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  1. added 2020-06-04
    Frege's Correlation.Agustín Rayo - 2004 - Analysis 64 (2):119–122.
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  2. added 2020-06-04
    Frege Y Los Nombres de Cursos de Valores.Matthias Schirn - 1994 - Theoria 9 (2):109-133.
    Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik (Volume I, 1893, Volume 11, 1903). More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this (...)
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  3. added 2020-06-04
    The Development of Arithmetic in Frege's Grundgesetze der Arithmetik.Richard Heck - 1993 - Journal of Symbolic Logic 58 (2):579-601.
    Frege's development of the theory of arithmetic in his Grundgesetze der Arithmetik has long been ignored, since the formal theory of the Grundgesetze is inconsistent. His derivations of the axioms of arithmetic from what is known as Hume's Principle do not, however, depend upon that axiom of the system--Axiom V--which is responsible for the inconsistency. On the contrary, Frege's proofs constitute a derivation of axioms for arithmetic from Hume's Principle, in (axiomatic) second-order logic. Moreover, though Frege does prove each of (...)
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  4. added 2020-06-04
    Frege: The Royal Road From Geometry.Mark Wilson - 1992 - Noûs 26 (2):149-180.
  5. added 2020-06-04
    The Frege-Hilbert Controversy.Michael David Resnik - 1974 - Philosophy and Phenomenological Research 34 (3):386-403.
  6. added 2020-06-04
    On Frege's Way Out.W. V. Quine - 1955 - Mind 64 (254):145-159.
  7. added 2020-06-03
    A Logic for Frege's Theorem.Richard Heck - 2011 - In Frege’s Theorem: An Introduction. Oxford University Press.
    It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...)
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  8. added 2020-06-03
    The Concept of a Number and the Number of a Concept: An Analysis of the Grundlagen of Gottlob Frege.Stathos Psillos - 2008 - Noesis 3:79-113.
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  9. added 2020-06-03
    Dummett's Critique of Wright's Attempt to Resuscitate Frege.Bob Hale - 1994 - Philosophia Mathematica 2 (2):122-147.
    Michael Dummett mounts, in Frege: Philosophy of Mathematics, a concerted attack on the attempt, led by Crispin Wright, to salvage defensible versions of Frege's platonism and logicism in which Frege's criterion of numerical identity plays a leading role. I discern four main strands in this attack—that Wright's solution to the Caesar problem fails; that explaining number words contextually cannot justify treating them as enjoying robust reference; that Wright has no effective counter to ontological reductionism; and that the attempt is vitiated (...)
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  10. added 2020-06-03
    Frege, Informative Identities, and Logicism.Peter Milne - 1989 - British Journal for the Philosophy of Science 40 (2):155-166.
  11. added 2020-06-03
    A Difficulty with the Frege-Russell Definition of Number.Robert Hambourger - 1977 - Journal of Philosophy 74 (7):409-414.
    An objection is offered to the frege-russell definition. the definition identifies the number 1 with the set of all unit sets. however, it is argued here that the identity conditions for sets require that if any member of a set had not existed, the set itself would not have. therefore, had any object whatever not existed, the unit set containing it would not have either, and thus the set with which the definition identifies 1 would not have. but then, 1 (...)
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  12. added 2020-06-02
    Frege's Definition of Numbers.Edwin Martin - 1987 - Philosophical Papers 16 (1):59-73.
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  13. added 2020-06-02
    Frege's Definition of Number.Steven Wagner - 1983 - Notre Dame Journal of Formal Logic 24 (1):1-21.
    Frege believes (1) that his definition of number is (partly) arbitrary; (2) that it "makes" numbers of certain extensions; (3) that without such a definition we cannot even think or understand arithmetical propositions. this position is part of a view according to which mathematics in general involves the free construction of objects, their properties, and the very contents of mathematical propositions. frege tries to avoid excess subjectivism by the kantian device of treating alternative systems of arithmetic (e.g.) as different appearances (...)
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  14. added 2020-06-01
    Frege, Dedekind, and Peano on the Foundations of Arithmetic. [REVIEW]J. P. Mayberry - 1984 - Philosophical Quarterly 34 (136):424.
    First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This (...)
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  15. added 2020-05-31
    Erkenntnistheorie der Zahldefinition Und Philosophische Grundlegung der Arithmetik Unter Bezugnahme Auf Einen Vergleich Von Gottlob Freges Logizismus Und Platonischer Philosophie (Syrian, Theon Von Smyrna U.A.).Markus Schmitz - 2001 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 32 (2):271-305.
    The epistomology of the definition of number and the philosophical foundation of arithmetic based on a comparison between Gottlob Frege's logicism and Platonic philosophy (Syrianus, Theo Smyrnaeus, and others). The intention of this article is to provide arithmetic with a logically and methodologically valid definition of number for construing a consistent philosophical foundation of arithmetic. The – surely astonishing – main thesis is that instead of the modern and contemporary attempts, especially in Gottlob Frege's Foundations of Arithmetic, such a definition (...)
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  16. added 2020-05-31
    Frege's `Series of Natural Numbers'.T. J. Smiley - 1988 - Mind 97 (388):583-584.
  17. added 2020-05-30
    Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
    This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in ...
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  18. added 2020-05-30
    Frege: Evidence for Self-Evidence.Robin Jeshion - 2004 - Mind 113 (449):131-138.
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  19. added 2020-05-30
    Frege and the Rigorization of Analysis.William Demopoulos - 1994 - Journal of Philosophical Logic 23 (3):225 - 245.
    This paper has three goals: (i) to show that the foundational program begun in the Begriffsschroft, and carried forward in the Grundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence of 'intuitive' reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue (...)
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  20. added 2020-05-30
    Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
    In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...
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  21. added 2020-05-30
    Relativism and the Sociology of Mathematics: Remarks on Bloor, Flew, and Frege.Timm Triplett - 1986 - Inquiry: An Interdisciplinary Journal of Philosophy 29 (1-4):439-450.
    Antony Flew's ?A Strong Programme for the Sociology of Belief (Inquiry 25 {1982], 365?78) critically assesses the strong programme in the sociology of knowledge defended in David Bloor's Knowledge and Social Imagery. I argue that Flew's rejection of the epistemological relativism evident in Bloor's work begs the question against the relativist and ignores Bloor's focus on the social relativity of mathematical knowledge. Bloor attempts to establish such relativity via a sociological analysis of Frege's theory of number. But this analysis only (...)
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  22. added 2020-05-29
    On the Philosophical Interest of Frege Arithmetic.William Demopoulos - 2003 - Philosophical Books 44 (3):220-228.
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  23. added 2020-05-29
    Review of M. Dummett, Frege: Philosophy of Mathematics[REVIEW]Mary Tiles - 1993 - Philosophy 68 (265):405-411.
  24. added 2020-05-29
    Frege: The Last Logicist.Paul Benacerraf - 1981 - Midwest Studies in Philosophy 6 (1):17-36.
  25. added 2020-05-28
    Concepts and Counting.Ian Rumfitt - 2001 - Proceedings of the Aristotelian Society 102 (1):41-68.
    Frege's analysis of Zahlangaben is expounded and evaluated.
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  26. added 2020-05-28
    Critical Notice of Michael Dummett, Frege: Philosophy of Mathematics. [REVIEW]Richard Heck - 1993 - Philosophical Quarterly 43:223-33.
  27. added 2020-05-27
    What Are Numbers?Joongol Kim - 2013 - Synthese 190 (6):1099-1112.
    This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and (...)
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  28. added 2020-05-27
    Platonic and Fregean Numbers.N. White - 2012 - Philosophia Mathematica 20 (2):224-244.
    Rather than reading Plato's philosophy of arithmetic ‘charitably’, it is better to try to explain its failure to generate any fruitful ideas. Prominent in the explanation is Plato's focus on predicates assigning cardinalities and on ‘groups’ falling under them. This focus left Plato unable to envisage the possibility, emerging in Dedekind and Frege but which arithmetic in Plato's time would not easily have suggested, of regarding numbers as objects essentially ranged in the structure of a progression.
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  29. added 2020-05-27
    Liberté Et Vérité: Pensée Mathématique & Spéculation Philosophique.Imre Tóth - 2009 - Éclat.
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  30. added 2020-05-27
    Frege: Philosophy of Mathematics. [REVIEW]William Demopoulos - 1993 - Canadian Journal of Philosophy 23 (3):477-497.
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  31. added 2020-05-26
    Review of "Frege: Philosophy of Mathematics". [REVIEW]Marco Antonio Ruffino - forthcoming - Manuscrito.
    In this review I briefly explain the most important points of each chapter of Dummett's book, and critically discuss some of them. Special attention is given to the criticisms of Crispin Wright's interpretation of Frege's Platonism, and also to Dummett's interpretation of the role(s) of the context principle in Frege's thought.
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  32. added 2020-05-26
    Neologicism, Frege's Constraint, and the Frege‐Heck Condition.Eric Snyder, Richard Samuels & Stewart Shapiro - forthcoming - Noûs.
    One of the more distinctive features of Bob Hale and Crispin Wright’s neologicism about arithmetic is their invocation of Frege’s Constraint – roughly, the requirement that the core empirical applications for a class of numbers be “built directly into” their formal characterization. In particular, they maintain that, if adopted, Frege’s Constraint adjudicates in favor of their preferred foundation – Hume’s Principle – and against alternatives, such as the Dedekind-Peano axioms. In what follows we establish two main claims. First, we show (...)
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  33. added 2020-05-26
    Euclid Strikes Back at Frege.Joongol Kim - 2014 - Philosophical Quarterly 64 (254):20-38.
    Frege’s argument against the ancient Greek conception of numbers as 'multitudes of units’ has been hailed as one of the most successful in his "Grundlagen". The aim of this paper is to show that despite Frege’s best efforts, the Euclidean conception remains a viable alternative to the Fregean conception of numbers by arguing that neither a dilemma argument Frege brings against the Euclidean conception nor a possible argument against it based on the truth of what is known as "Hume’s Principle" (...)
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  34. added 2020-05-26
    A Reflection on Frege's Definition of the Number.Marta Vlasakova - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (3):339-353.
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  35. added 2020-05-26
    Zamyšlení nad Fregovou definicí čísla.Marta Vlasáková - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (3):339-353.
    In his treatise Die Grundlagen der Arithmetik, Gottlob Frege tries to find a definition of number. First he rejects the idea that number could be a property of external objects. Then he comes with a suggestion that a numerical statement expresses a property of a concept, namely it indicates how many objects fall under the concept. Subsequently Frege rejects, or at least essentially modifies, also this definition, because in his view that a number cannot be a property – it should (...)
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  36. added 2020-05-26
    Les Nombres Réels: Frege Critique de Cantor Et de Dedekind/The Real Numbers: Frege's Criticism of Cantor and Dedekind.Jean Pierre Belna - 1997 - Revue d'Histoire des Sciences 50 (1):131-158.
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  37. added 2020-05-25
    Some Naturalistic Comments on Frege's Philosophy of Mathematics.Y. E. Feng - 2012 - Frontiers of Philosophy in China 7 (3):378-403.
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  38. added 2020-05-25
    Frege's Result: Frege's Theorem and Related Matters.Hirotoshi Tabata - 2012 - Frontiers of Philosophy in China 7 (3):351-366.
    One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.
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  39. added 2020-05-25
    Frege and the Philosophy of Mathematics. [REVIEW]J. E. Tiles - 1982 - Philosophical Books 23 (3):164-166.
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  40. added 2020-05-24
    Richard G. Heck, Jr.: Frege’s Theorem. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-733.
  41. added 2020-05-24
    Variations of Frege's Grundgesetze.J. Wolfgang Degen - 2007 - Travaux de Logique 18:15-31.
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  42. added 2020-05-24
    Objectivité et principe de dualité : Le paragraphe 26 des Fondements de l'arithmétique de Frege.Jean-Pierre Belna - 2006 - Revue d'Histoire des Sciences 2 (2):319-344.
    The idea of objectivity is primary in Gottlob Frege’s thought, not only for his conception of logic and mathematics, but also for his philosophy as a whole. He deals with the topic for the first time in 1884, in Grundlagen der Arithmetik, precisely in paragraph 26. He distinguishes the objective from the subjective, of course, but also from the real, what he calls the actual (wirklich in German). In order to be perfectly understood, he gives as example the colors but, (...)
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  43. 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 (...)
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  44. added 2020-05-24
    Frege: Philosophy of Mathematics. [REVIEW]Crispin Wright - 1995 - Philosophical Books 36 (2):89-102.
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  45. added 2020-05-24
    Frege's Conception of Numbers as Objects. [REVIEW]J. E. Tiles - 1984 - Philosophical Books 25 (3):159-161.
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  46. added 2020-05-24
    Die Revisionbedürftigkeit der logischen Semantik Freges.Christian Thiel - 1983 - Anuario Filosófico 16 (1):293-302.
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  47. 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 (...)
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  48. 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.
  49. added 2020-05-23
    The Logicism of Frege, Dedekind, and Russell.William Demopoulos & Peter Clark - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 129--165.
    The common thread running through the logicism of Frege, Dedekind, and Russell is their opposition to the Kantian thesis that our knowledge of arithmetic rests on spatio-temporal intuition. Our critical exposition of the view proceeds by tracing its answers to three fundamental questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified?
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  50. added 2020-05-23
    Frege's and Bolzano's Rationalist Conceptions of Arithmetic.Charles Chihara - 1999 - Revue d'Histoire des Sciences 52 (3):343-362.
    In this article, I compare Gottlob Frege's and Bernard Bolzano's rationalist conceptions of arithmetic. Each philosopher worked out a complicated system of propositions, all of which were set forth as true. The axioms, or basic truths, make up the foundations of the subject of arithmetic. Each member of the system which is not an axiom is related (objectively) to the axioms at the base. Even though this relation to the base may not yet be scientifically proven, the propositions of the (...)
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