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Frege: Begriffsschrift
  1. Begriffsschrift.Gottlob Frege - 1967 - In Jean Van Heijenoort (ed.), From Frege to Gödel. Cambridge: Harvard University Press. pp. 1-83.
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  2. On Frege’s Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs.Dirk Schlimm - 2018 - History and Philosophy of Logic 39 (1):53-79.
    Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...)
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  3. Frege's Begriffsschrift is Indeed First-Order Complete.Yang Liu - 2017 - History and Philosophy of Logic 38 (4):342-344.
    It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness is (...)
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  4. Conceptual Notation and Related Articles. Translated [From the German] and Edited with a Biography and Introd. By Terrell Ward Bynum. --.Terrell Ward Bynum (ed.) - 1972 - Clarendon Press.
    This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography.
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  5. Frege’s Begriffsschrift as a Lingua Characteristica.Tapio Korte - 2010 - Synthese 174 (2):283-294.
    In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begriffsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz’s lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: it is (...)
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  6. Gottlob Frege, Between Philosophy and Mathematics: A Study of His 1879 Concept-Script and its Modern Context.Pierre Adler - 2003 - Dissertation, New School University
    The dissertation seeks to gain a comprehensive understanding of Frege's watershed work of logic, the 1879 Begriffsschrift . The treatise is the first since Aristotle's instauration of the discipline to have succeeded in completely recasting logic. Very generally stated, the dissertation aims at making explicit the conceptual origins of modern logic. To do that will require that each of the achievements of Concept-script be examined from one or more vantage points: either within the perspective of Frege's larger and guiding ambition, (...)
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  7. Frege, G. -Begriffsschrift, Eine der Arithmetischen Nachgebildete Formelsprache des Reinen Denkens. [REVIEW]John Venn - 1880 - Mind 5 (18):297.
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  8. FREGE, G.: 'Conceptual Notation' and Related Articles. [REVIEW]V. H. Dudman - 1974 - Australasian Journal of Philosophy 52:177.
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  9. Concepts and Frege's Concept-Script.Gerald K. Callaghan - 2000 - Dissertation, The University of Western Ontario (Canada)
    This dissertation is a largely historical study in the theory of concepts. My discussion centers on the notion of a "complex concept" or, more illuminatingly, on varieties of logical complexity that attach specifically to concepts. My main contention is that one of the principal innovations associable with the logical doctrine of Frege's Begriffsschrift is the introduction of a novel conception of complex concepts. The innovation of Frege's position can only be appreciated by seeing it against the background of the logical (...)
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  10. Idéographie (French Translation of Gottlob Frege's Begriffsschrift (Conceptual Notation)).Corine Besson - 1999 - Paris: Librairie J. Vrin.
    Complete French translation of Gottlob Frege's Begriffsschrift.
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  11. Conceptual Notation and Related Articles. [REVIEW]John Corcoran & David Levin - 1972 - Philosophy of Science 36 (1):148-149.
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  12. The Heritage of Frege's Begriffsschrift.G. Svob - 2001 - Acta Analytica 25 (20):61-82.
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  13. Frege’s Begriffsschrift as a Lingua Characteristica.Tapio Korte - 2010 - Synthese 174 (2):283-294.
    In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begriffsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz’s lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: it is (...)
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  14. L'IDÉOGRAPHIE FRÉGÉENNE : UN LANGAGE LIBÉRÉ DES CONTRAINTES DE L'INTERLOCUTION.Francis Jacques - 1979 - Revue Internationale de Philosophie 33 (130):694-715.
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  15. Begriffsschrift. A Formula Language of Pure Thought Modelled on That of Arithmetic.Gottlob Frege - 1997 - In Michael Beaney (ed.), The Frege Reader. Blackwell.
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  16. The Next Best Thing to Sense in Begriffsschrift.Peter Simons - 1995 - In Petr Kotatko & John Biro (eds.), Frege: Sense and Reference One Hundred Years Later. Kluwer Academic Publishers. pp. 129--140.
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  17. La Primera Begriffsschrift Fregeana.Luis Felipe Segura - 1999 - Signos Filosóficos 1 (1):13-32.
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  18. Conceptual Notation and Related Articles. [REVIEW]J. E. Llewelyn - 1973 - Philosophical Books 14 (2):5-6.
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  19. What Frege's Theory of Identity is Not.Robert May - 2012 - Thought: A Journal of Philosophy 1 (1):41-48.
    The analysis of identity as coreference is strongly associated with Frege ; it is the view in Begriffsschrift, and, some have argued, henceforth throughout his work. This thesis is incorrect: Frege never held that identity is coreference. The case is made not by interpretation of “proof-quotes”, but rather by exploring how Frege actually deploys the concept. Two cases are considered. The first, from Grundgesetze, are the definitions of the core concepts, zero and truth; the second, from Begriffsschrift, is the validity (...)
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  20. Diagrammatic Reasoning in Frege’s Begriffsschrift.Danielle Macbeth - 2012 - Synthese 186 (1):289-314.
    In Part III of his 1879 logic Frege proves a theorem in the theory of sequences on the basis of four definitions. He claims in Grundlagen that this proof, despite being strictly deductive, constitutes a real extension of our knowledge, that it is ampliative rather than merely explicative. Frege furthermore connects this idea of ampliative deductive proof to what he thinks of as a fruitful definition, one that draws new lines. My aim is to show that we can make good (...)
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  21. Gottlob Frege: Conceptual Notation and Related Articles. [REVIEW]Patrick K. Bastable - 1972 - Philosophical Studies (Dublin) 21:277-278.
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  22. Frege's 'Beurtheilbarer Inhalt'.Mark Helme - 1983 - Analysis 43 (2):70 - 72.
  23. Reading Begriffsschrift.Danielle Macbeth - 2005 - The Harvard Review of Philosophy 13 (1):4-24.
    It is a familiar fact that different systems of notation can function in radically different ways. Consider, to take a very simple example, the difference between the sign-designs ‘twenty-three’, ‘XXIII’, and ‘23’. The first is an expression of English tracing the sounds a speaker makes in uttering the words ‘twenty’ and ‘three’. The second is a Roman numeral that uses signs for collections of things—‘X’ for ten things and ‘I’ for one thing—to present by addition the idea of ten and (...)
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  24. Frege Against the Booleans.Hans Sluga - 1987 - Notre Dame Journal of Formal Logic 28 (1):80-98.
  25. On an Alleged Contradiction Lurking in Frege's Begriffsschrift.Terrell Ward Bynum - 1973 - Notre Dame Journal of Formal Logic 14 (2):285-287.
  26. Note on Frege's Begriffsschrift.Ignacio Angelelli & Terrell Ward Bynum - 1966 - Notre Dame Journal of Formal Logic 7 (4):369-370.
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  27. Some Comments on the Begriffsschrift and Natural Language.Alan Schwerin - 1983 - Philosophical Papers 12 (2):32-38.
    If the begriffsschrift from Frege does represent the logical form of natural language it either lacks a logical form itself, or its logical form is different to that of natural language. But Frege insists that his notation has a logical form. So the second disjunct holds. This suggests that Frege's notation will generate consequences different to those that can be derived with natural language, with its different logical form. For anyone looking for "a means of avoiding misunderstandings", as Frege does, (...)
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  28. Book Review:Conceptual Notation and Related Articles Gottlob Frege, Terrell Ward Bynum. [REVIEW]John Corcoran & David Levin - 1973 - Philosophy of Science 40 (3):454-.
  29. Functional Operations in Frege's Begriffsschrift.Peter M. Simons - 1988 - History and Philosophy of Logic 9 (1):35-42.
    Frege uses Greek letters in two different ways in his Begriffsschrift. One way is the familiar use of bound variables, in conjunction with variable-binding operators, to mark and close argument-places. The other, which is quite unfamiliar, employs letters to mark places for operators to reach into, without thereby closing these places. Frege thereby invents a powerful and compact notation for functional operations which can be recommended even today. His regrettable double use of Greek letters obscured his invention, and this, together (...)
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  30. Begriffsschrift: Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens.Gottlob Frege - 1879 - Halle a.d.S.: Louis Nebert.
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  31. 'Function' in Frege's Begriffsschrift: Dissolving the Problem.Gordon Baker - 2001 - British Journal for the History of Philosophy 9 (3):525 – 544.
  32. What is a Begriffsschrift?Jonathan Barnes - 2002 - Dialectica 56 (1):65–80.
    Before Frege, the term Begriffsschrift'was used to indicate a language the expressions of which adequately represent the structure of the judgements or concepts which they signify, and a language the written signs of which designate ideas rather than sounds. In 1879 Frege follows . Later he adopts —and with it the Aristotelian theory of language in which it is embedded.
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  33. Reading the Begriffsschrift.George Boolos - 1985 - Mind 94 (375):331-344.
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  34. What Does a Concept Script Do?Cora Diamond - 1984 - Philosophical Quarterly 34 (136):343-368.
  35. A Poor Concept Script.Hartley Slater - 2004 - Australasian Journal of Logic 2:44-55.
    The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...)
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  36. Definability and Logical Structure in Frege.John M. Vickers - 1979 - Journal of the History of Philosophy 17 (3):291-308.
Frege: Grundlagen
  1. Die Grundlagen der Arithmetik, §§82–3.George Boolos & Richard Kimberly Heck - 1998 - In Matthias Schirn (ed.), The philosophy of mathematics today. Oxford: Clarendon Press. pp. 407-428.
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  2. IX—Saving Frege From Contradiction.George Boolos - 1987 - Proceedings of the Aristotelian Society 87 (1):137-152.
  3. XII-Grundlagen S64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (3):243-261.
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  4. Frege on Number Properties.Andrew D. Irvine - 2010 - Studia Logica 96 (2):239-260.
    In the Grundlagen , Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.
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  5. 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 (...)
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  6. The Foundations of Arithmetic a Logico-Mathematical Enquiry Into the Concept of Number. English Translation by J.L. Austin. [REVIEW]Gottlob Frege - 1953
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  7. Gottlob Frege: The Foundations of Arithmetic. [REVIEW]W. H. McCrea - 1951 - Philosophy 26 (97):178-180.
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  8. Grundlagen §64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (3):243-261.
  9. FREGE, GOTTLOB. "The Foundations of Arithmetic". [REVIEW]Brian Coffey - 1951 - Modern Schoolman 29:157.
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  10. Reinterpreting §56 of Frege's The Foundations of Arithmetic.K. Brad Wray - 1995 - Auslegung 20 (2):76-82.
    I defend an alternative reading of §56 of Frege's Grundlagen, one that rescues Frege from Dummett's charge that this section is the weakest in the whole book. On my reading, Frege is not presenting arguments against the adjectival strategy. Rather, Frege presents the definitions in §55 in order to convince his reader that numbers must be objects. In §56 Frege suggests that these definitions contain two shortcomings that adequate definitions of numbers must overcome. And these short-comings, he argues, can only (...)
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  11. 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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  12. El Principio Fregeano Del Contexto En Die Grundlagen Der Arithmetik: Una Revisión a la Interpretación de Dummett.María Gabriela Fulugonio - 2008 - Análisis Filosófico 28 (2):205-238.
    En su obra de 1884, Die Grundlagen der Arithmetik [Gl.], Frege establece el principio del contexto como uno de sus principios fundamentales y propone valerse de él para dar con el concepto adecuado de número. Así, ofrece una definición de tipo contextual de número cardinal, pero ante una objeción que le resulta insalvable se decide por una definición explicita. La cuestión acerca de cuál ha sido entonces el sentido de establecer con tanto énfasis el principio del contexto admite más de (...)
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  13. Grundlagen der Arithmetik.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.
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  14. Gottlob Frege: The Foundations of Arithmetic (Die Grundlagen der Arithmetik). Translation by J. L. Austin. (Oxford: Basil Blackwell. 1950. Pp. 132 (Xii + 119). Price 16s.). [REVIEW]W. H. McCrea - 1951 - Philosophy 26 (97):178-180.
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