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  1. Timothy Bays, Multi-Cardinal Phenomena in Stable Theories.
    In this dissertation we study two-cardinal phenomena—both of the admitting cardinals variety and of the Chang’s Conjecture variety—under the assumption that all our models have stable theories. All our results involve two, relatively widely accepted generalizations of the traditional definitions in this area. First, we allow the relevant subsets of our models to be picked out by (perhaps infinitary) partial types; second we consider δ-cardinal problems as well as two-cardinal problems.
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  2. Timothy Bays, Reflections on Skolem's Paradox.
    The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these two theorems induce a puzzle known as Skolem's Paradox: the very axioms of (first-order) set theory which prove the existence of uncountable sets can themselves be satisfied by a merely countable model.
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  3. Timothy Bays (2009). Beth's Theorem and Deflationism. Mind 118 (472):1061-1073.
    In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge this (...)
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  4. Timothy Bays (2009). Erratum To: More on Putnam's Models: A Reply to Bellotti. [REVIEW] Erkenntnis 70 (2):283-283.
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  5. Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
    Skolem's Paradox involves a seeming conflict between two theorems from classical logic. The Löwenheim Skolem theorem says that if a first order theory has infinite models, then it has models whose domains are only countable. Cantor's theorem says that some sets are uncountable. Skolem's Paradox arises when we notice that the basic principles of Cantorian set theory—i.e., the very principles used to prove Cantor's theorem on the existence of uncountable sets—can themselves be formulated as a collection of first order sentences. (...)
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  6. Timothy Bays (2008). Two Arguments Against Realism. Philosophical Quarterly 58 (231):193–213.
    I present two generalizations of Putnam's model-theoretic argument against realism. The first replaces Putnam's model theory with some new, and substantially simpler, model theory, while the second replaces Putnam's model theory with some more accessible results from astronomy. By design, both of these new arguments fail. But the similarities between these new arguments and Putnam's original arguments illuminate the latter's overall structure, and the flaws in these new arguments highlight the corresponding flaws in Putnam's arguments.
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  7. Timothy Bays (2007). More on Putnam's Models: A Reply to Belloti. [REVIEW] Erkenntnis 67 (1):119--35.
    In an earlier paper, I claimed that one version of Putnam's model-theoretic argument against realism turned on a subtle, but philosophically significant, mathematical mistake. Recently, Luca Bellotti has criticized my argument for this claim. This paper responds to Bellotti's criticisms.
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  8. Timothy Bays (2007). The Problem with Charlie: Some Remarks on Putnam, Lewis, and Williams. Philosophical Review 116 (3):401 - 425.
    In his new paper, “Eligibility and Inscrutability,” J. R. G. Williams presents a surprising new challenge to David Lewis’ theory of interpretation. Although Williams frames this challenge primarily as a response to Lewis’ criticisms of Putnam’s model-theoretic argument, the challenge itself goes to the heart of Lewis’ own account of interpretation. Further, and leaving Lewis’ project aside for a moment, Williams’ argument highlights some important—and some fairly general—points concerning the relationship between model theory and semantic determinacy.
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  9. Timothy Bays (2006). Review of John Burgess, Fixing Frege. [REVIEW] Notre Dame Philosophical Reviews 2006 (6).
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  10. Timothy Bays (2006). The Mathematics of Skolem's Paradox. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 615--648.
    Over the years, Skolem’s Paradox has generated a fairly steady stream of philosophical discussion; nonetheless, the overwhelming consensus among philosophers and logicians is that the paradox doesn’t constitute a mathematical problem (i.e., it doesn’t constitute a real contradiction). Further, there’s general agreement as to why the paradox doesn’t constitute a mathematical problem. By looking at the way firstorder structures interpret quantifiers—and, in particular, by looking at how this interpretation changes as we move from structure to structure—we can give a technically (...)
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  11. Timothy Bays (2005). Review of Michael Potter, Set Theory and its Philosophy: A Critical Introduction. [REVIEW] Notre Dame Philosophical Reviews 2005 (3).
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  12. Jonathan Bain, Timothy Bays, Katherine A. Brading, Stephen G. Brush, Murray Clarke, Sharyn Clough, Jonathan Cohen, Giancarlo Ghirardi, Brendan S. Gillon & Robert G. Hudson (2004). First Page Preview. International Studies in the Philosophy of Science 18 (2-3).
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  13. Timothy Bays (2004). Comments and Criticism. Journal of Philosophy 101 (4):197-210.
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  14. Timothy Bays (2004). On Floyd and Putnam on Wittgenstein on Gödel. Journal of Philosophy 101 (4):197 - 210.
    odel’s theorem than he has often been credited with. Substantively, they find in Wittgenstein’s remarks “a philosophical claim of great interest,” and they argue that, when this claim is properly assessed, it helps to vindicate some of Wittgenstein’s broader views on G¨.
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  15. Timothy Bays (2004). Review of David Corfield, Towards a Philosophy of Real Mathematics. [REVIEW] Notre Dame Philosophical Reviews 2004 (1).
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  16. Timothy Bays (2003). Hudson on Receptacles. Australasian Journal of Philosophy 81 (4):569 – 572.
    This note concerns a recent paper by Hud Hudson on the nature of 'receptacles'. It simplifies the mathematics in Hudson's paper, and it eliminates almost all of the topology in Hudson's arguments.
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  17. Timothy Bays (2001). On Putnam and His Models. Journal of Philosophy 98 (7):331-350.
    It is not my claim that the ‘L¨ owenheim-Skolem paradox’ is an antinomy in formal logic; but I shall argue that it is an antinomy, or something close to it, in philosophy of language. Moreover, I shall argue that the resolution of the antinomy—the only resolution that I myself can see as making sense—has profound implications for the great metaphysical dispute about realism which has always been the central dispute in the philosophy of language.
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  18. Timothy Bays (2001). On Tarski on Models. Journal of Symbolic Logic 66 (4):1701-1726.
    This paper concerns Tarski’s use of the term “model” in his 1936 paper “On the Concept of Logical Consequence.” Against several of Tarski’s recent defenders, I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski’s detractors, I argue that this non-standard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski’s ω-rule example.
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  19. Timothy Bays (2001). Partitioning Subsets of Stable Models. Journal of Symbolic Logic 66 (4):1899-1908.
    This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B |<κ(T ) pieces, Ai | i < |B |<κ(T ) , such that for each Ai there is a Bi ⊆ B where |Bi| < κ(T ) and Ai..
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  20. Timothy Bays (2000). The Fruits of Logicism. Notre Dame Journal of Formal Logic 41 (4):415-421.
    You’ll be pleased to know that I don’t intend to use these remarks to comment on all of the papers presented at this conference. I won’t try to show that one paper was right about this topic, that another was wrong was about that topic, or that several of our conference participants were talking past one another. Nor will I try to adjudicate any of the discussions which took place in between our sessions. Instead, I’ll use these remarks to make (...)
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  21. Timothy Bays (1998). Some Two-Cardinal Results for o-Minimal Theories. Journal of Symbolic Logic 63 (2):543-548.
    We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ , λ ). We also prove that every “reasonable” variant of Chang’s Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the δ-cardinal case for arbitrary ordinals δ.
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