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  1. Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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  2. Andrew Bacon (2013). Paradoxes of Logical Equivalence and Identity. Topoi:1-10.
    In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.
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  3. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  4. Andrew Boucher, A Comprehensive Solution to the Paradoxes.
    A solution to the paradoxes has two sides: the philosophical and the technical. The paradoxes are, first and foremost, a philosophical problem. A philosophical solution must pinpoint the exact step where the reasoning that leads to contradiction is fallacious, and then explain why it is so.
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  5. Manuel Bremer (2010). Universality in Set Theories. Ontos.
    The book discusses the fate of universality and a universal set in several set theories.
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  6. Arthur W. Burks & Irving M. Copi (1950). Lewis Carroll's Barber Shop Paradox. Mind 59 (234):219-222.
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  7. Hector-Neri Castañeda (1976). Ontology and Grammar: I. Russell's Paradox and the General Theory of Properties in Natural Language. Theoria 42 (1-3):44-92.
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  8. Nino Cocchiarella (2000). Russell's Paradox of the Totality of Propositions. 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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  9. John Corcoran (1973). Book Review:Philosophy of Logic Hilary Putnam. [REVIEW] Philosophy of Science 40 (1):131-.
    Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) is largely correct as (...)
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  10. J. N. Crossley (1973). A Note on Cantor's Theorem and Russell's Paradox. 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.
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  11. Arnold Cusmariu (1979). Russell's Paradox Re-Examined. 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 (...)
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  12. Fernando Ferreira & Kai F. Wehmeier (2002). On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze. Journal of Philosophical Logic 31 (4):301-311.
    It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...)
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  13. Harty Field (2004). The Consistency of the Naïve Theory of Properties. Philosophical Quarterly 54 (214):78 - 104.
    If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering paradox. (...)
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  14. Danny Frederick, The Unsatisfactoriness of Unsaturatedness.
    Frege proposed his doctrine of unsaturatedness as a solution to the problems of the unity of the proposition and the unity of the sentence. I show that Frege’s theory is mystical, ad hoc, ineffective, paradoxical and entails that singular terms cannot be predicates. I explain the traditional solution to the problem of the unity of the sentence, as expounded by Mill, which invokes a syncategorematic sign of predication and the connotation and denotation of terms. I streamline this solution, bring it (...)
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  15. Harvey M. Friedman, From Russell's Paradox To.
    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.
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  16. Michael Glanzberg (2003). Minimalism and Paradoxes. Synthese 135 (1):13 - 36.
    This paper argues against minimalism about truth. It does so by way of acomparison of the theory of truth with the theory of sets, and considerationof where paradoxes may arise in each. The paper proceeds by asking twoseemingly unrelated questions. First, what is the theory of truth about?Answering this question shows that minimalism bears important similaritiesto naive set theory. Second, why is there no strengthened version ofRussell's paradox, as there is a strengthened Liar paradox? Answering thisquestion shows that like naive (...)
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  17. Laurence Goldstein (2004). The Barber, Russell's Paradox, Catch-22, God, Contradiction and More: A Defence of a Wittgensteinian Conception of Contradiction. In Graham Priest, Jc Beall & Bradley Armour-Garb (eds.), The law of non-contradiction: new philosophical essays. Oxford University Press. 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.
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  18. K. Grelling & L. Nelson (1907/1908). Bemerkungen Zu den Paradoxien von Russell Und Burali-Forti. Abhandlungen Der Fries'schen Schule (Neue Serie) 2:300-334.
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  19. Reinhardt Grossmann (1972). Russell's Paradox and Complex Properties. 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 a paradox rather (...)
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  20. F. Graf Hoensbroech (1939). On Russell's Paradox. Mind 48 (191):355-358.
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  21. Luca Incurvati & Julien Murzi (forthcoming). Maximally Consistent Sets of Instances of Naive Comprehension. Mind.
    Paul Horwich (1990) once suggested restricting the T-Schema to the maximal consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...)
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  22. Kelly Dean Jolley (2004). Logic's Caretaker–Wittgenstein, Logic, and the Vanishment of Russell's Paradox. Philosophical Forum 35 (3):281–309.
  23. 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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  24. 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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  25. William C. Kneale (1971). Russell's Paradox and Some Others. 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.
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  26. Giorgio Lando (2012). Russell's Relations, Wittgenstein's Objects, and the Theory of Types. Teorema (2):21-35.
    We discuss a previously unnoticed resemblance between the theory of relations and predicates in The Philosophy of Logical Atomism [TPLA] by Russell and the theory of objects and names in the Tractatus Logico-Philosophicus [TLP] by Wittgenstein. Points of likeness are detected on three levels: ontology, syntax, and semantics. This analogy explains the prima facie similarities between the informal presentation of the theory of types in TPLA and the sections of the TLP devoted to this same topic. Eventually, we draw some (...)
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  27. James Levine (2001). On Russell's Vulnerability to Russell's Paradox. 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 was thus (...)
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  28. Godehard Link (ed.) (2004). One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy. Walter 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 ...
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  29. Bernard Linsky (2002). The Resolution of Russell's Paradox in "Principia Mathematica". Noûs 36 (s16):395 - 417.
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  30. Laureano Luna (2013). Satisfiable and Unsatisfied Paradoxes. How Closely Related? The Reasoner 7 (5):56-7.
  31. Laureano Luna & William Taylor (2014). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica 22 (2):198-208.
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  32. Francis Moorcroft (1993). Why Russell's Paradox Won't Go Away. Philosophy 68 (263):99 - 103.
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  33. James Moulder (1974). Is Russell's Paradox Genuine? Philosophy 49 (189):295 - 302.
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  34. Francesco Orilia (1996). A Contingent Russell's Paradox. 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.
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  35. Francesco Orilia (1991). Type-Free Property Theory, Exemplification and Russell's Paradox. Notre Dame Journal of Formal Logic 32 (3):432-447.
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  36. T. Parent (forthcoming). Theory Dualism and the Metalogic of Mind-Body Problems. In Christopher Daly (ed.), The Palgrave Handbook to Philosophical Methods. Palgrave.
    The paper defends the philosophical method of "regimentation" by example, especially in relation to the theory of mind. The starting point is the Place-Smart after-image argument: A green after-image will not be located outside the skull, but if we cracked open your skull, we won't find anything green in there either. (If we did, you'd have some disturbing medical news.) So the after-image seems not to be in physical space, suggesting that it is non-physical. In response, I argue that the (...)
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  37. Andrew M. Pitts & Paul Taylor (1989). A Note on Russell's Paradox in Locally Cartesian Closed Categories. 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 terms of (...)
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  38. Michael D. Potter (2004). Set Theory and its Philosophy: A Critical Introduction. Oxford University Press.
    Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...)
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  39. Gonçalo Santos (2010). A Not So Fine Version of Generality Relativism. Theoria 25 (2):149-161.
    The generality relativist has been accused of holding a self-defeating thesis. Kit Fine proposed a modal version of generality relativism that tries to resist this claim. We discuss his proposal and argue that one of its formulations is self-defeating.
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  40. K. Simmons (2000). Sets, Classes and Extensions: A Singularity Approach to Russell's Paradox. Philosophical Studies 100 (2):109-149.
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  41. Hartley Slater (2006). Frege's Hidden Assumption (El Supuesto Escondido de Frege). Critica 38 (113):27 - 37.
    This paper is concerned with locating the specific assumption that led Frege into Russell's Paradox. His understanding of reflexive pronouns was weak, for one thing, but also, by assimilating concepts to functions he was misled into thinking one could invariably replace a two-place relation with a one-place property. /// Este trabajo se ocupa de localizar el supuesto específico que llevó a Frege a la Paradoja de Russell. Por una parte, su comprensión de los pronombres reflexivos era débil pero, por otra, (...)
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  42. Graham Stevens (2004). From Russell's Paradox to the Theory of Judgement: Wittgenstein and Russell on the Unity of the Proposition. Theoria 70 (1):28-61.
  43. J. P. Studd (2012). The Iterative Conception of Set: A (Bi-)Modal Axiomatisation. Journal of Philosophical Logic 42 (5):1-29.
    The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...)
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  44. W. W. Tait (2003). Zermelo's Conception of Set Theory and Reflection Principles. In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
  45. Rafal Urbaniak (2008). Lesniewski and Russell's Paradox: Some Problems. 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 a specific (...)
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  46. Christopher Viger (2002). St. Anselm's Ontological Argument Succumbs to Russell's Paradox. International Journal for Philosophy of Religion 52 (3):123-128.
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  47. Zach Weber (2010). Explanation And Solution In The Inclosure Argument. Australasian Journal of Philosophy 88 (2):353-357.
    In a recent article, Emil Badici contends that the inclosure schema substantially fails as an analysis of the paradoxes of self-reference because it is question-begging. The main purpose of this note is to show that Badici's critique highlights a necessity condition for the success of dialectic about paradoxes. The inclosure argument respects this condition and remains solvent.
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  48. Kai F. Wehmeier (2004). Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik. 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.
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  49. Kai F. Wehmeier (1999). Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects. Synthese 121 (3):309-328.
    In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T (...)
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