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  1. Definition and Logical Analysis in Frege.Edward Kanterian - forthcoming - In Siegener Beiträge zur Geschichte und Philosophie der Mathematik, 9.
    Joan Weiner has argued that Frege’s definitions of numbers are linguistic stipulations, with no content-preserving or ontological point: they don’t capture any determinate content of numerals, as they have none, and don’t present numbers as preexisting objects. I show that this view is based on exegetical and systematic errors. First, I demonstrate that Weiner misrepresents the Fregean notions of ‘Foundations-content’, sense, reference, and truth. I then consider the role of definitions, demonstrating that they cannot be mere linguistic stipulations, since they (...)
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  2. Frege and Peano on Definitions.Edoardo Rivello - forthcoming - In Proceedings of the "Frege: Freunde und Feinde" conference, held in Wismar, May 12-15, 2013.
    Frege and Peano started in 1896 a debate where they contrasted the respective conceptions on the theory and practice of mathematical definitions. Which was (if any) the influence of the Frege-Peano debate on the conceptions by the two authors on the theme of defining in mathematics and which was the role played by this debate in the broader context of their scientific interaction?
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  3. Arithmetic, Logicism, and Frege’s Definitions.Timothy Perrine - 2021 - International Philosophical Quarterly 61 (1):5-25.
    This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are inconsistent (...)
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  4. Frege’s Unification.Rachel Boddy - 2018 - History and Philosophy of Logic 40 (2):135-151.
    What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of defin...
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  5. Conceptual Analysis and Analytical Definitions in Frege.Gilead Bar‐Elli - 2017 - European Journal of Philosophy 25 (4):963-984.
    Logical analysis is in Frege primarily not an analysis of a concept but of its sense. Five Fregean philosophical principles are presented as constituting a framework for a theory of logical or conceptual analysis, which I call analytical explication. These principles, scattered and sometime latent in his writings are operative in Frege's critique of other views and in his constructive development of his own view. The proposed conception of analytical explication is partially rooted in Frege's notion of analytical definition. It (...)
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  6. Blanchette on Frege on Analysis and Content.Marcus Rossberg - 2015 - Journal for the History of Analytical Philosophy 3 (7).
    All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.
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  7. Frege’s Logicism and the Neo-Fregean Project.Matthias Schirn - 2014 - Axiomathes 24 (2):207-243.
    Neo-logicism is, not least in the light of Frege’s logicist programme, an important topic in the current philosophy of mathematics. In this essay, I critically discuss a number of issues that I consider to be relevant for both Frege’s logicism and neo-logicism. I begin with a brief introduction into Wright’s neo-Fregean project and mention the main objections that he faces. In Sect. 2, I discuss the Julius Caesar problem and its possible Fregean and neo-Fregean solution. In Sect. 3, I raise (...)
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  8. Frege, Carnap, and Explication: ‘Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science’.Gregory Lavers - 2013 - History and Philosophy of Logic 34 (3):225-41.
    This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...)
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  9. Frege's Conception of Logic.Patricia A. Blanchette - 2012 - Oup Usa.
    In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic.
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  10. Gottloba Fregego Koncepcja Analizy Filozoficznej.Gabriela Besler - 2010 - Wydawn. Uniwersytetu Śląskiego.
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  11. Frege and Hilbert.M. Hallett - 2010 - In Michael Potter Tom Ricketts (ed.), The Cambridge Companion to Frege. Cambridge University Press. pp. 413--464.
  12. Frege on Conceptual and Propositional Analysis.Mark Textor - 2010 - Grazer Philosophische Studien 81 (1):235-257.
    In his Foundations of Arithmetic, Frege aims to extend our a priori arithmetical knowledge by answering the question what a natural number is. He rejects conceptual analysis as a method to acquire a priori knowledge . Later he unsuccessfully tried to solve the problems that beset conceptual analysis . If these problems remain unsolved, which rational method can he use to extend our a priori knowledge about numbers? I will argue that his fundamental arithmetical insight that numbers belong to concepts (...)
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  13. Understanding Frege's Project.Joan Weiner - 2010 - In Thomas G. Ricketts & Michael Potter (eds.), The Cambridge companion to Frege. Cambridge: Cambridge University Press. pp. 32-62.
    Frege begins Die Grundlagen der Arithmetik, the work that introduces the project which was to occupy him for most of his professional career, with the question, 'What is the number one?' It is a question to which even mathematicians, he says, have no satisfactory answer. And given this scandalous situation, he adds, there is small hope that we shall be able to say what number is. Frege intends to rectify the situation by providing definitions of the number one and the (...)
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  14. Teaching & Learning Guide For: Frege on Definitions.Sanford Shieh - 2009 - Philosophy Compass 4 (5):885-888.
    Three clusters of philosophically significant issues arise from Frege’s discussions of definitions. First, Frege criticizes the definitions of mathematicians of his day, especially those of Weierstrass and Hilbert. Second, central to Frege’s philosophical discussion and technical execution of logicism is the so‐called Hume’s Principle, considered in The Foundations of Arithmetic . Some varieties of neo‐Fregean logicism are based on taking this principle as a contextual definition of the operator ‘the number of …’, and criticisms of such neo‐Fregean programs sometimes appeal (...)
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  15. Frege on Definitions: A Case Study of Semantic Content.John Horty - 2008 - Oup Usa.
    In this short monograph, John Horty explores the difficulties presented for Gottlob Frege's semantic theory, as well as its modern descendents, by the treatment of defined expressions. The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the treatment of simple stipulative definitions led Frege to important difficulties. Horty is able to suggest ways out of these difficulties that are both philosophically and logically plausible and Fregean in (...)
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  16. Frege and the Paradox of Analysis.Michael Nelson - 2008 - Philosophical Studies 137 (2):159-181.
    In an unpublished manuscript of 1914 titled ‘Logic in mathematics’, Gottlob Frege offered a rich account of the paradox of analysis. I argue that Frege there claims that the explicandum and explicans of a successful analysis express the same sense and that he furthermore appreciated that this requires that one cannot conclude that two sentences differ in sense simply because it is possible for a (minimally) competent speaker to accept one without accepting the other. I claim that this is shown (...)
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  17. Frege on Definitions.Sanford Shieh - 2008 - Philosophy Compass 3 (5):992-1012.
    This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to (...)
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  18. Frege on Consistency and Conceptual Analysis.Patricia A. Blanchette - 2007 - Philosophia Mathematica 15 (3):321-346.
    Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent (...)
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  19. Michael Beaney on Frege and the Paradox of Analysis.Nora Grigore - 2007 - Croatian Journal of Philosophy 7 (3):487-498.
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  20. Frege on Definitions: A Case Study of Semantic Content.John Horty - 2007 - Oxford University Press.
    The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the ...
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  21. Analysis and Abstraction Principles in Russell and Frege.James Levine - 2007 - In Michael Beaney (ed.), The Analytic Turn. Routledge. pp. 51-74.
  22. 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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  23. What's in a Numeral? Frege's Answer.J. Weiner - 2007 - Mind 116 (463):677-716.
    Frege wanted to define the number 1 and the concept of number. What is required of a satisfactory definition? A truly arbitrary definition will not do: to stipulate that the number one is Julius Caesar is to change the subject. One might expect Frege to define the number 1 by giving a description that picks out the object that the numeral '1' already names; to define the concept of number by giving a description that picks out precisely those objects that (...)
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  24. Logical Analysis Versus Phenomenological Descriptions.Denis Fisette - 2004 - In R. Feist (ed.), Husserl and the Sciences. Ottawa: University of Ottawa Press. pp. 69-98.
    Husserl and Frege on the analysis of the concept of number and primitive logical concepts.
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  25. Analysis and Decomposition in Frege and Russell.James Levine - 2002 - Philosophical Quarterly 52 (207):195-216.
    Michael Dummett has long argued that Frege is committed to recognizing a distinction between two sorts of analysis of propositional contents: 'analysis', which reveals the entities that one must grasp in order to apprehend a given propositional content; and 'decomposition', which is used in recognizing the validity of certain inferences. Whereas any propositional content admits of a unique ultimate 'analysis' into simple constituents, it also admits of distinct 'decompositions', no one of which is ultimately privileged over the others. I argue (...)
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  26. Conceptions of Analysis in Early Analytic Philosophy.Michael Beaney - 2000 - Acta Analytica 15:97-115.
  27. What is a Definition?James Robert Brown - 1998 - Foundations of Science 3 (1):111-132.
    According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further examples that suggest (...)
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  28. Frege, Semantics, and the Double Definition Stroke.Juliet Floyd - 1998 - In Anat Biletzki & Anat Matar (eds.), The Story of Analytic Philosophy: Plot and Heroes. Routledge. pp. 141-166.
  29. 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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  30. 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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  31. Extending Knowledge and `Fruitful Concepts': Fregean Themes in the Foundations of Mathematics.Jamie Tappenden - 1995 - Noûs 29 (4):427-467.
  32. Expression, Analysis and Understanding: Three Essays in the Philosophy of Language.David Alexander Hunter - 1994 - Dissertation, Massachusetts Institute of Technology
    Chapter 1 concerns the role non-linguistic contextual factors play in the expression of thought. It is argued that contextual factors play a role in determining what is expressed by predicates. Several strategies for avoiding this conclusion are discussed and rejected. One strategy maintains that contextual factors determine, not what is expressed, but only what is otherwise communicated. Another contends that whatever can be expressed context dependently can also be expressed context independently. The chapter concludes by suggesting that context dependence indicates (...)
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  33. Frege on the Psychological Significance of Definitions.John F. Horty - 1993 - Philosophical Studies 72 (2-3):223 - 263.
  34. Frege in Perspective. [REVIEW]Reinhardt Grossmann - 1991 - Review of Metaphysics 45 (1):156-157.
    This book claims to provide a revisionist interpretation of Frege's philosophy. According to the author, Frege uses words "that to us have odd meanings derived from a foreign and dated philosophical framework". His philosophy is said to be deeply flawed, beset by fatal errors.
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  35. Definability and Logical Structure in Frege.John M. Vickers - 1979 - Journal of the History of Philosophy 17 (3):291-308.
  36. Freges Analyse der Hilbertschen Axiomatik.Peter Hinst - 1977 - Grazer Philosophische Studien 3 (1):47-57.
    Gegen die vielfach vertretene Auffassung, Frege habe die Hilbertsche Axiomatik nicht verstanden, wird nachzuweisen versucht, daß Frege die neue Methode nicht nur verstanden, sondem auch begrifflich präzise analysiert hat. Er definiert eine formale Theorie im Hilbertschen Sinn als eine Klasse von logisch beweisbaren Wenn-dann-Sätzen, die freie Variable enthalten und deren Wenn-Satz eine Konjunktion der Axiome im Hilbertschen Sinn ist. Er untersucht ferner das Verhältnis zwischen einer Hilbertschen Theorie und ihren Modellen und wendet seine allgemeinen Ergebnisse in erhellender Weise auf Hilberts (...)
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  37. Frege and Wittgenstein on Elucidations.P. M. S. Hacker - 1975 - Mind 84 (336):601-609.
    AB THE DIFFICULTIES RAISED BY "TRACTATUS" 3.263 AND ITS USE OF THE TERM "ERLAUTERUNG" ARE EXAMINED. LIGHT IS THROWN ON THE MATTER BY THE SYSTEMATIC USE OF THIS TERM BY FREGE IN HIS DISCUSSION OF UNDEFINABLES. RUSSELL'S VIEWS ON UNDEFINABLES ARE ALSO TOUCHED UPON. IT IS SUGGESTED THAT THE "TRACTATUS" CONCEPTION OF AN 'ELUCIDATION' CONFUSEDLY COMBINED THE INCOMPATIBLE ROLES OF EMPIRICAL STATEMENT AND GRAMMATICAL SENTENCE (AN OSTENSIVE DEFINITION).
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  38. The Frege-Hilbert Controversy.Michael David Resnik - 1974 - Philosophy and Phenomenological Research 34 (3):386-403.
  39. Contextual Definition: What Frege Might Have Meant but Probably Didn't.John W. Snapper - 1974 - Noûs 8 (3):259-272.
  40. Frege on Definition.V. H. Dudman - 1973 - Mind 82 (328):609-610.
    For frege, To define a symbol is to show how to do without it. Frege originated the distinction between metalanguage and object language. But he formulates his definitions within the begriffsschrift itself, Not seeing that, According to his own account of them, They go better in the metalanguage.
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  41. On the Church-Frege Solution of the Paradox of Analysis.Morton G. White - 1948 - Philosophy and Phenomenological Research 9 (2):305-308.
    Church has recently proposed a solution of the paradox of analysis as propounded by Langford in which Church makes use of Frege's distinction between the sense (Sinn) of a name and its denotation (Bedeutung). The main purpose of the present note. is to show that a, version of the paradox may be presented which is not directly solved by Church in his review but which, in turn, may be solved by using; another distinction of Frege-that between the ordinary (gewihnlich) and (...)
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