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  1. added 2020-06-02
    Cantor's Power-Set Theorem Versus Frege's Double-Correlation Thesis.Nino B. Cocciharella - 1992 - History and Philosophy of Logic 13 (2):179-201.
  2. added 2020-06-02
    Reforming Logic (and Set Theory).Jaakko Hintikka - unknown
    1. Frege’s mistake Frege is justifiably considered the most important thinker in the development of our contemporary “modern” logic. One corollary to this historical role of Frege’s is that his mistakes are found in a magnified form in the subsequent development of logic. This paper examines one such mistake and its later history. Diagnosing this history also reveals ways of overcoming some of the limitations that Frege’s mistake has unwittingly imposed on current forms of modern logic. Frege’s mistake concerns the (...)
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  3. added 2020-06-01
    Quantification: Transcending Beyond Frege’s Boundaries: A Case Study in Transcendental-Metaphysical Logic.Aleksy Molczanow - 2012 - Brill.
    Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely ...
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  4. added 2020-06-01
    Frege's Horizontal and the Liar-Paradox.Dirk Greimann - 2003 - Manuscrito 26 (2):359-387.
    According to Peter Aczel, the inconsistency of Frege’s system in Grundgesetze is due, not to the introduction of sets, as is usually thought, but to the introduction of the Horizontal. His argument is that the principles governing sets are intuitively correct and therefore consistent, while the scheme introducing the Horizontal amounts to an internal definition of truth conflicting with Tarski’s classic result on the undefinability of truth in the object language. The aim of this paper is to show that the (...)
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  5. added 2020-06-01
    Allgemeinheit Und Existenz: Zur Analyse des Kategorischen Urteils Bei Herbart, Sigwart, Brentano Und Frege.Roger Schmit - 1985 - Grazer Philosophische Studien 23 (1):59-78.
    Die auf G. Frege zurückgehende logische Urteilslehre, die die universalen Aussagen im Sinne existenzfreier und die partikulären im Sinne existenzmitbehauptender Urteile deutet, hat ihren Ursprung in der nicht-mathematischen Logik des 19. Jahrhunderts. Bei J.F. Herbart findet sich die hypothetische Konzeption der Allaussage, die eine bedeutsame, Fregesche Gedankengänge antizipierende Verfeinerung durch Chr. Sigwart erfährt. Die genaue Struktur der partikulären Aussage bleibt vorerst noch im Dunkel. Erst F. Brentano gelingt es, die universalen wie die partikulären Aussagen in ihrer Eigenart herauszustellen. In dieser (...)
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  6. added 2020-05-31
    Logic and the Inexpressible in Frege and Heidegger.Edward Witherspoon - 2002 - Journal of the History of Philosophy 40 (1):89-113.
    Frege and Heidegger appear to appear to have diametrically opposed attitudes towards logic. Frege thinks logic must govern any investigation whatsoever, whereas Heidegger (in "What is Metaphysics?") apparently wants to dismantle logic. But when they try to explicate the nature of judgment, a striking similarity emerges. For while their accounts of judgment are radically different, each finds his account to be, by his own lights, _inexpressible<D>. This paper shows how Heidegger and Frege arrive at their respective accounts of judgment, explains (...)
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  7. added 2020-05-31
    Frege and His Groups.Tuomo Aho - 1998 - History and Philosophy of Logic 19 (3):137-151.
    Frege's docent's dissertation Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen(1874) contains indications of a bold attempt to extend arithmetic. According to it, arithmetic means the science of magnitude, and magnitude must be understood structurally without intuitive support. The main thing is insight into the formal structure of the operation of ?addition?. It turns out that a general ?magnitude domain? coincides with a (commutative) group. This is an interesting connection with simultaneous developments in abstract algebra. As his main application, (...)
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  8. added 2020-05-31
    Completeness and Categoricity: Frege, Gödel and Model Theory.Stephen Read - 1997 - History and Philosophy of Logic 18 (2):79-93.
    Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or (...)
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  9. added 2020-05-31
    Frege and the Resolution Calculus.Peter Schroeder-Heister - 1997 - History and Philosophy of Logic 18 (2):95-108.
    We reconstruct Frege?s treatment of certain deducibility problems posed by Boole. It turns out that in his formalization and solution of Boole?s problems Frege anticipates the idea of propositional resolution.
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  10. added 2020-05-31
    Frege's Logic.H. R. Smart - 1945 - Philosophical Review 54 (5):489-505.
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  11. added 2020-05-30
    PM's Circumflex, Syntax and Philosophy of Types.Kevin C. Klement - 2013 - In Bernard Linsky & Nicholas Griffin (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan. pp. 218-246.
    Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...)
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  12. added 2020-05-30
    The Skeleton in Frege's Cupboard: The Standard Versus Nonstandard Distinction.Jaakko Hintikka & Gabriel Sandu - 1992 - Journal of Philosophy 89 (6):290-315.
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  13. added 2020-05-29
    Frege's Logic - by Danielle Macbeth. [REVIEW]Thomas J. Brommage - 2007 - Philosophical Books 48 (3):262-265.
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  14. added 2020-05-29
    Frege: The Last Logicist.Paul Benacerraf - 1981 - Midwest Studies in Philosophy 6 (1):17-36.
  15. added 2020-05-28
    Der Begriff der Logischen Form in der Analytischen Philosophie. Russell in Auseinandersetzung MIT Frege, Meinong Und Wittgenstein – By Elena Tatievskaya. [REVIEW]Jan Woleński - 2011 - Theoria 77 (1):87-89.
  16. added 2020-05-28
    Der Begriff der logischen Form in der analytischen Philosophie. Russell in Auseinandersetzung mit Frege, Meinong und Wittgenstein.Elena Tatievskaya - 2005 - Frankfurt a.M.: Ontos Verlag.
  17. added 2020-05-28
    Frege, Logic, and the Theory of Knowledge.Jacques Bouveresse - 1982 - The Monist 65 (1):52-67.
    One of Frege’s basic philosophical convictions has been that “a large part of the philosopher’s work consists—or at least should consist—in a fight against language.”. Besides, it is partly to his having yielded too easily to the deceptive suggestions of natural language that he himself attibuted, at the very end of his life, the failure of his attempt at defining numbers in logicist terms Nevertheless, he remained to the end convinced that the hopes raised by logic, one of whose tasks (...)
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  18. added 2020-05-27
    On Frege's Logical Diagrams.Iulian D. Toader - 2004 - In Diagrammatic Representation and Inference. Springer: Lecture Notes in Computer Science, vol. 2980,. pp. 22-25.
    This paper argues that a particular point raised by Schröder – that Frege's logical notation fails to be modelled on arithmetical notation – is based on a misunderstanding, for the modelling was meant as conceptual, rather than notational.
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  19. added 2020-05-26
    The Universal Set and Diagonalization in Frege Structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.
    In this paper we summarize some results about sets in Frege structures. The resulting set theory is discussed with respect to its historical and philosophical significance. This includes the treatment of diagonalization in the presence of a universal set.
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  20. added 2020-05-24
    Internal and External Logic.V. A. Smirnov - 1988 - Bulletin of the Section of Logic 17 (3/4):170-181.
    In an essential way I make use of Frege’s and Vasilev’s ideas. N. A. Vasilev distinguished two levels in a logic. The abstract logic depends on gnoeologic assumptions while the empirical part of logic depends on ontological ones. Vasilev did not change the external logic but he did change the internal one. His system can be viewed as a non-standard syllogistics based on classical propositional logic . Vasilev’s ideas become plain if we discern cleary acts of predication and acts of (...)
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  21. added 2020-05-24
    Frege and Illogical Behaviour.J. Mc Kenzie - 1984 - American Philosophical Quarterly 21 (4):339-348.
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  22. added 2020-05-23
    Macbeth Danielle. Frege's Logic. Harvard University Press, Cambridge, Massachusetts, 2005, Xii+ 206 Pp. [REVIEW]Norma B. Goethe - 2006 - Bulletin of Symbolic Logic 12 (3):496-498.
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  23. added 2020-05-22
    Reply to Hintikka and Sandu: Frege and Second-Order Logic.Richard Heck & Jason Stanley - 1993 - Journal of Philosophy 90 (8):416-424.
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  24. added 2020-05-21
    Semantic Descent.Joan Weiner - 2005 - Mind 114 (454):321-354.
    Does Frege have a metatheory for his logic? There is an obvious and uncontroversial sense in which he does. Frege introduces and discusses his new logic in natural language; he argues, in response to criticisms of Begriffsschrift, that his logic is superior to Boole's by discussing formal features of both systems. In so far as the enterprise of using natural language to introduce, discuss, and argue about features of a formal system is metatheoretic, there can be no doubt: Frege has (...)
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  25. added 2020-05-21
    Broadened Logic.Avrum Stroll - 2003 - Topoi 22 (1):93-104.
    The early formal logicians (Frege, Russell, Peano et al.) were worried about differentiating logic from psychology. As a result, they interpreted logic in the most abstract way possible: as a theory about inference patterns whose terms lacked descriptive content. Such a theory was also acontextual. What they did not realize was that psychological concepts like expecting someone, doubting, pain etc. each had their own logic, a logic that had two features: it was contextually oriented and its concepts had a restricted (...)
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  26. added 2020-05-21
    Frege's Two Definitions of Quantification.Leslie Stevenson - 1973 - Philosophical Quarterly 23 (92):207-223.
  27. added 2020-05-21
    Note on a Doctrine of Frege.R. H. Stoothoff - 1963 - Mind 72 (287):406-408.
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  28. added 2020-05-20
    Frege's Elucidatory Holism.Clinton Tolley - 2011 - Inquiry: An Interdisciplinary Journal of Philosophy 54 (3):226-251.
    Abstract I argue against the two most influential readings of Frege's methodology in the philosophy of logic. Dummett's ?semanticist? reading sees Frege as taking notions associated with semantical content?and in particular, the semantical notion of truth?as primitive and as intelligible independently of their connection to the activity of judgment, inference, and assertion. Against this, the ?pragmaticist? reading proposed by Brandom and Ricketts sees Frege as beginning instead from the independent and intuitive grasp that we allegedly have on the latter activity (...)
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  29. added 2020-05-20
    Reconciling Aristotle and Frege.Alex Orenstein - 1999 - Notre Dame Journal of Formal Logic 40 (3):391-413.
    An account of Aristotle's syllogistic (including a full square of opposition and allowing for empty nouns) as an integral part of first-order predicate logic is lacking. Some say it is not possible. It is not found in the tradition stemming from ukasiewicz's attempt nor in less formal approaches such as Strawson's. The ukasiewicz tradition leaves Aristotle's syllogistic as an autonomous axiomatized system. In this paper Aristotle's syllogistic is presented within first-order predicate logic with special restricted quantifiers. The theory is not (...)
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  30. added 2020-05-20
    Frege's Permutation Argument.A. W. Moore & Andrew Rein - 1987 - Notre Dame Journal of Formal Logic 28 (1):51-54.
  31. added 2020-05-19
    Positive Frege and its Scott‐Style Semantics.Thierry Libert - 2008 - Mathematical Logic Quarterly 54 (4):410-434.
    We show that the untyped λ -calculus can be extended with Frege's interpretation of propositional notions, provided we restrict β -conversion to positive expressions. The system of illative λ -calculus so obtained admits a natural Scott-style semantics.
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  32. added 2020-05-19
    Understanding the Goodness of Inference: Modality and Relevance in Frege's System of Logic.Danielle Macbeth - 2007 - Soochow Journal of Philosophical Studies 16:133 - 151.
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  33. added 2020-05-18
    Fregean Quantification Theory.Saul A. Kripke - 2013 - Journal of Philosophical Logic (5):1-3.
    Frege’s system of first-order logic is presented in a contemporary framework. The system described is distinguished by economy of expression and an unusual syntax.
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  34. added 2020-05-18
    Reply to Hintikka and Sandu: Frege and Second-Order Logic.Jason Stanley & Richard Heck - 1993 - Journal of Philosophy 90 (8):416-424.
    Hintikka and Sandu had argued that 'Frege's failure to grasp the idea of the standard interpretation of higher-order logic turns his entire foundational project into a hopeless daydream' and that he is 'inextricably committed to a non-standard interpretation' of higher-order logic. We disagree.
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  35. added 2020-05-18
    Frege's Logical Theory. [REVIEW]H. K. R. - 1969 - Review of Metaphysics 22 (3):579-580.
    This book is far more than an exposition of Frege's logical system and semantic concepts, although it is that. The author puts forward the challenging thesis that in trying to cope with Russell's paradox Frege deserted principles of his system which he had relied on throughout. Sternfeld attempts to show, by offering his own interpretation of Frege's logical theory, that if Frege had relied consistently on his previously formulated logical principles, Russell's paradox would have given him no trouble. Further, he (...)
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  36. added 2020-05-17
    Frege’s Horizontal.William C. Heck & William G. Lycan - 1979 - Canadian Journal of Philosophy 9 (3):479 - 492.
    Frege begins his exposition of the symbol system employed in his Begriffsschrift by introducing the sign ⟝, whereby, he says, “[a] judgment is always to be expressed”.[The judgment sign] stands to the left of the sign or complex of signs in which the content of the judgment is given. If we omit the little stroke at the left of the horizontal stroke, then the judgment is to be transformed into a mere complex of ideas; the author is not expressing his (...)
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  37. added 2020-05-16
    Il sistema senza variabili libere in Frege.I. Aimonetto - 1995 - Epistemologia 18 (1):143-166.
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  38. added 2020-05-16
    Frege and Peirce on Properties of Sentences in Classical Deductive Systems.Benjamin Sanford Hawkins - 1971 - Dissertation, University of Miami
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  39. added 2020-05-15
    Fregean Type Theory: Logical Aspects, Philosophical Implications, Historical Consequences.Phyllis Ann Rooney - 1982 - Dissertation, University of California, Berkeley
    Gottlob Frege's development of his logicist program has had a major impact on the history of logic and on the philosophy of mathematics. The year 1902 marked an important turning point for Frege: it was then that Russell discovered and communicated the inconsistency which could be derived in Frege's system. This problem arose because of the introduction of classes into this system, especially since Frege did not have type distinctions among his classes. ;Yet Frege had very clear type distinctions for (...)
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  40. added 2020-05-13
    Frege's Philosophy of Logic.E. D. Klemke - 1979 - Revue Internationale de Philosophie 33 (130):666-693.
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  41. added 2020-05-12
    What Is the Frege/Russell Analysis of Quantification?Scott Soames - 2014 - In Analytic Philosophy in America: And Other Historical and Contemporary Essays. Princeton University Press. pp. 191-199.
  42. added 2020-05-12
    Frege's Achievements and Literal Scientific Discourse.R. Sternfeld - 1979 - Revue Internationale de Philosophie 33 (130):723.
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  43. added 2020-05-11
    Frege's Notations: What They Are and How They Mean.Gregory Landini - 2012 - Palgrave-Macmillan.
  44. added 2020-05-11
    Peirce entre Frege e Boole: sobre a busca de diálogos possíveis com Wittgenstein.Rafael Duarte Oliveira Venancio - 2012 - Estudos Semioticos (USP) 8 (2):99-108.
    O presente artigo busca debater a posição de Charles Sanders Peirce e dos primeiros estudantes peirceanos de Lógica (Christine Ladd e O. H. Mitchell nos Studies in Logic, 1883) dentro do debate inspirador da visão da linguagem dentro da Filosofia Analítica, conhecido como “Lingua Universalis contra Calculus Ratiocinator”, cujos primórdios podem ser traçados desde a filosofia de Gottfried Leibniz. Para isso, comparamos esse campo do pensamento peirceano com o debate crucial entre a conceitografia de Gottlob Frege (Begriffsschrift, 1879) e a (...)
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  45. added 2020-05-11
    The Rise of Modern Logic: From Leibniz to Frege. [REVIEW]Joan Roselló Moya - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (1):115-119.
  46. added 2020-05-11
    Frege and the Surprising History of Logic: Introduction to Claude Imbert, “Gottlob Frege, One More Time”.Emily Grosholz - 2000 - Hypatia 15 (4):151-155.
    Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.
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  47. added 2020-05-11
    Gottlob Frege, One More Time1.Claude Imbert - 2000 - Hypatia 15 (4):156-173.
    Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...)
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  48. added 2020-05-11
    Frege and Hilbert on Consistency.Patricia A. Blanchette - 1996 - Journal of Philosophy 93 (7):317-336.
  49. added 2020-05-11
    Schwierigkeiten in Freges Grundlagen der Logik.S. O. Welding - 1977 - Kant-Studien 68 (1-4):420-445.
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  50. added 2020-05-11
    Frege's Logical Theory. Robert Sternfeld. [REVIEW]J. D. North - 1967 - Isis 58 (2):279-280.
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