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124Wittgensteinian : Looking at the World From the Viewpoint of Wittgenstein’s Philosophy (edited book)Springer Verlag. 2019.“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all sciences from the viewpoint of Wittgenstein’s philos…Read more
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7Russell's Theory of Definite Descriptions as a Paradigm for PhilosophyIn Dale Jacquette (ed.), A Companion to Philosophical Logic, Wiley-blackwell. 2002.This chapter contains sections titled: Russell's Paradigm The Description Theory and Logical Form Rigid Designators Russell on Logical Form.
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13The Paradoxes of Subjectivity and the Projective Structure of ConsciousnessIn Sofia Miguens & Gerhard Preyer (eds.), Consciousness and Subjectivity, Ontos Verlag. pp. 321-354. 2012.
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37A. Kenny, Frege, an introduction to the founder of modern analytic philosophy. London:Penguin, 1995. viii-h223pp. £7.99 T. Willamson, Vagueness. London:Routledge, 1994. xiii-f-325 pp. £35.00 TOM BU...
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9Wittgenstein Approached [review of Brian McGuinness, Approaches to Wittgenstein ]Russell: The Journal of Bertrand Russell Studies 25 (2): 165-167. 2005.In lieu of an abstract, here is a brief excerpt of the content:_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2502\REVIEWS.252 : 2006-02-27 11:52 eviews WITTGENSTEIN APPROACHED G L Philosophy / U. of Iowa Iowa City, , -@. Brian McGuinness. Approaches to Wittgenstein: Collected Papers. London and New York: Routledge, . Pp. xv, . .. his book is a joy to read. Brian McGuinness is among the foremost Tscholars of Wittgenstein’s life and…Read more
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47The Philosophy of Logical Atomism: A Centenary Reappraisal (edited book)Palgrave Macmillan. 2018.This book offers a comprehensive critical survey of issues of historical interpretation and evaluation in Bertrand Russell's 1918 logical atomism lectures and logical atomism itself. These lectures record the culmination of Russell's thought in response to discussions with Wittgenstein on the nature of judgement and philosophy of logic and with Moore and other philosophical realists about epistemology and ontological atomism, and to Whitehead and Russell’s novel extension of revolutionary ninete…Read more
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5Book reviews (review)History and Philosophy of Logic 17 (1-2): 85-119. 1996.A. Kenny, Frege, an introduction to the founder of modern analytic philosophy. London:Penguin, 1995. viii-h223pp. £7.99 T. Willamson, Vagueness. London:Routledge, 1994. xiii-f-325 pp. £35.00 TOM BU...
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48Stipulations Missing Axioms in Frege's Grundgesetze der ArithmetikHistory and Philosophy of Logic 43 (4): 347-382. 2022.Frege's Grundgesetze der Arithmetik offers a conception of cpLogic as the study of functions. Among functions are included those that are concepts, i.e. characteristic functions whose values are the logical objects that are the True/the False. What, in Frege's view, are the objects the True/the False? Frege's stroke functions are themselves concepts. His stipulation introducing his negation stroke mentions that it yields [...]. But curiously no accommodating axiom is given, and there is no such …Read more
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41Tractarian Logicism: Operations, Numbers, InductionReview of Symbolic Logic 14 (4): 973-1010. 2021.In his Tractatus, Wittgenstein maintained that arithmetic consists of equations arrived at by the practice of calculating outcomes of operations$\Omega ^{n}(\bar {\xi })$defined with the help of numeral exponents. Since$Num$(x) and quantification over numbers seem ill-formed, Ramsey wrote that the approach is faced with “insuperable difficulties.” This paper takes Wittgenstein to have assumed that his audience would have an understanding of the implicit general rules governing his operations. By…Read more
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177Solving the Conjunction Problem of Russell's Principles of MathematicsJournal for the History of Analytical Philosophy 8 (8). 2020.The quantification theory of propositions in Russell’s Principles of Mathematics has been the subject of an intensive study and in reconstruction has been found to be complete with respect to analogs of the truths of modern quantification theory. A difficulty arises in the reconstruction, however, because it presents universally quantified exportations of five of Russell’s axioms. This paper investigates whether a formal system can be found that is more faithful to Russell’s original prose. Russ…Read more
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12Showing in Wittgenstein’s ab-NotationIn A. C. Grayling, Shyam Wuppuluri, Christopher Norris, Nikolay Milkov, Oskari Kuusela, Danièle Moyal-Sharrock, Beth Savickey, Jonathan Beale, Duncan Pritchard, Annalisa Coliva, Jakub Mácha, David R. Cerbone, Paul Horwich, Michael Nedo, Gregory Landini, Pascal Zambito, Yoshihiro Maruyama, Chon Tejedor, Susan G. Sterrett, Carlo Penco, Susan Edwards-Mckie, Lars Hertzberg, Edward Witherspoon, Michel ter Hark, Paul F. Snowdon, Rupert Read, Nana Last, Ilse Somavilla & Freeman Dyson (eds.), Wittgensteinian : Looking at the World From the Viewpoint of Wittgenstein’s Philosophy, Springer Verlag. pp. 193-226. 2019.Perhaps it is not overly pedantic to say that one will find Wittgenstein’s Tractatus Logico-Philosophicus very difficult even if one first understands Russell’s philosophical logic. But the question remains as to whether the work is intended in alliance with Russell’s research program for a scientific method in philosophy or splits from that program. This paper endeavors to answer the question by revealing new evidence that Wittgenstein held his Doctrine of Showing in 1913 and that it was a dema…Read more
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13Showing in Wittgenstein’s ab-NotationIn Shyam Wuppuluri & Newton da Costa (eds.), Wittgensteinian : Looking at the World From the Viewpoint of Wittgenstein's Philosophy, Springer Verlag. pp. 193-226. 2019.Perhaps it is not overly pedantic to say that one will find Wittgenstein’s Tractatus Logico-Philosophicus very difficult even if one first understands Russell’s philosophical logic. But the question remains as to whether the work is intended in alliance with Russell’s research program for a scientific method in philosophy or splits from that program. This paper endeavors to answer the question by revealing new evidence that Wittgenstein held his Doctrine of Showing in 1913 and that it was a dema…Read more
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27Philip A. Ebert and Marcus Rossberg, eds.*Essays on Frege’s Basic Laws of Arithmetic (review)Philosophia Mathematica 28 (2): 264-276. 2020.EbertPhilip A and RossbergMarcus, eds.* * _ Essays on Frege’s Basic Laws of Arithmetic_. Oxford: Oxford University Press, 2019. Pp. xii + 673. ISBN: 978-0-19-871208-4 ; 978-0-19-102005-6, 978-0-19-178024-0. doi: 10.1093/oso/9780198712084.001.0001
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31Fitch and MaryAxiomathes 30 (2): 193-199. 2020.There is a rather famous “Fitch argument” that not everything that is true is knowable. There is a rather famous “Mary argument” that is often used to argue that reductive physicalism is false. This paper sets out the two side by side as the Fitch Knowability Paradox and the Mary Knowability Paradox. It is found that they have the same logical form and thus the question of validity can be evaluated with the same tools. Likening the two is useful, since it avoids the problem that since the logica…Read more
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6Whitehead Versus RussellIn Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition, Springer Verlag. 2016.This paper sets out some of the most striking intellectual differences between Whitehead and Russell pertaining to logic, mind and matter. It may seem surprising that there are such striking differences given their philosophical collaboration and very close personal relationship. The Whitehead’s regarded Russell as one of the family. But family members have rows.
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162On the Curious Calculi of Wittgenstein and Spencer BrownJournal for the History of Analytical Philosophy 6 (10). 2018.In his Tractatus, Wittgenstein sets out what he calls his N-operator notation which can be used to calculate whether an expression is a tautology. In his Laws of Form, George Spencer Brown offers what he calls a “primary algebra” for such calculation. Both systems are perplexing. But comparing two blurry images can reduce noise, producing a focus. This paper reveals that Spencer Brown independently rediscovered the quantifier-free part of the N-operator calculus. The comparison sheds a flood lig…Read more
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81Truth, Predication and a Family of Contingent ParadoxesJournal of Philosophical Logic 48 (1): 113-136. 2019.In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as te…Read more
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6Russell: LogicInternet Encyclopedia of Philosophy. 2018.Bertrand Russell: Logic For Russell, Aristotelian syllogistic inference does not do justice to the subject of logic. This is surely not surprising. It may well be something of a surprise, however, to learn that in Russell’s view neither Boolean algebra nor modern quantification theory do justice to the subject. For Russell, logic is a synthetic … Continue reading Russell: Logic →
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19Well-Ordering in the Russell–Newman ControversyRussell: The Journal of Bertrand Russell Studies 37 (2). 2017.There is a curious letter of 24 April 1928, reproduced in Russell’s Autobiography. It is from Russell to Max Newman. It is my thesis that there is a crucial “not” missing from the text and interpretations of the letter. This small point, if it is correct, has a very large impact for clarifying how Russell saw Newman’s challenge to his structural realism according to which all of our empirical knowledge in physics concerns structure alone.
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36Meinong and Russell: Some Lessons on QuantificationAxiomathes 27 (5): 455-474. 2017.This paper explores the thesis that de re quantification into propositional attitudes has been wrongly conceived. One must never bind an individual variable in the context of a propositional attitude. Such quantification fails to respect the quantificational scaffolding of discursive thinking. This is the lesson of the Meinong–Russell debate over whether there are objects of thought about which it is true to say they are not. Respecting it helps to see how to solve contingent Liar paradoxes of p…Read more
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55The Ins and Outs of Frege's Way OutPhilosophia Mathematica 14 (1): 1-25. 2006.Confronted with Russell's Paradox, Frege wrote an appendix to volume II of his _Grundgesetze der Arithmetik_. In it he offered a revision to Basic Law V, and proclaimed with confidence that the major theorems for arithmetic are recoverable. This paper shows that Frege's revised system has been seriously undermined by interpretations that transcribe his system into a predicate logic that is inattentive to important details of his concept-script. By examining the revised system as a concept-script…Read more
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55Logicism and the Problem of Infinity: The Number of Numbers: ArticlesPhilosophia Mathematica 19 (2): 167-212. 2011.Simple-type theory is widely regarded as inadequate to capture the metaphysics of mathematics. The problem, however, is not that some kinds of structure cannot be studied within simple-type theory. Even structures that violate simple-types are isomorphic to structures that can be studied in simple-type theory. In disputes over the logicist foundations of mathematics, the central issue concerns the problem that simple-type theory fails to assure an infinity of natural numbers as objects. This pap…Read more
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Meinong Reconstructed Versus Early Russell Reconstructed: A Study in the Formal Ontology of FictionDissertation, Indiana University. 1986.This dissertation is a study in the comparative formal ontology of fiction. We deal primarily with the alternative ontological frameworks of Alexius Meinong and early Bertrand Russell as each appears in or has influenced the development of intensional logics reconstructing their basic insights. Our aim is to develop an early Russellian account of fiction--an account that can handle the semantics of stories about any manner of "object" of thought, purple gnomes, "round-squares", paradoxical sets,…Read more
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36Whitehead'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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36Gregory Landini. Zermelo and Russell’s Paradox: Is There a Universal Set?: Correction NoticePhilosophia Mathematica 22 (1): 142-142. 2014.
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93Cocchiarella’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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48Russellian 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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49Putnam's model-theoretic argument, natural realism, and the standard conception of theoriesPhilosophical Papers 16 (3): 209-233. 1987.No abstract
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 |