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  1. added 2020-05-24
    Variations of Frege's Grundgesetze.J. Wolfgang Degen - 2007 - Travaux de Logique 18:15-31.
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  2. added 2020-05-23
    Some Observations Related to Frege's Way Out'.Michael David Resnik - 1964 - Logique Et Analyse 7 (27):138-144.
    In this note I shall make some observations concerning both the original and repaired systems presented by Frege in his Grundgesetze der Arithmetik . These in tum lead to general considerations con- cerning related axáom systems and contemporary comparative set theory. I hope that my remarks will be useful to others - as they were to me - for obtaining some insight into Frege's and current systems.
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  3. added 2020-05-22
    Axiom V and Hume's Principle in Frege's Foundational Project.Matthias Schirn - 1995 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 30 (66):7-20.
  4. added 2020-05-22
    Frege Structures and the Notions of Truth and Proposition.P. Aczel - 1980 - In J. Barwise, H. J. Keisler & K. Kunen (eds.), The Kleene Symposium. North-Holland.
  5. added 2020-05-21
    How Did Frege Fall Into the Contradiction?Peter M. Sullivan - 2007 - Ratio 20 (1):91–107.
    Quine made it conventional to portray the contradiction that destroyed Frege’s logicism as some kind of act of God, a thunderbolt that descended from a clear blue sky. This portrayal suited the moral Quine was antecedently inclined to draw, that intuition is bankrupt, and that reliance on it must therefore be replaced by a pragmatic methodology. But the portrayal is grossly misleading, and Quine’s moral simply false. In the person of others – Cantor, Dedekind, and Zermelo – intuition was working (...)
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  6. added 2020-05-20
    Saving Frege From Contradiction.George Boolos - 1986 - Proceedings of the Aristotelian Society 87:137--151.
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  7. added 2020-05-20
    Frege's Way Out: A Footnote.Leonard Linsky & George F. Schumm - 1971 - Analysis 32 (1):5-7.
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  8. added 2020-05-19
    Husserl, Frege and 'the Paradox'.Claire Hill - 2000 - Manuscrito 23 (2):101-132.
    In letters that Husserl and Frege exchanged during late 1906 and early 1907, when it is thought that Frege abandoned his attempts to solve Russell's paradox, Husserl expressed his views about the "paradox". Studied here are three deep-rooted differences between their approaches to pure logic present beneath the surface in these letters. These differences concern Husserl's ideas about avoiding paradoxical consequences by shunning three potentially para-dox producing practices. Specifically, he saw the need for: 1) correctly drawing the line between meaning (...)
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  9. added 2020-05-14
    Frege's Way Out: A Footnote.Leonard Linsky & George F. Schumm - 1971 - Analysis 32 (1):5-7.
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  10. added 2020-05-11
    Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
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  11. added 2020-05-11
    The Breadth of the Paradox.Patricia Blanchette - 2016 - Philosophia Mathematica 24 (1):30-49.
    This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...)
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  12. 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 (...)
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  13. 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 (...)
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  14. added 2020-05-11
    Basic Law (V).George Boolos & Peter Clark - 1993 - Aristotelian Society Supplementary Volume 67 (1):213 - 249.
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  15. added 2020-05-11
    Russell to Frege, 24 May 1903: `I Believe That I Have Discovered That Classes Are Completely Superfluous'.Gregory Landini - 1992 - Russell: The Journal of Bertrand Russell Studies 12 (2):160.
  16. added 2020-05-04
    Frege's Recipe.Roy T. Cook & Philip A. Ebert - 2016 - Journal of Philosophy 113 (7):309-345.
    In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and (...)
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  17. added 2020-05-04
    Julius Caesar and Basic Law V.Richard G. Heck - 2005 - Dialectica 59 (2):161–178.
    This paper dates from about 1994: I rediscovered it on my hard drive in the spring of 2002. It represents an early attempt to explore the connections between the Julius Caesar problem and Frege's attitude towards Basic Law V. Most of the issues discussed here are ones treated rather differently in my more recent papers "The Julius Caesar Objection" and "Grundgesetze der Arithmetik I 10". But the treatment here is more accessible, in many ways, providing more context and a better (...)
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  18. added 2020-05-04
    Sense and Basic Law V in Frege's Logicism.Jan Harald Alnes - 1999 - Nordic Journal of Philosophical Logic 4:1-30.
  19. added 2020-05-04
    Frege's Principle.Richard Heck - 1995 - In J. Hintikka (ed.), From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics. Kluwer Academic Publishers.
    This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.
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  20. 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 (...)
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  21. added 2020-05-03
    Did Frege Commit a Cardinal Sin?A. C. Paseau - 2015 - Analysis 75 (3):379-386.
    Frege’s _Basic Law V_ is inconsistent. The reason often given is that it posits the existence of an injection from the larger collection of first-order concepts to the smaller collection of objects. This article explains what is right and what is wrong with this diagnosis.
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  22. added 2020-05-03
    The Ins and Outs of Frege's Way Out.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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  23. added 2020-05-03
    Paradox Without Basic Law V: A Problem with Frege’s Ontology.Adam Rieger - 2002 - Analysis 62 (4):327-330.
  24. added 2020-05-03
    Frege's Way Out.James L. Hudson - 1975 - Philosophy Research Archives 1:135-140.
    I show that Frege's statement of a way to avoid Russell's paradox is defective, in that he presents two different methods as if they were one. One of these "ways out" is notably more plausible than the other, and is almost surely what Frege really intended. The well-known arguments of Lesniewski, Geach, and Quine that Frege's revision of his system is inadequate to avoid paradox are not affected by the ambiguity of Frede's statement. But a rectnt argument by Linsky and (...)
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