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Stephen Pollard [41]S. Pollard [5]Sidney Pollard [2]Steven R. Pollard [1]
Stephen Randall Pollard [1]
  1.  65
    Plural Quantification and the Axiom of Choice.Stephen Pollard - 1988 - Philosophical Studies 54 (3):393 - 397.
  2.  22
    Milne's Measure of Confirmation.Stephen Pollard - 1999 - Analysis 59 (4):335-338.
  3.  63
    Sets, Wholes, and Limited Pluralitiest.Stephen Pollard - 1996 - 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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  4.  58
    Milne's Measure of Confirmation.Stephen Pollard - 1999 - Analysis 59 (4):335–338.
  5.  60
    Mathematical Determinacy and the Transferability of Aboutness.Stephen Pollard - 2007 - 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 (...)
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  6.  45
    Plural Quantification and the Iterative Concept of Set.Stephen Pollard - 1985 - 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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  7.  50
    What is Abstraction?Stephen Pollard - 1987 - Noûs 21 (2):233-240.
  8.  8
    Plural Quantification and the Iterative Concept of Set.Stephen Pollard - 1985 - 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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  9.  24
    Reuben Hersh. Experiencing Mathematics: What Do We Do, When We Do Mathematics?. Providence, Rhode Island: American Mathematical Society, 2014. ISBN 978-0-8218-9420-0. Pp. Xvii + 291. [REVIEW]Stephen Pollard - 2014 - Philosophia Mathematica 22 (2):271-274.
  10. Closure Spaces and Logic.N. M. Martin & S. Pollard - 1999 - Studia Logica 63 (1):136-138.
     
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  11. More Axioms for the Set-Theoretic Hierarchy.S. Pollard - 1988 - Logique Et Analyse 31 (21):85-88.
     
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  12.  7
    The Expressive Truth Conditions of Two-Valued Logic.Stephen Pollard - 2002 - 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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  13.  41
    Mathematics for Property Theorists.Stephen Pollard & Norman M. Martin - 1986 - Philosophical Studies 49 (2):177 - 186.
  14.  61
    Carlo Cellucci. Rethinking Knowledge: The Heuristic View.Stephen Pollard - 2017 - Philosophia Mathematica 25 (3):413-418.
    CarloCellucci. Rethinking Knowledge: The Heuristic View. Cham, Switzerland: Springer International Publishing, 2017. ISBN 978-3-319-53236-3, 978-3-319-53237-0. Pp. xx + 428††.
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  15.  48
    Mathematical Naturalism: An Anthropological Perspective.Stephen Pollard & Robert Bates Graber - 1989 - Southern Journal of Philosophy 27 (3):427-441.
  16.  19
    Logic in the Land of Make-Believe.Stephen Pollard - forthcoming - Logic and Logical Philosophy:1.
    Philosophers call it “contagion” when pretense influences belief, behavior, perception, or emotion. This pejorative terminology is justified in some cases: fantasy and imagination can exercise a pathological influence. This essay, however, reviews some logical techniques that allow pretense to govern belief in a rational and beneficial way. Philosophers might want similar techniques in their tool-kits when they explore interactions between belief and pretense.
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  17.  51
    Dianoia Left and Right.S. Pollard - 2013 - Philosophia Mathematica 21 (3):309-322.
    In Plato's Phaedrus, Socrates offers two speeches, the first portraying madness as mere disease, the second celebrating madness as divine inspiration. Each speech is correct, says Socrates, though neither is complete. The two kinds of madness are like the left and right sides of a living body: no account that focuses on just one half can be adequate. In a recent paper, Hugh Benson gives a left-handed speech about a psychic condition endemic among mathematicians: dianoia. Benson acknowledges that his account (...)
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  18.  24
    Ethical Guidance From Literature and Mathematics.Stephen Pollard - 2017 - Journal of Speculative Philosophy 31 (4):517-537.
    That mathematics makes for poor literature is a conclusion as uninteresting as it is inevitable—inevitable because were mathematical prose to score high on a scale of literary value, this result would do more to discredit the scale than glorify the prose. It may, however, help us better understand our cultural landscape if, without attempting a literary appraisal of mathematics or a mathematical appraisal of literature, we search for some community of interest between the formal sciences and the literary arts. This (...)
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  19. Identity criteria.S. Pollard - 1986 - Logique Et Analyse 29 (15):373.
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  20. The European Economy Between the Wars. By Charles H. Feinstein, Peter Temin, and Gianni Toniolo.S. Pollard - 1998 - The European Legacy 3:129-129.
     
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  21.  60
    ‘As If’ Reasoning in Vaihinger and Pasch.Stephen Pollard - 2010 - 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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  22.  33
    A System of Logic Based on Conditional Proof.Stephen Pollard - 1987 - Teaching Philosophy 10 (2):129-134.
  23.  44
    Mathematics and the Good Life.Stephen Pollard - 2013 - Philosophia Mathematica 21 (1):93-109.
    We mathematical animals should be grateful that mathematics is instrumentally useful. We should not, however, forget its other contributions to human happiness. Bertrand Russell and John Dewey offer timely reminders that provide insight into the role of non-mathematicians in the evaluation of mathematics.
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  24.  8
    Contractions of Closure Systems.Stephen Pollard & Norman M. Martin - 1994 - 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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  25. Social and Moral Development From the Perspective of Psychosocial Theory.W. Kurtines, Ellen Mayock, Steven R. Pollard, Teresita Lanza & Gustavo Carlo - 1991 - In William M. Kurtines & Jacob L. Gewirtz (eds.), Handbook of Moral Behavior and Development. L. Erlbaum. pp. 303-333.
     
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  26.  45
    Book Review: Raymond M. Smullyan and Melvin Fitting. Set Theory and the Continuum Problem. [REVIEW]Stephen Pollard - 1997 - Notre Dame Journal of Formal Logic 38 (3):475-480.
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  27.  19
    Transfinite Recursion in a Theory of Properties.Stephen Pollard - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (19-24):307-314.
  28.  30
    Some Mathematical Facts About Peirce's Game.Stephen Pollard - 2005 - Transactions of the Charles S. Peirce Society 41 (1):189 - 201.
  29.  31
    Mathematical Naturalism: An Anthropological Perspective.Stephen Pollard & Robert Bates Graber - 1989 - Southern Journal of Philosophy 27 (3):427-441.
  30.  31
    Review of Matthew E. Moore (Ed.), New Essays on Peirce's Mathematical Philosophy[REVIEW]Stephen Pollard - 2011 - Notre Dame Philosophical Reviews 2011 (2).
  31.  26
    The Reality of Numbers: A Physicalist's Philosophy of Mathematics.Stephen Pollard - 1990 - Review of Metaphysics 43 (4):854-854.
    This book is about universals. "Mathematics," we learn, "is the theory of universals". Natural numbers turn out to be universals, as do real numbers, complex numbers, and sets. It is natural, therefore, that the reader demand some evidence that universals abound sufficiently to supply models of canonical mathematical theories. The author devotes nearly a third of his book to one potential source of such evidence: the Truthmaker axiom. In the case of some propositions P, Truthmaker entails that if P is (...)
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  32.  27
    A Peculiarity of the Empty Set.Stephen Pollard - 1985 - Southern Journal of Philosophy 23 (3):355-360.
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  33.  25
    Book Review: Penelope Maddy. Naturalism in Mathematics. [REVIEW]Stephen Pollard - 1999 - Notre Dame Journal of Formal Logic 40 (2):293-306.
  34.  24
    Philosophy of Mathematics and the New Conservation.Stephen Pollard - 1988 - Metaphilosophy 19 (1):1–10.
  35.  6
    Expressive Three-Valued Truth Functions.Stephen Pollard - 2006 - Australasian Journal of Logic 4:226-245.
    The expressive truth functions of two-valued logic have all been characterized, as have the expressive unary truth functions of finitely-many-valued logic. This paper introduces some techniques for identifying expressive functions in three-valued logics.
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  36.  10
    ‘As If’ Reasoning in Vaihinger and Pasch.Stephen Pollard - 2010 - 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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  37.  12
    Transfinite Recursion in a Theory of Properties.Stephen Pollard - 1986 - Mathematical Logic Quarterly 32 (19‐24):307-314.
  38.  63
    Who Needs Mereology?Stephen Pollard - 1997 - 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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  39.  6
    Philosophy of Mathematics and the New Conservation.Stephen Pollard - 1988 - Metaphilosophy 19 (1):1-10.
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  40.  12
    David Gruber, 1958-2005.Stephen Pollard - 2006 - Proceedings and Addresses of the American Philosophical Association 79 (5):125 -.
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  41.  12
    A Strengthening of Scott's ${\rm ZF}^{\not=}$ Result.Stephen Pollard - 1990 - Notre Dame Journal of Formal Logic 31 (3):369-370.
  42.  5
    A Stregthening of Scott's ZFØ Result.Stephen Pollard - 1990 - Notre Dame Journal of Formal Logic 31:369-370.
  43.  13
    The Expressive Unary Truth Functions of N -Valued Logic.Stephen Pollard - 2005 - 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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  44.  4
    A Peculiarity of The Empty Set.Stephen Pollard - 1985 - Southern Journal of Philosophy 23 (3):355-360.
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  45.  29
    Weyl on Sets and Abstraction.Stephen Pollard - 1988 - Philosophical Studies 53 (1):131 - 140.
  46.  28
    Choice Again.Stephen Pollard - 1992 - Philosophical Studies 66 (3):285 - 296.
  47.  10
    Homeomorphism and the Equivalence of Logical Systems.Stephen Pollard - 1998 - 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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