Results for 'Russell's Paradox'

1000+ found
Order:
See also
  1. A Neglected Resolution of Russell’s Paradox of Propositions.Gabriel Uzquiano - 2015 - Review of Symbolic Logic 8 (2):328-344.
    Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  2. Russell's Paradox and Some Others.William C. Kneale - 1971 - British Journal for the Philosophy of Science 22 (4):321-338.
    Though the phrase 'x is true of x' is well formed grammatically, it does not express any predicate in the logical sense, because it does not satisfy the principle of reduction for statements containing 'x is true of'. recognition of this allows for solution of russell's paradox without his restrictive theory of types.
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  3. 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  4.  71
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  5. From Russell's Paradox to the Theory of Judgement: Wittgenstein and Russell on the Unity of the Proposition.Graham Stevens - 2004 - Theoria 70 (1):28-61.
  6.  33
    Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik.Kai F. Wehmeier - 2004 - In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter.
    We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  7.  86
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  89
    Lesniewski and Russell's Paradox: Some Problems.Rafal Urbaniak - 2008 - History and Philosophy of Logic 29 (2):115-146.
    Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9.  71
    Russell's Paradox and Complex Properties.Reinhardt Grossmann - 1972 - Noûs 6 (2):153-164.
    The author argues that the primary lesson of the so-Called logical and semantical paradoxes is that certain entities do not exist, Entities of which we mistakenly but firmly believe that they must exist. In particular, Russell's paradox teaches us that there is no such thing as the property which every property has if and only if it does not have itself. Why should anyone think that such a property must exist and, Hence, Conceive of russell's argument as (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10. Zermelo and Russell's Paradox: Is There a Universal Set?G. Landini - 2013 - Philosophia Mathematica 21 (2):180-199.
    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 (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11.  30
    A Contingent Russell's Paradox.Francesco Orilia - 1996 - Notre Dame Journal of Formal Logic 37 (1):105-111.
    It is shown that two formally consistent type-free second-order systems, due to Cocchiarella, and based on the notion of homogeneous stratification, are subject to a contingent version of Russell's paradox.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  12. Modal Meinongianism, Russell’s Paradox, and the Language/Metalanguage Distinction.Maciej Sendłak - 2013 - Polish Journal of Philosophy (2):63-78.
    The subject of my article is the principle of characterization – the most controversial principle of Meinong’s Theory of Objects. The aim of this text is twofold. First of all, I would like to show that Russell’s well-known objection to Meinong’s Theory of Objects can be reformulated against a new modal interpretation of Meinongianism that is presented mostly by Graham Priest. Secondly, I would like to propose a strategy which gives uncontroversial restriction to the principle of characterization and which allows (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  13.  49
    Russell's Paradox Re-Examined.Arnold Cusmariu - 1979 - Erkenntnis 14 (3):365-370.
    I attempt to rescue Frege's naive conception of a set according to which there is a set for every property by redefining the technical concept of degree of an open sentence. Instead of making degree a function of the number of free variables, I make it a function of free variable occurrences. What Russell proved, then, is that there is not a relation-in-extension for every relation-in-intension. In a brief paper it is not possible to discuss how redefining the function-argument correlation (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  14.  51
    One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy.Godehard Link (ed.) - 2004 - De Gruyter.
    The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated ...
    Direct download  
     
    Export citation  
     
    Bookmark   6 citations  
  15.  14
    Russell's Paradox [Review of Alejandro Garciadiego, Bertrand Russell and the Origins of the Set-Theoretic `Paradoxes'].Volker Peckhaus - 1997 - Russell: The Journal of Bertrand Russell Studies 17 (2).
  16.  35
    The Reception of Russell’s Paradox in Early Phenomenology and the School of Brentano: The Case of Husserl’s Manuscript A I 35α.Carlo Ierna - 2016 - In Guillermo E. Rosado Haddock (ed.), Husserl and Analytic Philosophy. De Gruyter. pp. 119-142.
    Edmund Husserl’s engagement with Bertrand Russell’s paradox stands in a continuum of reciprocal reception and discussions about impossible objects in the School of Brentano. Against this broader context, we will focus on Husserl’s discussion of Russell’s paradox in his manuscript A I 35α from 1912. This highly interesting and revealing manuscript has unfortunately remained unpublished, which probably explains the scant attention it has received. I will examine Husserl’s approach in A I 35α by relating it to earlier discussions (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  11
    The Humble Origins of Russell's Paradox.J. Alberto Coffa - 1979 - Russell: The Journal of Bertrand Russell Studies 33:31.
  18. The Barber, Russell's Paradox, Catch-22, God, Contradiction, and More.Laurence Goldstein - 2004 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press. pp. 295--313.
    outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  19.  66
    Ontology and Grammar: I. Russell's Paradox and the General Theory of Properties in Natural Language.Hector-Neri Castañeda - 1976 - Theoria 42 (1-3):44-92.
  20.  46
    A Note on Russell's Paradox in Locally Cartesian Closed Categories.Andrew M. Pitts & Paul Taylor - 1989 - Studia Logica 48 (3):377 - 387.
    Working in the fragment of Martin-Löfs extensional type theory [12] which has products (but not sums) of dependent types, we consider two additional assumptions: firstly, that there are (strong) equality types; and secondly, that there is a type which is universal in the sense that terms of that type name all types, up to isomorphism. For such a type theory, we give a version of Russell's paradox showing that each type possesses a closed term and (hence) that all (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  21.  9
    The Humble Origins of Russell's Paradox.J. Alberto Coffa - 1979 - Russell: The Journal of Bertrand Russell Studies:31.
  22. One Hundred Years of Russell's Paradox. Mathematics, Logic.Godehard Link - 2004 - Philosophy 6.
     
    Export citation  
     
    Bookmark   5 citations  
  23.  25
    The Roots of Russell's Paradox.Gregory H. Moore - 1988 - Russell: The Journal of Bertrand Russell Studies 8 (1):46.
  24.  13
    Russell’s Paradox and Free Zig Zag Solutions.Ludovica Conti - forthcoming - Foundations of Science:1-19.
    I present the traditional debate about the so called explanation of Russell’s paradox and propose a new way to solve the contradiction that arises in Frege’s system. I briefly examine two alternative explanatory proposals—the Predicativist explanation and the Cantorian one—presupposed by almost all the proposed solutions of Russell’s Paradox. From the discussion about these proposals a controversial conclusion emerges. Then, I examine some particular zig zag solutions and I propose a third explanation, presupposed by them, in which I (...)
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  25. From Russell's Paradox To.Harvey M. Friedman - unknown
    Russell’s way out of his paradox via the impredicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.
     
    Export citation  
     
    Bookmark  
  26.  13
    Is Russell's Paradox Genuine?James Moulder - 1974 - Philosophy 49 (189):295 - 302.
    Copi, Quine and van Heijenoort have each claimed that there are two fundamentally different kinds of logical paradox; namely, genuine paradoxes like Russell's and pseudo-paradoxes like the Barber of Seville. I want to contest this claim and will present my case in three stages. Firstly, I will characterize the logical paradoxes; state standard versions of three of them; and demonstrate that a symbolic formulation of each leads to a formal contradiction. Secondly, I will discuss the reasons Copi, Quine (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  27. 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  28. 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  29.  36
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  30.  33
    Why Russell's Paradox Won't Go Away.Francis Moorcroft - 1993 - Philosophy 68 (263):99 - 103.
    In ‘The Mind's I is Illiterate’, G. S. Miller discusses several paradoxes and paradoxical sentences which Miller claims are related by a common abuse of language. The Whiteley sentence ‘Lucas cannot consistently believe this sentence’ fails to be meaningful for want of a referent outside of the sentence for the phrase ‘this sentence’; the Liar Paradox when formulated as ‘I am lying’ is similarly disposed of when it is seen that the verb is defective and the sentence fails to (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  31. Whither Russell's Paradox of Predication?Nino Cocchiarella - 1973 - In Milton Karl Munitz (ed.), Logic and Ontology. New York: New York University Press. pp. 133--158.
  32.  10
    Russell’s Paradox and the Theory of Propositional Functions in The Principles of Mathematics.Yasushi Nomura - 2013 - Kagaku Tetsugaku 46 (1):17-33.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  33.  2
    Russell's Paradox and the Theory of Classes in The Principles of Mathematics.Yasushi Nomura - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):23-36.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  34.  26
    The Resolution of Russell’s Paradox in Principia Mathematica.Bernard Linsky - 2002 - Noûs 36 (s16):395 - 417.
  35.  5
    Russell's Paradox and the Residual Achilles.Nolan Kaiser - 1972 - Apeiron 6 (1):39 - 48.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  36.  5
    9 Russell's Paradoxes and His Theory of Definite Descriptions.David B. Haley - 2017 - In Rethinking Identity and Metaphysics. Yale University Press. pp. 91-110.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  37.  10
    Russell's Paradox and Others.W. V. Quine - 1942 - Journal of Symbolic Logic 7 (1):44-44.
  38.  82
    On Russell's Paradox.F. Graf Hoensbroech - 1939 - Mind 48 (191):355-358.
  39.  1
    On Russell's Paradox.C. H. Langford - 1939 - Journal of Symbolic Logic 4 (3):132-132.
    Direct download  
     
    Export citation  
     
    Bookmark  
  40.  79
    A Note on Cantor's Theorem and Russell's Paradox.J. N. Crossley - 1973 - Australasian Journal of Philosophy 51 (1):70 – 71.
    It is claimed that cantor had the technical apparatus available to derive russell's paradox some ten years before russell's discovery.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  41. Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic.Sean Walsh - 2016 - Journal of Philosophical Logic 45 (3):277-326.
    This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  42.  44
    Type-Free Property Theory, Exemplification and Russell's Paradox.Francesco Orilia - 1991 - Notre Dame Journal of Formal Logic 32 (3):432-447.
    This paper presents a type-free property-theoretic system in the spirit of a framework proposed by Menzel and then supplements it with a theory of truth and exemplification. The notions of a truth-relevantly complex (simple) sentence and of a truth-relevant subsentence are introduced and then used in order to motivate the proposed theory. Finally, it is shown how the theory avoids Russell's paradox and similar problems. Some potential applications to the foundations of mathematics and to natural language semantics are (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  43.  37
    On Russell's Vulnerability to Russell's Paradox.James Levine - 2001 - History and Philosophy of Logic 22 (4):207-231.
    Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ?the most important event? in ?the most important year in my intellectual life?. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  44.  65
    Russell's Way Out of the Paradox of Propositions.André Fuhrmann - 2002 - History and Philosophy of Logic 23 (3):197-213.
    In Appendix B of Russell's The Principles of Mathematics occurs a paradox, the paradox of propositions, which a simple theory of types is unable to resolve. This fact is frequently taken to be one of the principal reasons for calling ramification onto the Russellian stage. The paper presents a detaiFled exposition of the paradox and its discussion in the correspondence between Frege and Russell. It is argued that Russell finally adopted a very simple solution to the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  45.  65
    Sets, Classes and Extensions: A Singularity Approach to Russell's Paradox.K. Simmons - 2000 - Philosophical Studies 100 (2):109-149.
  46.  89
    St. Anselm's Ontological Argument Succumbs to Russell's Paradox.Christopher Viger - 2002 - International Journal for Philosophy of Religion 52 (3):123-128.
  47.  78
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  48.  22
    Russell's Separation of the Logical and Semantic Paradoxes.Gregory Landini - 2004 - Revue Internationale de Philosophie 3:257-294.
    Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   5 citations  
  49.  21
    Ekman’s Paradox.Peter Schroeder-Heister & Luca Tranchini - 2017 - Notre Dame Journal of Formal Logic 58 (4):567-581.
    Prawitz observed that Russell’s paradox in naive set theory yields a derivation of absurdity whose reduction sequence loops. Building on this observation, and based on numerous examples, Tennant claimed that this looping feature, or more generally, the fact that derivations of absurdity do not normalize, is characteristic of the paradoxes. Striking results by Ekman show that looping reduction sequences are already obtained in minimal propositional logic, when certain reduction steps, which are prima facie plausible, are considered in addition to (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  50.  5
    Balzer's Solution to Russell's Paradox.Jagat Pal - 1993 - Journal of Value Inquiry 27 (3-4):539-540.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
1 — 50 / 1000