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  1. Stipulations Missing Axioms in Frege's Grundgesetze der Arithmetik.Gregory Landini - forthcoming - History and Philosophy of Logic:1-36.
    Frege's Grundgesetze der Arithmetik offers a conception of cpLogic as the study of functions. Among functions are included those that are concepts, i.e. characteristic functions whose values are the logical objects that are the True/the False. What, in Frege's view, are the objects the True/the False? Frege's stroke functions are themselves concepts. His stipulation introducing his negation stroke mentions that it yields [...]. But curiously no accommodating axiom is given, and there is no such theorem. Why is it that some (...)
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  2. Two-Sorted Frege Arithmetic is Not Conservative.Stephen Mackereth & Jeremy Avigad - 2022 - Review of Symbolic Logic:1-34.
    Neo-Fregean logicists claim that Hume's Principle (HP) may be taken as an implicit definition of cardinal number, true simply by fiat. A longstanding problem for neo-Fregean logicism is that HP is not deductively conservative over pure axiomatic second-order logic. This seems to preclude HP from being true by fiat. In this paper, we study Richard Kimberly Heck's Two-sorted Frege Arithmetic (2FA), a variation on HP which has been thought to be deductively conservative over second-order logic. We show that it isn't. (...)
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  3. Twenty Fregean Ways to Quantify Over Frege's Senses.Jan Dejnožka - 2020 - Diametros:1-15.
    This paper continues my discussion with Michael Dummett on Frege’s senses, published in The Philosophy of Michael Dummett and further developed in Diametros. In his reply to my original paper, Dummett came to agree with me that senses are neither objects nor functions, since they have a categorially different kind of linguistico-metaphysical function to perform. He then asks how we might quantify over senses, if they are neither objects nor functions. He discusses two main options, and finds one unviable and (...)
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  4. Frege's Answer to Kripke.Tapio Korte - 2022 - Wiley: Theoria 88 (2):464-479.
    Theoria, Volume 88, Issue 2, Page 464-479, April 2022.
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  5. Does Frege Have Aristotle's Number?Emily Katz - forthcoming - Journal of the American Philosophical Association:1-19.
    Frege argues that number is so unlike the things we accept as properties of external objects that it cannot be such a property. In particular, number is arbitrary in a way that qualities are not, and number is not predicated of its subjects in the way that qualities are. Most Aristotle scholars suppose either that Frege has refuted Aristotle's number theory or that Aristotle avoids Frege's objections by not making numbers properties of external objects. This has led some to conclude (...)
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  6. Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientae 26:189-206.
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  7. Frege's Answer to Kripke.Tapio Korte - 2022 - Theoria 88 (2):464-479.
    Theoria, Volume 88, Issue 2, Page 464-479, April 2022.
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  8. Frege, Peano and the Construction of a Logical Calculus.Joan Bertran San Millán - 2021 - Logique Et Analyse 253:3-22.
    In contemporary historical studies Peano is usually linked to the logical tradition pioneered by Frege. In this paper I question this association. Specifically, I claim that Frege and Peano developed significantly different conceptions of a logical calculus. First, I clam that while Frege put the systematisation of the notion of inference at the forefront of his construction of an axiomatic logical system, Peano modelled his early logical systems as mathematical calculi and did not really attempt to justify reasoning. Second, I (...)
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  9. Wittgenstein's Reductio.Gilad Nir - 2022 - Journal for the History of Analytical Philosophy 10 (3).
    By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation and the reality it represents. (...)
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  10. Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientiae 26-1:189-206.
    In [Boccuni 2010], a predicative fragment of Frege’s blv augmented with Boolos’ unrestricted plural quantification is shown to interpret pa2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic fa because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret fa and consequently pa2 in a way that parallels Frege’s. In that way, the presented system will be (...)
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  11. Overcoming Frege’s curse: heuristic reasoning as the basis for teaching philosophy of science to scientists.Till Grüne-Yanoff - 2022 - European Journal for Philosophy of Science 12 (1):1-15.
    A lot of philosophy taught to science students consists of scientific methodology. But many philosophy of science textbooks have a fraught relationship with methodology, presenting it either a system of universal principles or entirely permeated by contingent factors not subject to normative assessment. In this paper, I argue for an alternative, heuristic perspective for teaching methodology: as fallible, purpose- and context-dependent, subject to cost-effectiveness considerations and systematically biased, but nevertheless subject to normative assessment. My pedagogical conclusion from this perspective is (...)
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  12. Weiner on the Standard Interpretation of Frege: Joan Weiner: Taking Frege at his word. Oxford: Oxford University Press, 2021, 352 pp, $85.00 HB, ISBN: 9780198865476.Gregory Lavers - 2022 - Metascience 31 (1):89-92.
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  13. Kant, Frege, and the Normativity of Logic: MacFarlane's Argument for Common Ground.Tyke Nunez - 2022 - Wiley: European Journal of Philosophy 29 (4).
    European Journal of Philosophy, Volume 29, Issue 4, Page 988-1009, December 2021.
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  14. An Essay on Compositionality of Thoughts in Frege’s Philosophy.Krystian Bogucki - forthcoming - Philosophical Papers:1-43.
    In the paper, I propose a novel approach to Frege’s view on the principle of compositionality, its relation to the propositional holism and the formation of concepts. The main idea is to distinguish three stages of constructing a logically perfect language. At the first stage, only a sentence as a whole expresses a Thought. It is impossible to assign meaning to less complex units. This is the stage of an ordinary language. The second phase concerns the proper level of construction (...)
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  15. Shareability of Thought and Frege's Constraint: A Reply to Onofri.Romain Bourdoncle - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Onofri [Onofri, A. 2018. ‘The Publicity of Thought.’ Philosophical Quarterly 68 (272): 521–541.] proposes an individuation criterion for thoughts that purports to satisfy both shareability (the notion that different thinkers, or a single thinker at different times, can and generally do think type-identical thoughts) and Frege's constraint (according to which two thoughts are different if it is possible for a rational subject to endorse one while rejecting the other). I argue that his proposal fails to satisfy Frege's constraint. Then I (...)
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  16. Review of Joan Weiner, Taking Frege At His Word. [REVIEW]Hans Sluga - 2022 - Journal for the History of Analytical Philosophy 10 (1).
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  17. Taking Frege at His Word, by Joan Weiner. [REVIEW]Junyeol Kim - forthcoming - Mind.
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  18. Questions to Danielle Macbeth on Frege's Logical Notation and Related Topics.Fabrice Pataut - unknown
    Danielle Macbeth's purpose in Macbeth 2005 is threefold. Her monograph proposes "to provide a logical justification for all aspects of Frege's peculiar notation, to motivate and explain the developments in Frege's views over the course of his intellectual life, and to explicate his most developed, critically reflective conception of his Begriffschrift, his formula language of pure thought". I shall focus here on a few selected aspects of the first and third points and leave on the side the discussion of the (...)
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  19. Conteo, cardinalidad y equinumerosidad: motivos para una revisión crítica de las objeciones de Husserl a Frege en "Filosofía de la Aritmética".Luis Alberto Canela Morales - forthcoming - Filosofia Unisinos:1-13.
    En el apartado Freges Versuch, incluido en Filosofía de la aritmética, Husserl abiertamente señala que en los Fundamentos de la aritmética de G. Frege no existe un análisis lógico adecuado del concepto de número en términos de equinumerosidad. Según Husserl, la caracterización de Frege del concepto de número cardinal, en estrecha conexión con la noción de correspondencia uno- a-uno, es errónea. El objetivo principal de este artículo es mostrar que esta interpretación de Husserl sobre la obra de Frege, específicamente en (...)
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  20. Objetores de Descartes, ¿y también de Frege? Apuntes críticos al artículo “La naturaleza de las entidades matemáticas. Gassendi y Mersenne: objetores de Descartes”.Emilio Méndez Pinto - 2021 - Dianoia 66 (86):129-144.
    Resumen En esta discusión expongo algunas objeciones a las siguientes tesis de Velázquez 2020: 1) que tanto Descartes como Frege sostienen que las entidades aritméticas son irreductibles a procesos empíricos; 2) que, en el caso de Descartes, dichas entidades son “perennes, inherentes a la propia constitución y funcionamiento de la mente” y 3) que Frege impugnó la filosofía matemática de Mill por psicologista. Sostengo que la segunda tesis no es, per se, controversial, pero que sí lo es en el contexto (...)
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  21. In What Sense is Frege's (Statement of the) Puzzle "Problematic"?Ludovic Soutif - 2014 - Revista de Filosofía de la Universidad de Costa Rica 53 (136):51-57.
    I take issue with Glezakos’s explanation of why Frege’s puzzle is un-puzzling. On her view, Frege’s statement – how can sentences of the form a=a and a=b, if true, differ in cognitive value if they express the same semantic content/are made true by the same object’s self-identity? – should not be considered any puzzling either because it is on the whole circular, or because, neutrally stated, it cannot even be set up. I argue against this that if, as she takes (...)
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  22. Frege, Singularism, and Thinking Episodes.Ludovic Soutif - 2020 - In Jean Philippe Narboux & Denis Perrin (eds.), New Essays On Frege’s Logical Investigations. São Paulo, State of São Paulo, Brazil: Nonada. pp. 167-198.
    Logical Investigations (notably, The Thought) is one of the works wherein Frege voices his hostility to psychologism in logic, science, and semantics. Such hostility lies, arguably, behind his threefold conceptual distinction between thought (Gedanke), thinking (Denken), and ideas (Vorstellungen). In this essay I investigate, to begin with, Frege’s motivations for drawing the distinction and keeping thinking episodes (one of the meanings of ‘thoughts’ in English) out of the picture. It turns out, or so I argue, that psychologism threatens, on Frege’s (...)
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  23. O Modo Analítico de Fazer Filosofia o 'Sinn' de Frege.Adriana Silva Graça - 2001 - Philosophica: International Journal for the History of Philosophy 9 (17-18):269-298.
    My aim in this paper is to show in what sense one might characterize ‘analytic philosophy’. In its first part I present some meta-philosophical ideas about the topic and in its following and more substantial parts I develop, as an example of what is being said, one and only one philosophical problem in the Philosophy of Language. The philosophical problem I consider, the so called ‘identity problem’ or ‘Frege Puzzle’ was first advanced by Frege and was treated and developed by (...)
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  24. Frege's Theorem in Plural Logic.Simon Hewitt - manuscript
    We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.
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  25. Davidson’s Main Arguments for the Necessity of Language for Thought (In Persian).Ali Hossein Khani - 2013 - Ketab-E-Mah-E-Falsafeh 6 (68):66-77.
  26. Ignacio Angelelli. Introduction. Two Soviet Studies on Frege, by B. V. Birjukov, Translated and Edited by Ignacio Angelelli, D. Reidel Publishing Company, Dordrecht, Holland, 1964, Pp. VII–XVIII. - B. V. Birjukov. On Frege's Works on Philosophical Problems of Mathematics. English Translation of XXXIX 366 by Ignacio Angelelli. D. Reidel Publishing Company, Dordrecht, Holland, 1964, Pp. 1–51. - B. V. Birjukov. The Theory of Sense of Gottlob Frege. English Translation of XXXIX 366 by Ignacio Angelelli. D. Reidel Publishing Company, Dordrecht, Holland, 1964, Pp. 52–99. [REVIEW]Michael D. Resnik - 1974 - Journal of Symbolic Logic 39 (2):355.
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  27. Frege: Fra Estensionalismo E Logicismo.Aldo Antonelli - manuscript
    Due programmi diversi si intersecano nel lavoro di Frege sui fondamenti dell’aritmetica: • Logicismo: l’aritmetica `e riducibile alla logica; • Estensionalismo: l’aritmetica `e riducibile a una teoria delle estensioni. Sia nei Fondamenti che nei Principi, Frege articola l’idea che l’aritmetica sia riducibile a una teoria logica delle estensioni.
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  28. Finite Sets and Frege Structures.John L. Bell - 1999 - Journal of Symbolic Logic 64 (4):1552-1556.
    Call a family F of subsets of a set E inductive if ∅ ∈ F and F is closed under unions with disjoint singletons, that is, if ∀X∈F ∀x∈E–X(X ∪ {x} ∈ F]. A Frege structure is a pair (E.
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  29. Gottlob Frege, One More Time.Claude Imbert & tr Bontea, Adriana - 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 (...)
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  30. Logicism and the Sense–Denotation Distinction.Mark Eli Kalderon - unknown
    Unless you are a Frege scholar, or a philosopher of mathematics, if you are familiar at all with Frege’s work, you are most likely familiar with his groundbreaking work in the philosophy of language. You might know that Frege was a mathematician who sought to establish the covertly logical subject matter of arithmetic, a project whose demands drove Frege to his logical investigations and reflections on language. But most likely the connection between Frege’s mathematical research and his philosophy of language (...)
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  31. Further Beyond the Frege Boundary.Edward L. Keenan - unknown
    avant propos This paper is basically Keenan (1992) augmented by some new types of properly polyadic quantification in natural language drawn from Moltmann (1992), Nam (1991) and Srivastav (1990). In addition I would draw the reader's attention to recent mathematical studies of polyadic quantiicationz Ben-Shalom (1992), Spaan (1992) and Westerstahl (1992). The first and third of these extend and generalize (in some cases considerably) the techniques and results in Keenan (1992). Finally I would like to acknowledge the stimulating and constructive (...)
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  32. Notes on Frege on Rules of Inference.Robert May - manuscript
    1. There is only one rule of inference, modus ponens. This is true both in the presentations of Begriffsschrift and Grundgesetze. There are other ways of making transitions between propositions in proofs, but these are never labeled by Frege “rules of inference.” These pertain to scope of quantification, parsing of formulas, introduction of definitions, conventions for the use and replacement of the various letters, and certain structural reorganizations, ; cf. the list in Gg §48.
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  33. A Set Theory with Frege-Russell Cardinal Numbers.Alan McMichael - 1982 - Philosophical Studies 42 (2):141 - 149.
    A frege-Russell cardinal number is a maximal class of equinumerous classes. Since anything can be numbered, A frege-Russell cardinal should contain classes whose members are cardinal numbers. This is not possible in standard set theories, Since it entails that some classes are members of members of themselves. However, A consistent set theory can be constructed in which such membership circles are allowed and in which, Consequently, Genuine frege-Russell cardinals can be defined.
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  34. Berka vs. Frege: několik poznámek.Jaroslav Peregrin - 1999 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 6 (4):410-413.
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  35. Jan Dejnožka: The Ontology of the Analytic Tradition and its Origins (Realism and Identity in Frege, Russell, Wittgenstein and Quine), Littlefield Adams Books, Maryland, 1996.Jaroslav Peregrin - manuscript
    Existuje překvapivě málo knih, které by se pokoušely o syntetizující pohled na analytickou filosofii. Je ovšem pravda, že ve druhé polovině našeho století se soubor filosofů, kteří se k analytické filosofii hlásí nebo kteří k ní bývají řazeni, stává natolik různorodý, že se jakákoli syntéza stává problematickou; překvapivě málo syntetizujících prací existuje ale i o ‘klasické’ analytické filosofii, to jest o analytické filosofii období zhruba od konce devatenáctého století do poloviny století dvacátého. Dejnožkova kniha je jednou z těch mála, které (...)
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  36. Frege-Russell Numbers: Analysis or Explication?Erich Reck - 2007 - In The Analytic Turn. London: 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 reconstructions, 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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  37. Frege's Natural Numbers: Motivations and Modifications.Erich Reck - 2005 - In Michael Beaney & Erich Reck (eds.), Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. III. London: Routledge. pp. 270-301.
    Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the motivations (...)
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  38. Logic and Arithmetic.Hartley Slater - manuscript
    Since there are non-sortal predicates Frege’s attempt to derive Arithmetic from Logic stumbles at its very first step. There are properties without a number, so the contingency of that condition shows Frege’s definition of zero is not obtainable from Logic. But Frege made a crucial mistake about concepts more generally which must be remedied, before we can be clear about those specific concepts which are numbers.
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  39. General Assessments and Historical Accounts of Frege's Philosophy.Hans D. Sluga (ed.) - 1993 - Garland.
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  40. Logic and Foundations of Mathematics in Frege's Philosophy.Hans D. Sluga (ed.) - 1993 - Garland.
    The four volumes of this collection bring together some of the major contributions to the literature on Gottlob Frege (1848-1925), one of the most formative influences on the course of philosophy during the last hundred years. The first volume provided general assessments of Frege's work and examined its historical context. The present volume deals with Frege's contributions to logic and the foundations of mathematics. The essays are arranged in order of their first publication, providing insight into the historical evolution of (...)
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  41. Meaning and Ontology in Frege's Philosophy.Hans D. Sluga (ed.) - 1993 - Garland.
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  42. Frege Versus Cantor and Dedekind: On the Concept of Number.William Tait - manuscript
    There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, (...)
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  43. Frege Proof System and TNC°.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709 - 738.
    A Frege proof systemFis any standard system of prepositional calculus, e.g., a Hilbert style system based on finitely many axiom schemes and inference rules. An Extended Frege systemEFis obtained fromFas follows. AnEF-sequence is a sequence of formulas ψ1, …, ψκsuch that eachψiis either an axiom ofF, inferred from previous ψuand ψv by modus ponens or of the formq↔ φ, whereqis an atom occurring neither in φ nor in any of ψ1,…,ψi−1. Suchq↔ φ, is called an extension axiom andqa new extension (...)
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  44. Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects.Kai F. Wehmeier - 1999 - Synthese 121 (3):309-328.
    In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T (...)
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  45. Frege's Mathematical Setting.Mark Wilson - unknown
    This survey article describes Frege's celebrated foundational work against the context of other late nineteenth century approaches to introducing mathematically novel "extension elements" within both algebra and geometry.
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  46. Lost on the Way From Frege to Carnap: How the Philosophy of Science Forgot the Applicability Problem.Torsten Wilholt - 2006 - Grazer Philosophische Studien 73 (1):69-82.
    This paper offers an explanation of how philosophy of science in the second half of the 20th century came to be so conspicuously silent on the problem of how to explain the applicability of mathematics. It examines the idea of the early logicists that the analyticity of mathematics accounts for its applicability, and how this idea was transformed during Carnap's efforts to establish a consistent and substantial philosophy of mathematics within the larger framework of Logical Empiricism. I argue that at (...)
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  47. Hans Sluga (Ed.), The Philosophy of Frege. A Four-Volume Collection of Scholarly Articles on All Aspects of Frege's Philosophy, Vol.1: General Assessments and Historical Accounts of Frege's Philosophy, Vol.2: Logic and Foundations of Mathematics in Frege's Philosophy, Vol.3: Meaning and Ontology in Frege's Philosophy, Vol.4: Sense and Reference in Frege's Philosophy. [REVIEW]Jan Wolenński - 1997 - Erkenntnis 46 (3):407-410.
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  48. Frege: Tradition & Influence.Crispin Wright (ed.) - 1984 - Blackwell.
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Frege: Philosophy of Language
  1. Conceptos clave de la filosofía de Gottlob Frege: Una introducción.Alejandro Villamor-Iglesias - 2022 - Cuestiones de Filosofía 8.
    El presente artículo tiene como principal objetivo introducir al lector algunos de los conceptos fundamentales de la filosofía de Gottlob Frege. Estos son: el binomio sentido/referencia, el valor veritativo de oraciones con elementos no referenciales, la distinción entre pensar, juzgar y aseverar, su concepción de los indéxicos y los demostrativos, así como su defensa de la existencia de un tercer reino. En algunos de ellos se mostrarán algunas problemáticas asociadas que han sido destacados por pensadores de renombre. Tal es el (...)
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  2. Frege and Semantics.Richard Heck & Robert May - 2006 - In Ernest Lepore & Barry C. Smith (eds.), The Oxford Handbook of Philosophy of Language. Oxford University Press.
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1 — 50 / 2387