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  1. added 2020-06-01
    The Consistency of Frege's Foundations of Arithmetic.George Boolos - 1987 - In J. Thomson (ed.), On Being and Saying: Essays in Honor of Richard Cartwright. MIT Press. pp. 3--20.
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  2. added 2020-05-30
    Gottlob Frege, The Basic Laws of Arithmetic: Exposition of the System. Translated and Edited, with an Introduction, by Montgomery Furth. (Cambridge University Press, Agents for University of California Press. 1964. Pp. Lxiii+144. Price 40s.)A Study of Frege. By Jeremy D. B. Walker. (Basil Blackwell. 1965. Pp. Xiv+201. Price 30s.). [REVIEW]P. W. E. Walters - 1967 - Philosophy 42 (159):92-.
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  3. added 2020-05-29
    The Basic Laws of Arithmetic.Gottlob Frege - 1964 - Berkeley: University of California Press.
    ... as 'logicism') that the content expressed by true propositions of arithmetic and analysis is not something of an irreducibly mathematical character, ...
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  4. added 2020-05-28
    Definition by Induction in Frege's Grundgesetze der Arithmetik.Richard Heck - 1995 - In W. Demopoulos (ed.), Frege's Philosophy of Mathematics. Oxford University Press.
    This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.
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  5. added 2020-05-28
    Class, Function, Concept, Relation.Gottlob Frege - 1917 - The Monist 27 (1):114-127.
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  6. added 2020-05-28
    The Fundamental Laws of Arithmetic.Gottlob Frege - 1915 - The Monist 25 (4):481-494.
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  7. added 2020-05-27
    "The Basic Laws of Arithmetic: Exposition of the System," by Gottlob Frege; Trans., and Ed. With Introd. By Montgomery Furth. [REVIEW]George P. Klubertanz - 1966 - Modern Schoolman 43 (3):299-300.
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  8. added 2020-05-24
    Variations of Frege's Grundgesetze.J. Wolfgang Degen - 2007 - Travaux de Logique 18:15-31.
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  9. 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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  10. added 2020-05-22
    Introductory Note to Frege Against the Formalists.Max Black - 1950 - Philosophical Review 59:77-78.
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  11. added 2020-05-21
    The Propositional Logic of Frege’s Grundgesetze: Semantics and Expressiveness.Eric D. Berg & Roy T. Cook - 2017 - Journal for the History of Analytical Philosophy 5 (6).
    In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show that (...)
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  12. added 2020-05-21
    The Convenience of the Typesetter; Notation and Typography in Frege’s Grundgesetze der Arithmetik.Jim J. Green, Marcus Rossberg & A. Ebert Philip - 2015 - Bulletin of Symbolic Logic 21 (1):15-30.
    We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.
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  13. added 2020-05-20
    The Consistency of Predicative Fragments of Frege's Grundgesetze der Arithmetik.Richard Heck - 1996 - History and Philosophy of Logic 17 (1):209-220.
    As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is (...)
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  14. added 2020-05-19
    Gottlob Frege. The Basic Laws of Arithmetic: Exposition of the System. Trans, and Ed., with Introd. By M. Furth. [REVIEW]Lee C. Rice - 1969 - Modern Schoolman 46 (2):160-161.
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  15. added 2020-05-18
    The Basic Laws of Arithmetic: Exposition of the System. [REVIEW]J. M. P. - 1966 - Review of Metaphysics 19 (4):810-810.
    This book is a translation of some of the more important parts of the Grundgesetze of Frege: the introduction, the first part of the first volume which gives an exposition of the construction, rules, axioms of Frege's formal system, and two appendices, one of which is from the second volume and gives Frege's analysis of the paradox found by Russell in his system. The editor has provided a long introduction "for those not familiar with Frege," although it will benefit those (...)
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  16. added 2020-05-16
    Gottlob Frege, the Basic Laws of Arithmetic: Exposition of the System. [REVIEW]P. W. E. Walters - 1967 - Philosophy 42 (159):92-93.
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  17. added 2020-05-16
    Frege Against the Formalists. III: A Translation of Part of Grundgesetze der Arithmetik.Gottlob Frege - 1950 - Philosophical Review 59:332-345.
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  18. added 2020-05-16
    Frege Against the Formalists (II): A Translation of Part of Grundgesetze der Arithmetik.Gottlob Frege - 1950 - Philosophical Review 59 (2):202-220.
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  19. added 2020-05-16
    Frege Against the Formalists. I: A Translation of Part of Grundgesetze der Arithmetik.Gottlob Frege - 1950 - Philosophical Review 59 (1):77-93.
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  20. added 2020-05-16
    Frege Against the Formalists. III: A Translation of Part of Grundgesetze der Arithmetik.Gottlob Frege - 1950 - Philosophical Review 59 (3):332-345.
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  21. 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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  22. added 2020-05-14
    FREGE, G. - "The Basic Law of Arithmetic, Exposition of the System". [REVIEW]W. Kneale - 1967 - Mind 76:293.
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  23. added 2020-05-12
    Basic Laws of Arithmetic. Derived Using Concept-Script. Volumes I & II. [REVIEW]Matthias Wille - 2015 - History and Philosophy of Logic 36 (1):92-93.
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  24. added 2020-05-12
    Appendix: How to Read Grundgesetze.Roy T. Cook - 2013 - In Philip A. Ebert & Marcus Rossberg (eds.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford: Oxford University Press. pp. A1-A42.
    This appendix is intended to assist the reader in becoming comfortable with the notations, rules, and definitions of Frege's Grundgesetze.
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  25. added 2020-05-12
    Gottlob Frege: Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford, UK: Oxford University Press.
    This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.
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  26. added 2020-05-12
    Reading Frege's Grundgesetze.Richard Heck - 2012 - Oxford University Press.
    Richard G. Heck presents a new account of Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, which establishes it as a neglected masterpiece at the center of Frege's philosophy. He explores Frege's philosophy of logic, and argues that Frege knew that his proofs could be reconstructed so as to avoid Russell's Paradox.
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  27. added 2020-05-12
    Amending Frege’s Grundgesetze der Arithmetik.Fernando Ferreira - 2005 - Synthese 147 (1):3 - 19.
    Frege's "Grundgesetze der Arithmetik" is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege's Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the "Grundgesetze" is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...)
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  28. added 2020-05-12
    On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - 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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  29. added 2020-05-12
    Grundgesetze der Arithmetic I §10.Richard Heck - 1999 - Philosophia Mathematica 7 (3):258-292.
    In section 10 of Grundgesetze, Frege confronts an indeterm inacy left by his stipulations regarding his ‘smooth breathing’, from which names of valueranges are formed. Though there has been much discussion of his arguments, it remains unclear what this indeterminacy is; why it bothers Frege; and how he proposes to respond to it. The present paper attempts to answer these questions by reading section 10 as preparatory for the (fallacious) proof, given in section 31, that every expression of Frege's formal (...)
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  30. added 2020-05-12
    The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck - 1998 - In Matthias Schirn (ed.), Philosophy of Mathematics Today. Oxford University Press.
    Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
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  31. added 2020-05-12
    Why is There so Little Sense in Grundgesetze?Peter Simons - 1992 - Mind 101 (404):753-766.
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  32. added 2020-05-12
    Grundgesetze, Section 10.Adrian W. Moore & Andrew Rein - 1986 - In L. Haaparanta & J. Hintikka (eds.), Frege Synthesized. D. Reidel Publishing Co.. pp. 375--384.
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  33. added 2020-05-12
    The Semantics of Frege's Grundgesetze.John N. Martin - 1984 - History and Philosophy of Logic 5 (2):143-176.
    Quantifiers in Frege's Grundgesetze like are not well-defined because the part Fx & Gx stands for a concept but the yoking conjunction is horizontalised and must stand for a truth-value. This standard interpretation is rejected in favor of a substitutional reading that, it is argued, both conforms better to the text and is well-defined. The theory of the horizontal is investigated in detail and the composite reading of Frege's connectives as made up of horizontals is rejected. The sense in which (...)
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  34. added 2020-05-12
    Referentiality in Frege's Grundgesetze.Martin Edward - 1982 - History and Philosophy of Logic 3 (2):151-164.
    In §§28-31 of his Grundgesetze der Arithmetik, Frege forwards a demonstration that every correctly formed name of his formal language has a reference. Examination of this demonstration, it is here argued, reveals an incompleteness in a procedure of contextual definition. At the heart of this incompleteness is a difference between Frege's criteria of referentiality and the possession of reference as it is ordinarily conceived. This difference relates to the distinction between objectual and substitutional quantification and Frege?s vacillation between the two.
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  35. added 2020-05-12
    Peano’s Review of Frege’s Grundgesetze.Victor Dudman - 1971 - Southern Journal of Philosophy 9 (1):25-37.
  36. added 2020-05-12
    Grundgesetze der Arithmetik. Section 56ff.Gottlob Frege - 1960 - In P. Geach & M. Black (eds.), Translations From the Philosophical Writings of Gottlob Frege. Blackwell.
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  37. added 2020-05-11
    Philip A. Ebert and Marcus Rossberg, Eds.Essays on Frege’s Basic Laws of Arithmetic. [REVIEW]Gregory Landini - forthcoming - Philosophia Mathematica:nkaa013.
    EbertPhilip A and RossbergMarcus, eds.* * _ Essays on Frege’s Basic Laws of Arithmetic_. Oxford: Oxford University Press, 2019. Pp. xii + 673. ISBN: 978-0-19-871208-4 ; 978-0-19-102005-6, 978-0-19-178024-0. doi: 10.1093/oso/9780198712084.001.0001.
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  38. added 2020-05-11
    Gottlob Frege, Basic Laws of Arithmetic. Derived Using Concept-Script. [REVIEW]Matthias Schirn - forthcoming - Philosophical Quarterly:pqv096.
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  39. 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 (...)
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  40. added 2020-05-11
    Book Review: Gottlob Frege, Basic Laws of Arithmetic. [REVIEW]Kevin Klement - 2016 - Studia Logica 104 (1):175-180.
    Review of Basic Laws of Arithmetic, ed. and trans. by P. Ebert and M. Rossberg (Oxford 2013).
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  41. added 2020-05-11
    Reading Frege's Grundgesetze. [REVIEW]O. Magal - 2014 - Philosophical Quarterly 64 (256):526-529.
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  42. 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 (...)
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  43. added 2020-05-11
    Frege’s Permutation Argument Revisited.Kai Frederick Wehmeier & Peter Schroeder-Heister - 2005 - Synthese 147 (1):43-61.
    In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument), by means of which he intends to show that an arbitrary value-range may be identified with the True, and any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identifiability thesis, following Schroeder-Heister (1987)). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation (...)
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  44. added 2020-05-11
    Decomposition and Analysis in Frege’s Grundgesetze.Gregory Landini - 1996 - History and Philosophy of Logic 17 (1-2):121-139.
    Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositions. Decomposition is then shown to be adequate (...)
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  45. added 2020-05-11
    O principio do contexto nas Grundgesetze de Frege.Matthias Schirn - 1996 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (3):177-201.
    Pretendo usar o exemplo dos nomes de percursos de valores como prova de que, contrariamente ao que Michael Resnik e Michael Dummett sustentam, Frege nunca abandonou o seu princípio do contexto: “Apenas no contexto de uma sentenya tem uma palavra significado”. Em particular, pretendo mostrar que a prova da completude com relação ao significado, que Frege tentou introduzir na linguagem formal das Grundgesetze der Arithmetik, baseia-se em uma aplicação do principio do contexto, e que, em consequencia, tambem nomes de percursos (...)
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  46. 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.
  47. added 2020-05-10
    The Basic Laws of Arithmetic: Exposition of the System. [REVIEW]R. H. Kane - 1966 - International Philosophical Quarterly 6 (2):316-319.
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  48. added 2020-05-07
    Essays on Frege's Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2019 - Oxford: Oxford University Press.
    The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege's masterpiece, not just for Frege scholars but for the study of the history (...)
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  49. added 2020-05-07
    Richard G. Heck Jr. Reading Frege's Grundgesetze. Oxford: Oxford University Press, 2012. ISBN: 978-0-19-923370-0 ; 978-0-19-874437-5 ; 978-0-19-165535-7 . Pp. Xvii + 296. [REVIEW]Philip A. Ebert - 2015 - Philosophia Mathematica 23 (2):289-293.
  50. added 2020-05-07
    Translators' Introduction.Philip A. Ebert & Marcus Rossberg - 2013 - In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & II. Oxford: Oxford University Press.
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