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  1. Stephen Pollard (2011). Review of Matthew E. Moore (Ed.), New Essays on Peirce's Mathematical Philosophy. [REVIEW] Notre Dame Philosophical Reviews 2011 (2).
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  2. Stephen Pollard (2010). 'As If' Reasoning in Vaihinger and Pasch. Erkenntnis 73 (1):83 - 95.
    Hans Vaihinger tried to explain how mathematical theories can be useful without being true or even coherent, arguing that mathematicians employ a special kind of fictional or "as if" reasoning that reliably extracts truths from absurdities. Moritz Pasch insisted that Vaihinger was wrong about the incoherence of core mathematical theories, but right about the utility of fictional discourse in mathematics. This essay explores this area of agreement between Pasch and Vaihinger. Pasch's position raises questions about structuralist interpretations of mathematics.
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  3. Stephen Pollard (2007). Mathematical Determinacy and the Transferability of Aboutness. Synthese 159 (1):83 - 98.
    Competent speakers of natural languages can borrow reference from one another. You can arrange for your utterances of ‘Kirksville’ to refer to the same thing as my utterances of ‘Kirksville’. We can then talk about the same thing when we discuss Kirksville. In cases like this, you borrow “aboutness” from me by borrowing reference. Now suppose I wish to initiate a line of reasoning applicable to any prime number. I might signal my intention by saying, “Let p be any (...)
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  4. Stephen Pollard (2006). David Gruber, 1958-2005. Proceedings and Addresses of the American Philosophical Association 79 (5):125 -.
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  5. Stephen Pollard (2005). Some Mathematical Facts About Peirce's Game. Transactions of the Charles S. Peirce Society 41 (1):189 - 201.
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  6. Stephen Pollard (2005). The Expressive Unary Truth Functions of N -Valued Logic. Notre Dame Journal of Formal Logic 46 (1):93-105.
    The expressive truth functions of two-valued logic have all been identified. This paper begins the task of identifying the expressive truth functions of n-valued logic by characterizing the unary ones. These functions have distinctive algebraic, semantic, and closure-theoretic properties.
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  7. Stephen Pollard (2002). The Expressive Truth Conditions of Two-Valued Logic. Notre Dame Journal of Formal Logic 43 (4):221-230.
    In a finitary closure space, irreducible sets behave like two-valued models, with membership playing the role of satisfaction. If f is a function on such a space and the membership of in an irreducible set is determined by the presence or absence of the inputs in that set, then f is a kind of truth function. The existence of some of these truth functions is enough to guarantee that every irreducible set is maximally consistent. The closure space is then said (...)
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  8. Stephen Pollard (1999). Milne's Measure of Confirmation. Analysis 59 (4):335–338.
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  9. Stephen Pollard (1999). Book Review: Penelope Maddy. Naturalism in Mathematics. [REVIEW] Notre Dame Journal of Formal Logic 40 (2):293-306.
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  10. Stephen Pollard (1998). Homeomorphism and the Equivalence of Logical Systems. Notre Dame Journal of Formal Logic 39 (3):422-435.
    Say that a property is topological if and only if it is invariant under homeomorphism. Homeomorphism would be a successful criterion for the equivalence of logical systems only if every logically significant property of every logical system were topological. Alas, homeomorphisms are sometimes insensitive to distinctions that logicians value: properties such as functional completeness are not topological. So logics are not just devices for exploring closure topologies. One still wonders, though, how much of logic is topological. This essay examines some (...)
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  11. Stephen Pollard (1997). Who Needs Mereology? Philosophia Mathematica 5 (1):65-70.
    This note examines the mereological component of Geoffrey Hellman's most recent version of modal structuralism. There are plausible forms of agnosticism that benefit only a little from Hellman's mereological turn.
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  12. Stephen Pollard (1997). Book Review: Raymond M. Smullyan and Melvin Fitting. Set Theory and the Continuum Problem. [REVIEW] Notre Dame Journal of Formal Logic 38 (3):475-480.
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  13. Stephen Pollard (1996). Sets, Wholes, and Limited Pluralitiest. Philosophia Mathematica 4 (1):42-58.
    This essay defends the following two claims: (1) liraitation-of-size reasoning yields enough sets to meet the needs of most mathematicians; (2) set formation and mereological fusion share enough logical features to justify placing both in the genus composition (even when the components of a set are taken to be its members rather than its subsets).
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  14. Stephen Pollard & Norman M. Martin (1994). Contractions of Closure Systems. Notre Dame Journal of Formal Logic 35 (1):108-115.
    This essay shows that some recent work by George Weaver can be reformulated in an especially perspicuous way within the theory of closure systems. Closure theoretic generalizations of some theorems of Robert Goldblatt are presented. And, more generally, the relation between closure systems and the deducibility relations of Goldblatt is explored.
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  15. Stephen Pollard (1992). Choice Again. Philosophical Studies 66 (3):285 - 296.
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  16. Stephen Pollard (1990). A Strengthening of Scott's ZF¬. Notre Dame Journal of Formal Logic 31 (3):369-370.
     
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  17. Stephen Pollard (1990). The Reality of Numbers. Review of Metaphysics 43 (4):854-854.
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  18. Stephen Pollard (1990). A Strengthening of Scott's ${Rm ZF}^{Not=}$ Result. Notre Dame Journal of Formal Logic 31 (3):369-370.
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  19. Stephen Pollard & Robert Bates Graber (1989). Mathematical Naturalism: An Anthropological Perspective. Southern Journal of Philosophy 27 (3):427-441.
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  20. Stephen Pollard (1988). Philosophy of Mathematics and the New Conservation. Metaphilosophy 19 (1):1–10.
  21. Stephen Pollard (1988). Plural Quantification and the Axiom of Choice. Philosophical Studies 54 (3):393 - 397.
  22. Stephen Pollard (1988). Weyl on Sets and Abstraction. Philosophical Studies 53 (1):131 - 140.
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  23. Stephen Pollard (1987). A System of Logic Based on Conditional Proof. Teaching Philosophy 10 (2):129-134.
  24. Stephen Pollard (1987). What is Abstraction? Noûs 21 (2):233-240.
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  25. Stephen Pollard (1986). Transfinite Recursion in a Theory of Properties. Mathematical Logic Quarterly 32 (19‐24):307-314.
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  26. Stephen Pollard & Norman M. Martin (1986). Mathematics for Property Theorists. Philosophical Studies 49 (2):177 - 186.
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  27. Stephen Pollard (1985). A Peculiarity of the Empty Set. Southern Journal of Philosophy 23 (3):355-360.
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  28. Stephen Pollard (1985). Plural Quantification and the Iterative Concept of Set. Philosophy Research Archives 11:579-587.
    Arecent paper by George Boolos suggests that it is philosophically respectable to use monadic second order logic in one’s explication of the iterative concept of set. I shall here give a partial indication of the new range of theories of the iterative hierarchy which are thus madeavailable to philosophers of set theory.
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