This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Subcategories:
88 found
Search inside:
(import / add options)   Sort by:
1 — 50 / 88
Material to categorize
  1. Roy T. Cook (2003). Review of J. Mayberry, The Foundations of Mathematics in the Theory of Sets. [REVIEW] British Journal for the Philosophy of Science 54 (2):347-352.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  2. Howard Whitley Eves (1965). An Introduction to the Foundations and Fundamental Concepts of Mathematics. New York, Holt, Rinehart and Winston.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  3. Geoffrey Hellman (2006). Pluralism and the Foundations of Mathematics. In ¸ Itekellersetal:Sp. 65--79.
    A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, raises issues of (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  4. Geoffrey Hellman (2006). What is Categorical Structuralism?. In. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. 151--161.
  5. Ignasi Jané (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  6. I. Jane (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  7. Ignagio Jane (2001). Reflections on Skolem's Relativity of Set-Theoretical Concepts. Philosophia Mathematica 9 (2):129-153.
    In this paper an attempt is made to present Skolem's argument, for the relativity of some set-theoretical notions as a sensible one. Skolem's critique of set theory is seen as part of a larger argument to the effect that no conclusive evidence has been given for the existence of uncountable sets. Some replies to Skolem are discussed and are shown not to affect Skolem's position, since they all presuppose the existence of uncountable sets. The paper ends with an assessment of (...)
    Remove from this list | Direct download (12 more)  
     
    My bibliography  
     
    Export citation  
  8. 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 (...)
    Remove from this list |
    Translate to English
    | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  9. Enrique V. Kortright (1994). Philosophy, Mathematics, Science and Computation. Topoi 13 (1):51-60.
    Attempts to lay a foundation for the sciences based on modern mathematics are questioned. In particular, it is not clear that computer science should be based on set-theoretic mathematics. Set-theoretic mathematics has difficulties with its own foundations, making it reasonable to explore alternative foundations for the sciences. The role of computation within an alternative framework may prove to be of great potential in establishing a direction for the new field of computer science.Whitehead''s theory of reality is re-examined as a foundation (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  10. G. Landini (2006). The Ins and Outs of Frege's Way Out. 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 (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  11. J. P. Mayberry (2000). The Foundations of Mathematics in the Theory of Sets. Cambridge University Press.
    This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  12. John Mayberry (1994). What is Required of a Foundation for Mathematics? Philosophia Mathematica 2 (1):16-35.
    The business of mathematics is definition and proof, and its foundations comprise the principles which govern them. Modern mathematics is founded upon set theory. In particular, both the axiomatic method and mathematical logic belong, by their very natures, to the theory of sets. Accordingly, foundational set theory is not, and cannot logically be, an axiomatic theory. Failure to grasp this point leads obly to confusion. The idea of a set is that of an extensional plurality, limited and definite in size, (...)
    Remove from this list | Direct download (11 more)  
     
    My bibliography  
     
    Export citation  
  13. John Mayberry (1977). The Consistency Problem for Set Theory: An Essay on the Cantorian Foundations of Mathematics (II). British Journal for the Philosophy of Science 28 (2):137-170.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  14. Stephen Pollard (1996). Sets, Wholes, and Limited Pluralitiest. Philosophia Mathematica 4 (1):42-58.
    This essay defends the following two claims: (1) liraitation-of-size reasoning yields enough sets to meet the needs of most mathematicians; (2) set formation and mereological fusion share enough logical features to justify placing both in the genus composition (even when the components of a set are taken to be its members rather than its subsets).
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  15. Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
    THE FOUNDATIONS OF MATHEMATICS () PREFACE The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with ...
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  16. Frank Plumpton Ramsey (1931/1978). Foundations: Essays in Philosophy, Logic, Mathematics, and Economics. Humanties Press.
  17. Michael D. Resnik (1999). Review of G. Boolos, Logic, Logic, and Logic. Philosophia Mathematica 7 (3):328-335.
Russell's Paradox
  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 (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  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.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  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 (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  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.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  5. Manuel Bremer (2010). Universality in Set Theories. Ontos.
    The book discusses the fate of universality and a universal set in several set theories.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  6. Arthur W. Burks & Irving M. Copi (1950). Lewis Carroll's Barber Shop Paradox. Mind 59 (234):219-222.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  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.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  8. Nino B. 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.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  9. 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.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  10. 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 (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  11. 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 (...)
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  12. 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. (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  13. 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 (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  14. 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.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  15. 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 (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  16. 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.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  17. 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.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  18. 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 (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  19. F. Graf Hoensbroech (1939). On Russell's Paradox. Mind 48 (191):355-358.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  20. Kelly Dean Jolley (2004). Logic's Caretaker–Wittgenstein, Logic, and the Vanishment of Russell's Paradox. Philosophical Forum 35 (3):281–309.
  21. 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 (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  22. 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 (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  23. 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.
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  24. 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 (...)
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  25. 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 (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  26. 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 ...
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  27. Bernard Linsky (2002). The Resolution of Russell's Paradox in "Principia Mathematica". Noûs 36 (s16):395 - 417.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  28. Laureano Luna (2013). Satisfiable and Unsatisfied Paradoxes. How Closely Related? The Reasoner 7 (5):56-7.
  29. 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.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  30. Francis Moorcroft (1993). Why Russell's Paradox Won't Go Away. Philosophy 68 (263):99 - 103.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  31. James Moulder (1974). Is Russell's Paradox Genuine? Philosophy 49 (189):295 - 302.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  32. 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.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  33. Francesco Orilia (1991). Type-Free Property Theory, Exemplification and Russell's Paradox. Notre Dame Journal of Formal Logic 32 (3):432-447.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
1 — 50 / 88