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23Mereological Singularism and ParadoxErkenntnis 88 (1): 1-20. 2021.The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting thr…Read more
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22Review of P. Benacerraf and H. Putnam (eds.) Philosophy of Mathematics (review)Philosophy of Science 52 (3): 488-. 1985.
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21Vagueness and LogicIn Giuseppina Ronzitti (ed.), Vagueness: A Guide, Springer Verlag. pp. 55--81. 2011.
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18Review: Wilfried Sieg, Step by Recursive Step: Church's Analysis of Effective Calculability (review)Journal of Symbolic Logic 64 (1): 398-399. 1999.
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17The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question what is second-order logic? and examine various interpretations of the Lowenheim-Skolem theorem.
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1726 Potential Infinity, Paradox, and the Mind of God: Historical SurveyIn Mirosław Szatkowski (ed.), Ontology of Divinity, De Gruyter. pp. 531-560. 2024.
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17Philosophy of Mathematics: Structure and OntologyOxford University Press USA. 1997.Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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162010 winter meeting of the association for symbolic logicBulletin of Symbolic Logic 16 (3): 438-444. 2010.
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16Varieties of Continua: From Regions to Points and BackOxford University Press. 2017.Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or space-time.
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16Do Not Claim Too Much: Second-order Logic and First-order LogicPhilosophia Mathematica 6 (3): 42-64. 1998.The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.
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16The Lindenbaum construction and decidabilityNotre Dame Journal of Formal Logic 29 (2): 208-213. 1988.
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16Perspectives on the history of mathematical logic, edited by Thomas Drucker, Birkhäuser, Boston, Basel, and Berlin, 1991, xxiii + 195 pp. - John W. Dawson Jr. The reception of Gödel's incompleteness theorems. Pp. 84–100 (review)Journal of Symbolic Logic 57 (4): 1487-1489. 1992.
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16Link’s Revenge: A Case Study in Natural Language MereologyIn Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, De Gruyter. pp. 3-36. 2019.Most philosophers are familiar with the metaphysical puzzle of the statue and the clay. A sculptor begins with some clay, eventually sculpting a statue from it. Are the clay and the statue one and the same thing? Apparently not, since they have different properties. For example, the clay could survive being squashed, but the statue could not. The statue is recently formed, though the clay is not, etc. Godehart Link 1983’s highly influential analysis of the count/mass distinction recommends tha…Read more
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15Essay ReviewHistory and Philosophy of Logic 6 (1): 215-221. 1985.D. GABBAY and F. GUENTHNER (eds.), Handbook of philosophical logic. Volume 1: Elements of classical logic. Dordrecht, Boston, and Lancaster: D. Reidel Publishing Company, 1983. xiv + 497 pp. Dfl225/$98.00
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14Arithmetic Sinn and EffectivenessDialectica 38 (1): 3-16. 1984.SummaryAccording to Dummett's understanding of Frege, the sense of a denoting expression is a procedure for determining its denotation. The purpose of this article is to pursue this suggestion and develop a semi‐formal interpretation of Fregean sense for the special case of a first‐order language of arithmetic. In particular, we define the sense of each arithmetic expression to be a hypothetical process to determine the denoted number or truth value. The sense‐process is “hypothetical” in that t…Read more
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13II—Patrick Greenough: Contextualism about Vagueness and Higher‐order VaguenessAristotelian Society Supplementary Volume 79 (1): 167-190. 2005.To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order vagueness…Read more
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13Matftematical ObjectsIn Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy, Mathematical Association of America. pp. 157. 2008.
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12Review: Stephen C. Kleene, Origins of Recursive Function Theory; Martin Davis, Why Godel Didn't have Church's Thesis; Stephen C. Kleene, Reflections on Church's Thesis (review)Journal of Symbolic Logic 55 (1): 348-350. 1990.
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12II—Patrick Greenough: Contextualism about Vagueness and Higher‐order VaguenessAristotelian Society Supplementary Volume 79 (1): 167-190. 2005.To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order vagueness…Read more
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12Mereological Singularism and ParadoxErkenntnis 88 (1): 215-234. 2021.The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting thr…Read more
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11Wilfried Sieg. Step by recursive step: Church's analysis of effective calculability. The bulletin of symbolic logic, vol. 3 , pp. 154–180 (review)Journal of Symbolic Logic 64 (1): 398-399. 1999.
Columbus, Ohio, United States of America
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Areas of Interest
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |