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58Frege’s Cardinals as Concept-correlatesErkenntnis 65 (2): 207-243. 2006.In his "Grundgesetze", Frege hints that prior to his theory that cardinal numbers are objects he had an "almost completed" manuscript on cardinals. Taking this early theory to have been an account of cardinals as second-level functions, this paper works out the significance of the fact that Frege's cardinal numbers is a theory of concept-correlates. Frege held that, where n > 2, there is a one—one correlation between each n-level function and an n—1 level function, and a one—one correlation betw…Read more
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42Russell's substitutional theory of classes and relationsHistory and Philosophy of Logic 8 (2): 171-200. 1987.This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a versi…Read more
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117 Russell's Substitutional TheoryIn Nicholas Griffin (ed.), The Cambridge companion to Bertrand Russell, Cambridge University Press. pp. 241. 2003.
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30Book review: Francisco A. Rodriguez-Consuegra. The mathematical philosophy of Bertrand Russell: Origins and development (review)Notre Dame Journal of Formal Logic 33 (4): 604-610. 1992.
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37New Evidence concerning Russell's Substitutional Theory of ClassesRussell: The Journal of Bertrand Russell Studies 9 (1): 26. 1989.
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92Wittgenstein's notes on logic – Michael Potter (review)Philosophical Quarterly 60 (240): 645-648. 2010.No Abstract
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61How to Russell Another MeinongianGrazer Philosophische Studien 37 (1): 93-122. 1990.This article compares the theory of Meinongian objects proposed by Edward Zalta with a theory of fiction formulated within an early Russellian framework. The Russellian framework is the second-order intensional logic proposed by Nino B. Cocchiarelly as a reconstruction of the form of Logicism Russell was examining shortly after writing The Principles of Mathematics. A Russellian theory of denoting concepts is developed in this intensional logic and applied as a theory of the "objects' of fiction…Read more
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36The Collected Papers of Bertrand Russell, Volume 5: Toward Principia Mathematica, 1905–1908History and Philosophy of Logic 36 (2): 162-178. 2015.For logicians and metaphysicians curious about the evolution of Russell's logic from The Principles of Mathematics to Principia Mathematica, no volume of the Collected Papers of Bertr...
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8Clark’s Paradox of Castañeda’s Guises: A Brief MemoirIn Adriano Palma (ed.), Castañeda and His Guises: Essays on the Work of Hector-Neri Castañeda, De Gruyter. pp. 67-82. 2014.
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39Quantification Theory in *8 of Principia Mathematica and the Empty DomainHistory and Philosophy of Logic 26 (1): 47-59. 2005.The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russ…Read more
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12Reading Frege's Grundgesetze, by Richard Heck. Oxford: Oxford University Press, 2012, xvii + 296 pp. ISBN 978‐0‐19‐923370‐0 £ 35.00 (review)European Journal of Philosophy 22 (1): 159-172. 2014.
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43RussellRoutledge. 2011.Landini discusses the second edition of Principia Mathematica, to show Russella (TM)s intellectual relationship with Wittgenstein and Ramsey.
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153Zermelo and Russell's Paradox: Is There a Universal set?Philosophia Mathematica 21 (2): 180-199. 2013.Zermelo once wrote that he had anticipated Russell's contradiction of the set of all sets that are not members of themselves. Is this sufficient for having anticipated Russell's Paradox — the paradox that revealed the untenability of the logical notion of a set as an extension? This paper argues that it is not sufficient and offers criteria that are necessary and sufficient for having discovered Russell's Paradox. It is shown that there is ample evidence that Russell satisfied the criteria and t…Read more
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60The persistence of counterexample: Re-examining the debate over Leibniz lawNoûs 25 (1): 43-61. 1991.
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101Frege's Cardinals Do Not Always Obey Hume's PrincipleHistory and Philosophy of Logic 38 (2): 127-153. 2017.Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's ‘no-classes’ theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theo…Read more
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50Words Without Objects: Semantics, Ontology, and Logic for Non-SingularityHistory and Philosophy of Logic 30 (2): 204-208. 2009.HENRY LAYCOCK, Words Without Objects: Semantics, Ontology, and Logic for Non-Singularity. Oxford: Clarendon Press, 2006. xvi + 202pp. £35.00. ISBN 0‐19‐928171‐8. Gregory Landini, Department of Phil...
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34Russell's Separation of the Logical and Semantic ParadoxesRevue Internationale de Philosophie 3 257-294. 2004.
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80Decomposition and analysis in Frege’s GrundgesetzeHistory and Philosophy of Logic 17 (1-2): 121-139. 1996.Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositi…Read more
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41Review: D. Bostock. Russell’s Logical Atomism (review)Journal for the History of Analytical Philosophy 2 (1). 2013.This is review of D. David Bostock. Russell’s Logical Atomism
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Wittgenstein reads RussellIn Oskari Kuusela & Marie McGinn (eds.), The Oxford Handbook of Wittgenstein, Oxford University Press. 2011.
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44How to Russell Another MeinongianGrazer Philosophische Studien 37 (1): 93-122. 1990.This article compares the theory of Meinongian objects proposed by Edward Zalta with a theory of fiction formulated within an early Russellian framework. The Russellian framework is the second-order intensional logic proposed by Nino B. Cocchiarelly as a reconstruction of the form of Logicism Russell was examining shortly after writing The Principles of Mathematics. A Russellian theory of denoting concepts is developed in this intensional logic and applied as a theory of the "objects' of fiction…Read more
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96The definability of the set of natural numbers in the 1925 principia mathematicaJournal of Philosophical Logic 25 (6). 1996.In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Godel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionalit…Read more
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64Erik C. Banks, The Realistic Empiricism of Mach, James and Russell (review)Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2): 329-333. 2016.
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35Quantification Theory in *9 of Principia MathematicaHistory and Philosophy of Logic 21 (1): 57-77. 2000.This paper examines the quantification theory of *9 of Principia Mathematica. The focus of the discussion is not the philosophical role that section *9 plays in Principia's full ramified type-theory. Rather, the paper assesses the system of *9 as a quantificational theory for the ordinary predicate calculus. The quantifier-free part of the system of *9 is examined and some misunderstandings of it are corrected. A flaw in the system of *9 is discovered, but it is shown that with a minor repair th…Read more
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70Russell's hidden substitutional theoryOxford University Press. 1998.This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the …Read more
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58Erich H. Reck and Steve Awodey, trans. and ed., Frege's Lectures on Logic: Carnap's Student Notes, 1910–1914. Publications of the Archive of Scientific Philosophy, Hillman Library, University of Pittsburgh. LaSalle, Illinois: Open Court, 2004. Pp. xiv + 170. ISBN 0-8126-9546-1 (cloth), 0-8126-9553-4 (paper) (review)Philosophia Mathematica 13 (2): 225-227. 2005.
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51Russell and the Ontological ArgumentRussell: The Journal of Bertrand Russell Studies 29 (2): 101-128. 2009.It is well known that in _Principia Mathematica_ Russell offers a theory of definite descriptions and holds that ‘existence’ is not a property. It is less well known that in “On Denoting” he discusses the version of Anselm’s ontological argument for God formulated by Descartes, accepting the premiss “Existence is a perfection” and assessing the argument as valid but question-begging. This is different from his later comments in _A History of Western Philosophy_ which find the argument invalid. I…Read more
Areas of Specialization
Philosophy of Mind |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Areas of Interest
Philosophy of Mind |
Logic and Philosophy of Logic |
Philosophy of Mathematics |