the A-Theory
    Philosophical Studies 156 (2). 2011.
    This paper presents a new argument against A-theories of time. A-theorists hold that there is an objective now (present moment) and an objective flow of time, the latter constituted by the movement of the objective now through time. A-theorists therefore want to draw different pictures of reality—showing the objective now in different positions—depending upon the time at which the picture is drawn. In this paper it is argued that the times at which the different pictures are drawn may be taken t…Read more
  •  135
    In this paper I present a new argument against vague identity — one that is more fundamental than existing arguments — and I also try to explain why we find the idea of vague identity puzzling, in a way that will dispel the puzzlement. In brief, my argument is this: to make clear sense of something, one must at least model it set-theoretically; but due to the special place of identity in set-theoretic models, any vague relation that one does model set-theoretically will not be identity, for real…Read more
  •  62
    Book Information Travels in Four Dimensions: The Enigmas of Space and Time. Travels in Four Dimensions: The Enigmas of Space and Time Robin Le Poidevin , Oxford : Clarendon Press , 2003 , xvii + 275 , £14.99 ( cloth ); £8.99 ( paper ) By Robin Le Poidevin. Clarendon Press. Oxford. Pp. xvii + 275. £14.99 (cloth:); £8.99 (paper:).
  •  23
    Comments on 'Inconstancy and Inconsistency’ by David Ripley
    In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical, and Linguistic Perspectives, College Publications. pp. 59-62. 2011.