This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories

17 found
Order:
  1. added 2020-05-24
    Frege’s Attack on “Abstraction” and His Defense of the “Applicability” of Arithmetic.Daniël F. M. Strauss - 2003 - South African Journal of Philosophy 22 (1):63-80.
    The traditional understanding of abstraction operates on the basis of the assumption that only entities are subject to thought processes in which particulars are disregarded and commonalities are lifted out (the so-called method of genus proximum and differentia specifica). On this basis Frege criticized the notion of abstraction and convincingly argued that (this kind of) “entitary- directed” abstraction can never provide us with any numbers. However, Frege did not consider the alternative of “property- abstraction.” In this article an argument for (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  2. added 2020-05-23
    Analysis and Abstraction Principles in Russell and Frege.James Levine - 2007 - In Michael Beaney (ed.), The Analytic Turn. Routledge. pp. 51-74.
  3. added 2020-05-23
    Frege-Russell Numbers: Analysis or Explication?Erich H. Reck - 2007 - In Michael Beaney (ed.), The Analytic Turn. New York: Routledge. pp. 33-50.
    For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or re-constructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the ‘Frege-Russell conception of the natural numbers’ or, more briefly, the Frege-Russell numbers. My main concern (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark   1 citation  
  4. added 2020-05-12
    Frege's Correlation.AgustÍn Rayo - 2004 - Analysis 64 (2):119-122.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5. added 2020-05-11
    Fragments of Frege’s Grundgesetze and Gödel’s Constructible Universe.Sean Walsh - 2016 - Journal of Symbolic Logic 81 (2):605-628.
    Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  6. added 2020-05-11
    Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171 - 227.
    In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege’s notion of evidence and its interpretation by Jeshion, the introduction (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  7. added 2020-05-11
    Frege’s Cardinals as Concept-Correlates.Gregory Landini - 2006 - Erkenntnis 65 (2):207-243.
    In his "Grundgesetze", Frege hints that prior to his theory that cardinal numbers are objects he had an "almost completed" manuscript on cardinals. Taking this early theory to have been an account of cardinals as second-level functions, this paper works out the significance of the fact that Frege's cardinal numbers is a theory of concept-correlates. Frege held that, where n > 2, there is a one—one correlation between each n-level function and an n—1 level function, and a one—one correlation between (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  8. added 2020-05-11
    Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic.Matthias Schirn - 2003 - Erkenntnis 59 (2):203 - 232.
    In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9. added 2020-05-11
    Grundlagen §64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (3):243-261.
  10. added 2020-05-11
    IX—Saving Frege From Contradiction.George Boolos - 1987 - Proceedings of the Aristotelian Society 87 (1):137-152.
  11. added 2020-05-07
    Abstraction and Identity.Roy T. Cook & Philip A. Ebert - 2005 - Dialectica 59 (2):121–139.
    A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  12. added 2020-05-05
    The Principle of Equivalence as a Criterion of Identity.Ryan Samaroo - forthcoming - Synthese:1-25.
    In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  13. added 2020-05-04
    Grundlagen, Section 64: Frege's Discussion of Definitions by Abstraction in Historical Context.Paolo Mancosu - 2015 - History and Philosophy of Logic 36 (1):62-89.
    I offer in this paper a contextual analysis of Frege's Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools . In addition, I put Frege's considerations in the context of a widespread debate in Germany (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  14. added 2020-05-04
    Frege's Other Program.Aldo Antonelli & Robert May - 2005 - Notre Dame Journal of Formal Logic 46 (1):1-17.
    Frege's logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the "neologicist" approach of Hale and Wright. Less attention has been given to Frege's extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  15. added 2020-05-04
    Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
    On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to (...)
    Remove from this list   Direct download (11 more)  
     
    Export citation  
     
    Bookmark   40 citations  
  16. added 2020-05-04
    Grundlagen §64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (3):243–261.
  17. added 2020-05-03
    Frege on Sense Identity, Basic Law V, and Analysis.Philip A. Ebert - 2016 - Philosophia Mathematica 24 (1):9-29.
    The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark