Kevin Klement University of Massachusetts, Amherst
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  • Faculty, University of Massachusetts, Amherst
  • PhD, University of Iowa, 2000.

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  1. Kevin C. Klement (forthcoming). PM's Circumflex, Syntax and Philosophy of Types. In Bernard Linsky & Nicholas Griffin (eds.), Principia Mathematica at 100. Cambridge.
    Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...)
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  2. Kevin C. Klement (2014). The Paradoxes and Russell's Theory of Incomplete Symbols. Philosophical Studies 169 (2):183-207.
    Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...)
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  3. Kevin C. Klement (2012). Frege's Changing Conception of Number. Theoria 78 (2):146-167.
    I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...)
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  4. Kevin C. Klement (2012). Neo-Logicism and Russell’s Logicism. Russell 32 (127):159.
    Most advocates of the so-called “neologicist” movement in the philosophy of mathematics identify themselves as “Neo-Fregeans” (e.g., Hale and Wright): presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature, and when it is, often dismissed as not really logicism at all (in lights of its assumption of axioms of infinity, reducibiity and so on). In this paper I have three aims: firstly, to identify more clearly the primary metaontological (...)
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  5. Kevin C. Klement (2012). Kevin C. Klement. Theoria 78:146-167.
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  6. Kevin C. Klement (2012). Review: Gregory Landini, Russell. London and New York, Routledge 2011. [REVIEW] Journal for the History of Analytical Philosophy 1 (2).
    This essay reviews Gregory Landini's book Russell.
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  7. Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part I. Philosophy Compass 5 (1):16-28.
    In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...)
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  8. Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part II. Philosophy Compass 5 (1):29-41.
    Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, (...)
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  9. Kevin C. Klement (2010). The Functions of Russell's No Class Theory. Review of Symbolic Logic 3 (4):633-664.
    §1. Introduction. Although Whitehead and Russell’s Principia Mathematica (hereafter, PM ), published almost precisely a century ago, is widely heralded as a watershed moment in the history of mathematical logic, in many ways it is still not well understood. Complaints abound to the effect that the presentation is imprecise and obscure, especially with regard to the precise details of the ramified theory of types, and the philosophical explanation and motivation underlying it, all of which was primarily Russell’s responsibility. This has (...)
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  10. Kevin C. Klement (2009). A Cantorian Argument Against Frege's and Early Russell's Theories of Descriptions. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "on Denoting". Routledge.
    It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...)
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  11. Kevin C. Klement (2009). Russell's Logical Atomism. Stanford Encyclopedia of Philosophy.
    Bertrand Russell (1872-1970) described his philosophy as a kind of “logical atomism”, by which he meant to endorse both a metaphysical view and a certain methodology for doing philosophy. The metaphysical view amounts to the claim that the world consists of a plurality of independently existing things exhibiting qualities and standing in relations. According to logical atomism, all truths are ultimately dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality, or mutliple simple (...)
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  12. Kevin C. Klement (2008). A New Century in the Life of a Paradox. Review of Modern Logic 11 (2):7-29.
    Review essay covering Godehard Link, ed. One Hundred Years of Russell’s Paradox (de Gruyter 2004).
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  13. Kevin C. Klement (2006). Review of Guido Imaguire, Bernard Linsky (Eds.), On Denoting 1905-2005. [REVIEW] Notre Dame Philosophical Reviews 2006 (10).
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  14. Kevin C. Klement (2005). Does Frege Have Too Many Thoughts? A Cantorian Problem Revisited. Analysis 65 (285):45–49.
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  15. Kevin C. Klement (2005). Does Frege Have Too Many Thoughts? A Cantorian Problem Revisited. Analysis 65 (1):44-49.
    This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for (...)
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  16. Kevin C. Klement (2005). Review of Richard L. Mendelsohn, The Philosophy of Gottlob Frege. [REVIEW] Notre Dame Philosophical Reviews 2005 (11).
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  17. Kevin C. Klement (2005). Review Of: The Philosophy of Gottlob Frege, by Richard Mendelsohn. [REVIEW] Notre Dame Philosophical Reviews.
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  18. Kevin C. Klement (2004). A Faithful Companion. The Bertrand Russell Society Quarterly (120):25-41.
    We can at last release our breath: the long awaited Russell volume in the popular Cambridge Companion series has finally arrived. It contains fifteen chapters written by well known Russell scholars dealing with a wide array of Russelliana, along with a quite extensive introductory essay by the volume editor. It is not difficult to see what took so long. Russell’s corpus, even considering only his philosophical writings, outstrips in both breadth and volume almost all the other figures covered in the (...)
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  19. Kevin C. Klement (2004). Putting Form Before Function: Logical Grammar in Frege, Russell, and Wittgenstein. Philosophers' Imprint 4 (2):1-47.
    The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...)
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  20. Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.
    Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts (...)
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  21. Kevin C. Klement, Argument. Internet Encyclopedia of Philosophy.
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  22. Kevin C. Klement, Deductive and Inductive Arguments. Internet Encyclopedia of Philosophy.
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  23. Kevin C. Klement (2003). Russell's 1903 - 1905 Anticipation of the Lambda Calculus. History and Philosophy of Logic 24 (1):15-37.
    Philosophy Dept, Univ. of Massachusetts, 352 Bartlett Hall, 130 Hicks Way, Amherst, MA 01003, USA Received 22 July 2002 It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church’s ‘Lambda Calculus’ for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903 and 1905—surely unknown to Church—contain a more extensive anticipation of the essential details of (...)
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  24. Kevin C. Klement (2003). Reck, Erich H., Ed. From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Review of Metaphysics 57 (1):177-178.
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  25. Kevin C. Klement, Russell-Myhill Paradox. Internet Encyclopedia of Philosophy.
    The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox, is a contradiction that arises in the logical treatment of classes and "propositions", where "propositions" are understood as mind-independent and language-independent logical objects. If propositions are treated as objectively existing objects, then they can be members of classes. But propositions can also be about classes, including classes of propositions. Indeed, for each class of propositions, there is a proposition stating that all propositions in that class are true. (...)
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  26. Kevin C. Klement (2003). The Number of Senses. Erkenntnis 58 (3):303 - 323.
    Many philosophers still countenance senses or meanings in the broadly Fregean vein.However, it is difficult to posit the existence of senses without positing quite a lot ofthem, including at least one presenting every entity in existence. I discuss a number ofCantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and non-traditional understandings of senses, and to what extent they fare better in solving the problems, are also discussed. In the (...)
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  27. Kevin C. Klement (2002). Frege and the Logic of Sense and Reference. Routledge.
    This book aims to develop certain aspects of Gottlob Frege's theory of meaning, especially those relevant to intentional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege.
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  28. Kevin C. Klement (2002). When Is Genetic Reasoning Not Fallacious? Argumentation 16 (4):383-400.
    Attempts to evaluate a belief or argument on the basis of its cause or origin are usually condemned as committing the genetic fallacy. However, I sketch a number of cases in which causal or historical factors are logically relevant to evaluating a belief, including an interesting abductive form that reasons from the best explanation for the existence of a belief to its likely truth. Such arguments are also susceptible to refutation by genetic reasoning that may come very close to the (...)
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  29. Kevin C. Klement, Gottlob Frege. Internet Encyclopedia of Philosophy.
    Gottlob Frege (1848-1925) was a German logician, mathematician and philosopher who played a crucial role in the emergence of modern logic and analytic philosophy. Frege's logical works were revolutionary, and are often taken to represent the fundamental break between contemporary approaches and the older, Aristotelian tradition. He invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic. In (...)
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  30. Kevin C. Klement, Russell's Paradox. Internet Encyclopedia of Philosophy.
    Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (or (...)
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  31. Kevin C. Klement (2001). Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's Response Adequate? History and Philosophy of Logic 22 (1):13-28.
    In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...)
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  32. Kevin C. Klement, Early Russell on Types and Plurals.
    In 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before PoM even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...)
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  33. Kevin Klement, Frege and Russell on Logic and Language.
    Russell, and his German predecessor Gottlob Frege (1848-1925). Logicism is the position in the philosophy of mathematics that mathematical truth is a species of logical truth.
     
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