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213Number determiners, numbers, and arithmeticPhilosophical Review 114 (2): 179-225. 2005.In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (2) Jupiter has green mo…Read more
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128Infinitesimal ChancesPhilosophers' Imprint 14. 2014.It is natural to think that questions in the metaphysics of chance are independent of the mathematical representation of chance in probability theory. After all, chance is a feature of events that comes in degrees and the mathematical representation of chance concerns these degrees but leaves the nature of chance open. The mathematical representation of chance could thus, un-controversially, be taken to be what it is commonly taken to be: a probability measure satisfying Kolmogorov’s axioms. The…Read more
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54Validity, paradox, and the ideal of deductive logicIn J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.I express my dissatisfaction with the common ways to treat the semantic paradoxes. Not only do they give rise to revenge paradoxes, they ignore the wisdom contained in the ordinary reaction to paradoxes. I instead propose an account that vindicates the ordinary reaction to paradox by putting the blame on us philosophers. It is the wrong conception of what a valid inference is, one that is central to “the ideal of deductive logic” that gives rise to the problem. The solution outlined gives us a n…Read more
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102Empty Names, Fiction, and the Puzzles of Non-Existence (edited book)CSLI Publications. 2000.Philosophers and theorists have long been puzzled by humans' ability to talk about things that do not exist, or to talk about things that they think exist but, in fact, do not. _Empty Names, Fiction, and the Puzzles of Non-Existence_ is a collection of 13 new works concerning the semantic and metaphysical issues arising from empty names, non-existence, and the nature of fiction. The contributors include some of the most important researchers working in these fields. Some of the papers develop an…Read more
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190Ambitious, yet modest, metaphysicsIn David Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology, Oxford University Press. pp. 260--289. 2009.There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns. Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes (historically) been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to the…Read more
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143Supervenience and Object-Dependant PropertiesJournal of Philosophy 102 (1): 5-32. 2005.I argue that the semantic thesis of direct reference and the meta- physical thesis of the supervenience of the non-physical on the physical cannot both be true. The argument first develops a necessary condition for supervenience, a so-called conditional locality requirement, which is then shown to be incompatible with some physical object having object dependent properties, which in turn is required for the thesis of direct reference to be true. We apply this argument to formulate a new argument …Read more
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153Review of "Philosophy of mathematics: An introduction to the world of proofs and pictures" by James Robert Brown (review)British Journal for the Philosophy of Science 52 (2): 413-416. 2001.
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157Innocent statements and their metaphysically loaded counterpartsPhilosophers' Imprint 7 1-33. 2007.One puzzling feature of talk about properties, propositions and natural numbers is that statements that are explicitly about them can be introduced apparently without change of truth conditions from statements that don't mention them at all. Thus it seems that the existence of numbers, properties and propositions can be established`from nothing'. This metaphysical puzzle is tied to a series of syntactic and semantic puzzles about the relationship between ordinary, metaphysically innocent stateme…Read more
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Areas of Specialization
Metaphysics |
Philosophy of Language |
Philosophy of Mathematics |