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  1. Frege and the Logic of Sense and Reference.Kevin C. Klement - 2001 - 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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  • The Ways of Paradox and Other Essays.W. V. O. Quine - 1966 - Harvard University Press.
    A respected Harvard logician and philosopher gathers together twenty-nine writings dealing with the foundations of mathematics, Rudolf Carnap, lin-guistics, ...
  • Essays in Analysis.Bertrand Russell - 1973 - London: Allen & Unwin.
  • My Philosophical Development.Bertrand Russell - 1959 - London: Allen & Unwin.
    A survey such as this by one of the world's leading thinkers of his entire philosophical canon, is clearly as important as it is fascinating.
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  • The Ins and Outs of Frege's Way Out †Special Thanks to Kevin Klement, Ed Mares, Francesco Orilia, and Anonymous Referees for Helpful Comments on This Paper.Gregory Landini - 2006 - Philosophia Mathematica 14 (1):1-25.
    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, we see how Frege imagined (...)
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  • Prolegomenon To Any Future Neo‐logicist Set Theory: Abstraction And Indefinite Extensibility.Stewart Shapiro - 2003 - British Journal for the Philosophy of Science 54 (1):59-91.
    The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? (...)
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  • Mysticism and Logic and Other Essays.Bertrand Russell - 1917 - Barnes & Noble.
  • The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
  • Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
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  • 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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  • 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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  • Semantical Antinomies in the Logic of Sense and Denotation.C. Anthony Anderson - 1987 - Notre Dame Journal of Formal Logic 28 (1):99-114.
  • The Origins of the Propositional Functions Version of Russell's Paradox.Kevin Klement - 2004 - Russell: The Journal of Bertrand Russell Studies 24 (2).
    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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  • Paradox Without Basic Law V: A Problem with Frege’s Ontology.Adam Rieger - 2002 - Analysis 62 (4):327-330.
  • On Frege's Way Out.W. V. Quine - 1955 - Mind 64 (254):145-159.
  • 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 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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  • Russell's Paradox of the Totality of Propositions.Nino B. Cocchiarella - 2000 - Nordic Journal of Philosophical Logic 5 (1):25-37.
    Russell's "new contradiction" about "the totality of propositions" has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell's paradox of the totality of propositions was left unexplained, however. We reconstruct Russell's argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in these intensional logics.
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  • New Foundations for Mathematical Logic.W. V. Quine - 1937 - Journal of Symbolic Logic 2 (2):86-87.
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  • Problems Arising in the Formalization of Intensional Logic.John Myhill - 1958 - Logique Et Analyse 1 (1):78-83.
  • Rieger's Problem with Frege's Ontology.N. Denyer - 2003 - Analysis 63 (2):166-170.
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  • Logic, Logic and Logic.George Boolos - 1998 - Harvard University Press.
    This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...
  • Rieger's Problem with Frege's Ontology.Nicholas Denyer - 2003 - Analysis 63 (2):166–170.
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  • A Problem in Possible Worlds Semantics.David Kaplan - 1995 - In Walter Sinnott-Armstrong, Diana Raffman & Nicholas Asher (eds.), Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus. Cambridge University Press. pp. 41-52.
  • Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Dover Publications.
    Seminal work by great modern philosopher and mathematician focuses on certain issues of mathematical logic that Russell believed invalidated much traditional and contemporary philosophy. Topics include number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into the realm where mathematics and philosophy meet.
  • Collected Papers on Mathematics, Logic, and Philosophy.Gottlob Frege - 1991 - Wiley-Blackwell.
  • Autobiography.Bertrand Russell - 1975 - Routledge.
    Bertrand Russell remains one of the greatest philosophers and most complex and controversial figures of the twentieth century. Here, in this frank, humorous and decidedly charming autobiography, Russell offers readers the story of his life – introducing the people, events and influences that shaped the man he was to become. Originally published in three volumes in the late 1960s, _Autobiography_ by Bertrand Russell is a revealing recollection of a truly extraordinary life written with the vivid freshness and clarity that has (...)
     
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  • Philosophical and Mathematical Correspondence.Gottlob Frege, Gottfried Gabriel, Brian Mcguinness & Hans Kaal - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
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