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42Michael Potter Tom Ricketts, eds. The cambridge companion to Frege. Cambridge: Cambridge university press, 2010. Isbn 978-0-521-62479-4. Pp. XVII+639 (review)Philosophia Mathematica 20 (3): 372-387. 2012.
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57Gregory Landini. Zermelo and Russell’s Paradox: Is There a Universal Set?: Correction NoticePhilosophia Mathematica 22 (1): 142-142. 2014.
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38Whitehead's (Badly) Emended PrincipiaHistory and Philosophy of Logic 37 (2): 114-169. 2016.There are many wonderful puzzles concerning Principia Mathematica, but none are more striking than those arising from the crisis that befell Whitehead in November of 1910. Volume 1 appeared in December of 1910. Volume 2 on cardinal numbers and Russell's relation arithmetic might have appeared in 1911 but for Whitehead's having halted the printing. He discovered that inferences involving the typically ambiguous notation ‘Nc‘α’ for the cardinal number of α might generate fallacies. When the volume…Read more
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90Cocchiarella’s Formal Ontology and the Paradoxes of HyperintensionalityAxiomathes 19 (2): 115-142. 2009.This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.
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32
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48Putnam's model-theoretic argument, natural realism, and the standard conception of theoriesPhilosophical Papers 16 (3): 209-233. 1987.No abstract
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46Russellian Facts About the SlingshotAxiomathes 24 (4): 533-547. 2014.The so-called “Slingshot” argument purports to show that an ontology of facts is untenable. In this paper, we address a minimal slingshot restricted to an ontology of physical facts as truth-makers for empirical physical statements. Accepting that logical matters have no bearing on the physical facts that are truth-makers for empirical physical statements and that objects are themselves constituents of such facts, our minimal slingshot argument purportedly shows that any two physical statements …Read more
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13Pierre Joray (ed.), Contemporary perspectives on logicism and the foundation of mathematics. Switzerland: Centre de recherches semiologiques universite de neuchaˆtel, 2007. VI þ 208 pp. issn 1420-8520, no. 18 (review)History and Philosophy of Logic 29 (4): 383. 2008.
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31Logic as a Universal Science: Russell's Early Logicism and Its Philosophical ContextPhilosophical Quarterly 64 (255): 361-364. 2014.
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19Yablo’s Paradox and Russellian PropositionsRussell: The Journal of Bertrand Russell Studies 28 (2): 127-142. 2008.In lieu of an abstract, here is a brief excerpt of the content:January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd russell: the Journal of Bertrand Russell Studies n.s. 28 (winter 2008–09): 127–42 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 YABLO’S PARADOX AND RUSSELLIAN PROPOSITIONS Gregory Landini Philosophy / U. of Iowa Iowa City, ia 52242–1408, usa [email protected] Is self-reference necessary for the production of Liar parado…Read more
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94Frege’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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36Typos of Principia MathematicaHistory and Philosophy of Logic 34 (4). 2013.Principia Mathematic goes to great lengths to hide its order/type indices and to make it appear as if its incomplete symbols behave as if they are singular terms. But well-hidden as they are, we cannot understand the proofs in Principia unless we bring them into focus. When we do, some rather surprising results emerge ? which is the subject of this paper
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38Russell'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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29Book 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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31New Evidence concerning Russell's Substitutional Theory of ClassesRussell: The Journal of Bertrand Russell Studies 9 (1): 26. 1989.
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57How 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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89Wittgenstein's notes on logic – Michael Potter (review)Philosophical Quarterly 60 (240): 645-648. 2010.No Abstract
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7Clark’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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32The 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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38Quantification 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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10Reading 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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42RussellRoutledge. 2011.Landini discusses the second edition of Principia Mathematica, to show Russella (TM)s intellectual relationship with Wittgenstein and Ramsey.
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143Zermelo 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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94Frege'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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58The persistence of counterexample: Re-examining the debate over Leibniz lawNoûs 25 (1): 43-61. 1991.
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46Words 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.
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 |