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Kevin C. Klement [51]Kevin Charles Klement [1]
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Kevin Klement
University of Massachusetts, Amherst
  1. Frege and the Logic of Sense and Reference.Kevin C. Klement - 2001 - New York: Routledge.
    This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional 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. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others (...)
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  2. Russell's logical atomism.Kevin C. Klement - 2019 - Stanford Encyclopedia of Philosophy 2005.
    A summary of Russell’s logical atomism, understood to include 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. The methodological view recommends a process of analysis, whereby one attempts to define or reconstruct more complex notions or vocabularies in terms of simpler ones. The origins of this theory, and its influence and reception are also (...)
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  3. The functions of Russell’s no class theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.
    Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...)
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  4. Higher-Order Metaphysics in Frege and Russell.Kevin C. Klement - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press. pp. 355-377.
    This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...)
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  5. Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's response adequate?Kevin C. Klement - 2001 - 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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  6. Putting form before function: Logical grammar in Frege, Russell, and Wittgenstein.Kevin C. Klement - 2004 - Philosophers' Imprint 4:1-47.
    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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  7. Russell, His Paradoxes, and Cantor's Theorem: Part II.Kevin C. Klement - 2010 - 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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  8. Neo-Logicism and Russell's Logicism.Kevin C. Klement - 2012 - Russell: The Journal of Bertrand Russell Studies 32 (2):127-159.
    Abstract:Certain advocates of the so-called “neo-logicist” 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 light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary meta-ontological (...)
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  9. Peano, Frege and Russell’s Logical Influences.Kevin C. Klement - forthcoming - Forthcoming.
    This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics as classes, functions, meaning (...)
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  10. Russell, His Paradoxes, and Cantor's Theorem: Part I.Kevin C. Klement - 2010 - 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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  11. Frege's Changing Conception of Number.Kevin C. Klement - 2012 - 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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  12. The number of senses.Kevin C. Klement - 2003 - 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 of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also (...)
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  13. The Origins of the Propositional Functions Version of Russell's Paradox.Kevin C. Klement - 2004 - Russell: The Journal of Bertrand Russell Studies 24 (2):101–132.
    Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does not appear in the (...)
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  14. When Is Genetic Reasoning Not Fallacious?Kevin C. Klement - 2002 - 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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  15. A Generic Russellian Elimination of Abstract Objects.Kevin C. Klement - 2017 - Philosophia Mathematica 25 (1):91-115.
    In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system (...)
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  16. The Constituents of the Propositions of Logic.Kevin C. Klement - 2015 - In Donovan Wishon & Bernard Linsky (eds.), Acquaintance, Knowledge, and Logic: New Essays on Bertrand Russell's The Problems of Philosophy. Stanford: CSLI Publications. pp. 189–229.
    In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but if, (...)
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  17. New Logic and the Seeds of Analytic Philosophy.Kevin C. Klement - 2019 - In John Shand (ed.), A Companion to Nineteenth‐Century Philosophy. Hoboken, NJ, USA: Wiley. pp. 454–479.
    Analytic philosophy has been perhaps the most successful philosophical movement of the twentieth century. While there is no one doctrine that defines it, one of the most salient features of analytic philosophy is its reliance on contemporary logic, the logic that had its origin in the works of George Boole and Gottlob Frege and others in the mid‐to‐late nineteenth century. Boolean algebra, the heart of Boole's contributions to logic, has also come to represent a cornerstone of modern computing. Frege had (...)
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  18. The senses of functions in the logic of sense and denotation.Kevin C. Klement - 2010 - Bulletin of Symbolic Logic 16 (2):153-188.
    This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...)
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  19. The paradoxes and Russell's theory of incomplete symbols.Kevin C. Klement - 2014 - 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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  20. Russell's Logicism.Kevin C. Klement - 2018 - In Russell Wahl (ed.), The Bloomsbury Companion to Bertrand Russell. London, UK: BloomsburyAcademic. pp. 151-178.
    Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of arithmetical (...)
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  21. Does Frege have too many thoughts? A Cantorian problem revisited.Kevin C. Klement - 2005 - Analysis 65 (1):45–49.
    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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  22. Russell-Myhill paradox.Kevin C. Klement - 2003 - 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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  23. Russell on "Disambiguating with the Grain".Kevin C. Klement - 2001 - Russell: The Journal of Bertrand Russell Studies 21 (2).
    Fregeans face the difficulty finding a notation for distinguishing statements about the sense or meaning of an expression as opposed to its reference or denotation. Famously, in "On Denoting", Russell rejected methods that begin with an expression designating its denotation, and then alter it with a "the meaning of" operator to designate the meaning. Such methods attempt an impossible "backward road" from denotation to meaning. Contemporary neo-Fregeans, however, have suggested that we can disambiguate _with_, rather than _against_, the grain, by (...)
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  24. Russell on Ontological Fundamentality and Existence.Kevin C. Klement - 2018 - In Landon D. C. Elkind & Gregory Landini (eds.), The Philosophy of Logical Atomism: A Centenary Reappraisal. New York, NY, USA: Palgrave Macmillan. pp. 155–79.
    Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the earlier period where (...)
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  25.  31
    Morality, Schmorality.Kevin C. Klement - 2023 - Personal Homepage.
    This is not a research project so much as a kind of “personal manifesto” on meta-ethics, or my personal take on how to best think about and improve morality. Since my take on “morality” is not necessarily meant to be compatible with current or past understandings, I am amenable to calling it “schmorality” instead. I argue that (sch)morality can be taken to be teleological by definition, but that the objects of comparison for what produces the best results value-wise need not (...)
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  26. The Russell–Dummett Correspondence on Frege and his Nachlaß.Kevin C. Klement - 2014 - The Bertrand Russell Society Bulletin 150:25–29.
    Russell corresponded with Sir Michael Dummett (1925–2011) between 1953 and 1963 while the latter was working on a book on Frege, eventually published as Frege: Philosophy of Language (1973). In their letters they discuss Russell’s correspondence with Frege, translating it into English, as well as Frege’s attempted solution to Russell’s paradox in the appendix to vol. 2 of his Grundgesetze der Arithmetik. After Dummett visited the University of Münster to view Frege’s Nachlaß, he sent reports back to Russell concerning both (...)
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  27. Grundgesetze and the Sense/Reference Distinction.Kevin C. Klement - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 142-166.
    Frege developed the theory of sense and reference while composing his Grundgesetze and considering its philosophical implications. The Grundgesetze is thus the most important test case for the application of this theory of meaning. I argue that evidence internal and external to the Grundgesetze suggests that he thought of senses as having a structure isomorphic to the Grundgesetze expressions that would be used to express them, which entails a theory about the identity conditions of senses that is relatively fine-grained, though (...)
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  28. Logical Form and the Development of Russell’s Logicism.Kevin C. Klement - 2022 - In F. Boccuni & A. Sereni (eds.), Origins and Varieties of Logicism. Routledge. pp. 147–166.
    Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not at all (...)
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  29. Three Unpublished Manuscripts from 1903: "Functions", "Proof that no function takes all values", "Meaning and Denotation".Kevin C. Klement - 2016 - Russell: The Journal of Bertrand Russel Studies 36 (1):5-44.
    I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor’s proof that there is no greatest cardinal number in the variation of (...)
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  30. Is Pacifism Irrational?Kevin C. Klement - 1999 - Peace Review 11 (1):65-70.
    In this paper, I counter arguments to the effect that pacifism must be irrational which cite hypothetical situations in which violence is necessary to prevent a far greater evil. I argue that for persons similar to myself, for whom such scenarios are extremely unlikely, promoting in oneself the disposition to avoid violence in any circumstances is more likely to lead to better results than not cultivating such a disposition just for the sake of such unlikely eventualities.
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  31.  99
    Introduction to G.E. Moore's Unpublished Review of The Principles of Mathematics.Kevin C. Klement - 2019 - Russell: The Journal of Bertrand Russell Studies 38:131-164.
    Several interesting themes emerge from G. E. Moore’s previously unpub­lished review of _The Principles of Mathematics_. These include a worry concerning whether mathematical notions are identical to purely logical ones, even if coextensive logical ones exist. Another involves a conception of infinity based on endless series neglected in the Principles but arguably involved in Zeno’s paradox of Achilles and the Tortoise. Moore also questions the scope of Russell’s notion of material implication, and other aspects of Russell’s claim that mathematics reduces (...)
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  32. Propositional logic.Kevin C. Klement - 2004 - 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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  33. Russell's Logicism through Kantian Spectacles [review of Anssi Korhonen, Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context ].Kevin C. Klement - 2014 - Russell: The Journal of Bertrand Russell Studies 34 (1):79-84.
    Review of Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context, by Anssi Korhonen (Palgrave Macmillan 2013).
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  34. Agency, Character and the Real Failure of Consequentialism.Kevin C. Klement - 2000 - Auslegung 23 (1):1-34.
    Certain consequentialists have responded to deontological worries regarding personal projects or options and agent-centered restrictions or constraints by pointing out that it is consistent with consequentialist principles that people develop within themselves, dispositions to act with such things in mind, even if doing so does not lead to the best consequences on every occasion. This paper argues that making this response requires shifting the focus of moral evaluation off of evaluation of individual actions and towards evaluation of whole character traits (...)
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  35. A New Century in the Life of a Paradox.Kevin C. Klement - 2008 - 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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  36. A Cantorian argument against Frege's and early Russell's theories of descriptions.Kevin C. Klement - 2009 - In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "On Denoting". Routledge. pp. 65-77.
    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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  37. Argument.Kevin C. Klement - 2003 - Internet Encyclopedia of Philosophy.
     
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  38. Deductive and inductive arguments.Kevin C. Klement - 2003 - Internet Encyclopedia of Philosophy.
    A simple summary of the difference between induction and deduction.
     
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  39. Gottlob Frege.Kevin C. Klement - 2001 - 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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  40. Russell's paradox.Kevin C. Klement - 2001 - 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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  41.  8
    The Oxford Handbook of the History of Analytic Philosophy (review).Kevin C. Klement - 2014 - Notre Dame Philosophical Reviews.
    Review of _The Oxford Handbook of the History of Analytic Philosophy_ edited by Michael Beaney.
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  42.  96
    The Cambridge Companion to Bertrand Russell (Review). [REVIEW]Kevin C. Klement - 2003 - Review of Modern Logic 10 (1-2):161-170.
    Review of The Cambridge Companion to Bertrand Russell.
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  43. Book Review: Gottlob Frege, Basic Laws of Arithmetic. [REVIEW]Kevin C. Klement - 2016 - Studia Logica 104 (1):175-180.
    Review of Basic Laws of Arithmetic, ed. and trans. by P. Ebert and M. Rossberg (Oxford 2013).
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  44. Jolen Galaugher, Russell’s Philosophy of Logical Analysis: 1897–1905. [REVIEW]Kevin C. Klement - 2015 - Journal for the History of Analytical Philosophy 3 (2).
    Review of Russell’s Philosophy of Logical Atomism 1897–1905, by Jolen Galaugher (Palgrave Macmillan 2013).
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  45.  9
    On the Genealogy of Universals: The Metaphysical Origins of Analytic Philosophy (review). [REVIEW]Kevin C. Klement - 2018 - Notre Dame Philosophical Reviews.
  46. A faithful companion. [REVIEW]Kevin C. Klement - 2004 - 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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  47.  31
    Reck, Erich H., ed. From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. [REVIEW]Kevin C. Klement - 2003 - Review of Metaphysics 57 (1):177-178.
  48.  27
    Review: Gregory Landini, Russell. London and New York, Routledge 2011. [REVIEW]Kevin C. Klement - 2012 - Journal for the History of Analytical Philosophy 1 (2).
    This essay reviews Gregory Landini's book Russell.
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  49.  38
    Review of Guido Imaguire, Bernard Linsky (eds.), On Denoting 1905-2005[REVIEW]Kevin C. Klement - 2006 - Notre Dame Philosophical Reviews 2006 (10).
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  50.  57
    Review of Richard L. Mendelsohn, The Philosophy of Gottlob Frege[REVIEW]Kevin C. Klement - 2005 - Notre Dame Philosophical Reviews 2005 (11).
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