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  1. Platonism in Lotze and Frege Between Psyschologism and Hypostasis.Nicholas Stang - 2019 - In Sandra Lapointe (ed.), Logic from Kant to Russell. Routledge. pp. 138–159.
    In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...)
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  2. Gottlob Frege: del Platonismo a la Fenomenología.Mario Ariel González Porta - 2015 - Revista de Humanidades de Valparaíso 4:21.
    El hecho de que Frege remita a la psicología el problema respecto a cómo se capturan pensamientos, ha llevado a que se imponga entre los críticos la idea de que toda consideración de la subjetividad está ausente en este autor. Como consecuencia de lo anterior, existe un cierto modo de concebir la relación entre Frege y Husserl como un hiato absoluto entre ambos autores respecto al punto mencionado anteriormente. En la presente contribución se defiende una visión en extremo diferente, a (...)
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  3. Was Frege a Realist? And, If so, in What Sense?Fred Wilson - 2014 - In Javier Cumpa, Greg Jesson & Guido Bonino (eds.), Defending Realism: Ontological and Epistemological Investigations. De Gruyter. pp. 141-196.
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  4. 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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  5. Frege's Changing Conception of Number.Kevin C. Klement - 2012 - Theoria 78 (2):146-167.
    I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...)
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  6. A Definição Do Zero Em Frege: O Compromisso Do Platonismo Fregeano Com a "Eternidade" de Bolzano.Walter Gomide - 2011 - Dissertatio 33:299-315.
    Neste artigo, tento mostrar como o Platonismo de Frege relaciona-se muito intimamente com a noção de eternidade de Bolzano. Compreendida como o domínio total de variação do tempo, a eternidade de Bolzano nos oferece um interessante instrumento para estipular o que é eterno: um objeto é eterno se é imutável em relação ao fluxo do tempo. Desta forma, a definição do zero proposta por Frege faz uso tácito de tal noção, na medida em que o zero é definido como “o (...)
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  7. Frege's Definition of Number: No Ontological Agenda?Edward Kanterian - 2010 - Hungarian Philosophical Review 54 (4):76-92.
    Joan Weiner has argued that Frege’s definitions of numbers constitute linguistic stipulations that carry no ontological commitment: they don’t present numbers as pre-existing objects. This paper offers a critical discussion of this view, showing that it is vitiated by serious exegetical errors and that it saddles Frege’s project with insuperable substantive difficulties. It is first demonstrated that Weiner misrepresents the Fregean notions of so-called Foundations-content, and of sense, reference, and truth. The discussion then focuses on the role of definitions in (...)
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  8. Frege and Numbers as Self-Subsistent Objects.Gregory Lavers - 2010 - Discusiones Filosóficas 11 (16):97-118.
    This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege’s project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett’s interpretation of §§55-61 of Grundlagen. These sections fall under the heading ‘Every number is a self-subsistent (...)
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  9. Frege's Context Principle and Reference to Natural Numbers.Øystein Linnebo - 2009 - In Sten Lindström (ed.), Logicism, Intuitionism, and Formalism: What Has Become of Them. Springer.
    Frege proposed that his Context Principle—which says that a word has meaning only in the context of a proposition—can be used to explain reference, both in general and to mathematical objects in particular. I develop a version of this proposal and outline answers to some important challenges that the resulting account of reference faces. Then I show how this account can be applied to arithmetic to yield an explanation of our reference to the natural numbers and of their metaphysical status.
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  10. Why and How Platonism?Guillermo Rosado Haddock - 2007 - Logic Journal of the IGPL 15 (5-6):621-636.
    Probably the best arguments for Platonism are those directed against its rival philosophies of mathematics. Frege's arguments against formalism, Gödel's arguments against constructivism and those against the so-called syntactic view of mathematics, and an argument of Hodges against Putnam are expounded, as well as some arguments of the author. A more general criticism of Quine's views follows. The paper ends with some thoughts on mathematics as a sort of Platonism of structures, as conceived by Husserl and essentially endorsed by the (...)
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  11. Frege, as-If Platonism, and Pragmatism.Robert Arp - 2005 - Journal of Critical Realism 4 (1):1-27.
    This paper is divided into two main sections. In the first, I attempt to show that the characterization of Frege as a redundancy theorist is not accurate. Using one of Wolfgang Carl's recent works as a foil, I argue that Frege countenances a realm of abstract objects including truth, and that Frege's Platonist commitments inform his epistemology and embolden his antipsychologistic project. In the second section, contrasting Frege's Platonism with pragmatism, I show that even though Frege's metaphysical position concerning truth (...)
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  12. The Pragmatic Value of Frege's Platonism for the Pragmatist.Robert Arp - 2005 - Journal of Speculative Philosophy 19 (1):22-41.
  13. Our Knowledge of Numbers as Self-Subsistent Objects.William Demopoulos - 2005 - Dialectica 59 (2):141–159.
    A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...)
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  14. Frege on Numbers: Beyond the Platonist Picture.Erich H. Reck - 2005 - The Harvard Review of Philosophy 13 (2):25-40.
    Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws of (...)
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  15. Frege, Boolos, and Logical Objects.David J. Anderson & Edward N. Zalta - 2004 - Journal of Philosophical Logic 33 (1):1-26.
    In this paper, the authors discuss Frege's theory of "logical objects" and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for (...)
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  16. Rieger's Problem with Frege's Ontology.Nicholas Denyer - 2003 - Analysis 63 (2):166–170.
  17. L’Existence des Objets Logiques Selon Frege.François Rivenc - 2003 - Dialogue 42 (2):291-320.
    Un trait du langage qui menace de saper la sûreté de la pensée est sa tendance à former des noms propres auxquels aucun objet ne correspond. [...] Un exemple particulièrement remarquable de cela est la formation d’un nom propre selon le schéma «l’extension du concept a», par exemple «l’extension du concept étoile». À cause de l’article défini, cette expression semble désigner un objet; mais il n’y a aucun objet pour lequel cette expression pour-rait être une désignation appropriée. De là les (...)
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  18. Why Frege Would Not Be a Neo‐Fregean.Marco Ruffino - 2003 - Mind 112 (445):51-78.
    In this paper, I seek to clarify an aspect of Frege's thought that has been only insufficiently explained in the literature, namely, his notion of logical objects. I adduce some elements of Frege's philosophy that elucidate why he saw extensions as natural candidates for paradigmatic cases of logical objects. Moreover, I argue (against the suggestion of some contemporary scholars, in particular, Wright and Boolos) that Frege could not have taken Hume's Principle instead of Axiom V as a fundamental law of (...)
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  19. Individuating Abstract Objects: The Methodologies of Frege and Quine.Dirk Greimann - 2001 - History of Philosophy & Logical Analysis 4.
    According to Frege, the introduction of a new sort of abstract object is methodologically sound only if its identity conditions have been satisfactorily explained. Ironically, this ontological restriction has come to be known by Quine's criticism of Frege's intensional semantics, as the precept "No entity without identity." The aim of the paper is to reconstruct Frege's methodology of the introduction of abstract objects in detail, and to defend it against the more restrictive methodology underlying Quine's criticism of the recognition of (...)
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  20. Syntactic Reductionism.Richard Heck - 2000 - Philosophia Mathematica 8 (2):124-149.
    Syntactic Reductionism, as understood here, is the view that the ‘logical forms’ of sentences in which reference to abstract objects appears to be made are misleading so that, on analysis, we can see that no expressions which even purport to refer to abstract objects are present in such sentences. After exploring the motivation for such a view, and arguing that no previous argument against it succeeds, sentences involving generalized quantifiers, such as ‘most’, are examined. It is then argued, on this (...)
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  21. On Frege's Alleged Platonism.V. Kolman - 2000 - Filosoficky Casopis 48 (4):577-599.
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  22. Frege in Context.Delbert Pard Reed - 2000 - Dissertation, University of Minnesota
    In Part One of this dissertation I examine the relationship between reason and objectivity in Frege's thought, concentrating on the question of whether or not Frege should be interpreted as a platonist. By platonism I mean the view that objects such as numbers or propositions are objective, non-spatial and timeless, existing in a realm distinct from the external world of physical objects and the internal realm of the mind; and that statements about or involving such objects are true independently of (...)
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  23. Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory.Edward N. Zalta - 1999 - Journal of Philosophical Logic 28 (6):619-660.
    In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...)
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  24. Platonism and Metaphor in the Texts of Mathematics: Gödel and Frege on Mathematical Knowledge.Clevis Headley - 1997 - Man and World 30 (4):453-481.
    In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on (...)
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  25. Frege's Notion of Logical Objects.Marco Antonio Caron Ruffino - 1996 - Dissertation, University of California, Los Angeles
    In the dissertation I seek to clarify an aspect of Frege's thought that has been insufficiently explained in the literature, namely, his notion of logical object. It is well known that the core of Frege's philosophical enterprise up to Grundgesetze der Arithmetik was the reduction of arithmetic to logic. Since Frege regarded numbers as objects, logic must have an ontological basis, i.e., an adequate class of objects to which numbers are reducible. These objects are, for Frege, extensions of concepts and (...)
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  26. Burge's Literal Interpretation of Frege.Joan Weiner - 1995 - Mind 104 (415):585-597.
  27. Realism Bei Frege: Reply to Burge.Joan Weiner - 1995 - Synthese 102 (3):363 - 382.
    Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings (...)
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  28. Dummett's Critique of Wright's Attempt to Resuscitate Frege.Bob Hale - 1994 - Philosophia Mathematica 2 (2):122-147.
    Michael Dummett mounts, in Frege: Philosophy of Mathematics, a concerted attack on the attempt, led by Crispin Wright, to salvage defensible versions of Frege's platonism and logicism in which Frege's criterion of numerical identity plays a leading role. I discern four main strands in this attack—that Wright's solution to the Caesar problem fails; that explaining number words contextually cannot justify treating them as enjoying robust reference; that Wright has no effective counter to ontological reductionism; and that the attempt is vitiated (...)
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  29. Frege on Knowing the Third Realm.Tyler Burge - 1992 - Mind 101 (404):633-650.
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  30. Frege, Wittgenstein, and Platonism in Mathematics.Erich H. Reck - 1992 - Dissertation, University of Chicago
  31. Frege, Objectivity, and the Three Realms.Carol Anne Mickett - 1988 - Dissertation, University of Minnesota
    For Frege the objective is independent of our inner world and the same for everyone. I argue that Frege's demand for objectivity is the result of his concern to make sense out of the practices of science. I point out that science, for Frege, requires agreement and purposeful disagreement among its participants. Without such interaction science reduces to useless, self-indulgent babble. It is the social nature of science that ushers in objectivity. I compare Frege's demand for objectivity with Locke's views (...)
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  32. Frege's Conception of Numbers as Objects. [REVIEW]Linda Wetzel - 1988 - Noûs 22 (1):147-149.
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  33. Was Frege a Platonist?Pirmin Stekeler-Weithofer & W. P. Mendonça - 1987 - Ratio (Misc.) 29 (2):96-110.
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  34. Frege's Conception of Numbers as Objects. [REVIEW]Gregory Currie - 1985 - British Journal for the Philosophy of Science 36 (4):475-479.
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  35. WRIGHT, C.: "Frege's Conception of Numbers as Objects". [REVIEW]A. Hazen - 1985 - Australasian Journal of Philosophy 63:251.
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  36. Frege's Theory of Number and the Distinction Between Function and Object.Michael Kremer - 1985 - Philosophical Studies 47 (3):313 - 323.
  37. Objectivity, Rationality, and the Third Realm: Justification and the Grounds of Psychologism: A Study of Frege and Popper.Mark Amadeus Notturno - 1985 - Kluwer Academic Publishers.
  38. Frege's Conception of Numbers as Objects. [REVIEW]John P. Burgess - 1984 - Philosophical Review 93 (4):638-640.
  39. Frege's Conception of Numbers as Objects. [REVIEW]Hartry Field - 1984 - Canadian Journal of Philosophy 14 (4):637-662.
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  40. Platonism for Cheap? Crispin Wright on Frege's Context Principle.Hartry Field - 1984 - Canadian Journal of Philosophy 14:637--62.
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  41. WRIGHT, C. "Frege's Conception of Numbers as Objects". [REVIEW]D. Gillies - 1984 - Mind 93:613.
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  42. Frege's Conception of Numbers as Objects. [REVIEW]Donald Gillies - 1984 - Mind 93 (372):613-617.
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  43. Frege's Platonism.Bob Hale - 1984 - Philosophical Quarterly 34 (136):225-241.
  44. I. Interpreting Frege: A Reply to Michael Dummett.Gregory Currie - 1983 - Inquiry: An Interdisciplinary Journal of Philosophy 26 (3):345 – 359.
    Two claims the present author has made about Frege's philosophy are defended against Michael Dummett's criticisms (The Interpretation of Frege's Philosophy and ?Objectivity and Reality in Lotze and Frege?, this journal, 1982). The claim that Frege was concerned primarily with epistemological problems rather than with the theory of meaning, and the claim (this journal, 1978) that the ascription of Wirklichkeit to Thoughts is evidence of Frege's realism, are clarified and defended. Dummett's own characterization of Frege's realism is considered and rejected.
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  45. Frege's Conception of Numbers as Objects.Crispin Wright - 1983 - Aberdeen University Press.
  46. Criteria of Abstractness. The Ontologies of Husserl, Frege and Strawson Against the Background of Classical Metaphysics.Wolfgang Künne - 1982 - In Barry Smith (ed.), Parts and Moments: Studies in Logic and Formal Ontology. Philosophia Verlag. pp. 401--437.
  47. Ii. The Origin of Frege's Realism.Gregory Currie - 1981 - Inquiry: An Interdisciplinary Journal of Philosophy 24 (4):448 – 454.
    An explanation of Frege's change from objective idealism to platonism is offered. Frege had originally thought that numbers are transparent to reason, but the character of his Axiom of Courses of Values undermined this view, and led him to think that numbers exist independently of reason. I then use these results to suggest a view of Frege's mathematical epistemology.
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  48. Are Truth Values Objects?Robert Ray - 1979 - Philosophical Studies 35 (2):199 - 211.
    Both Dummett and Tugendhat seem to conclude that Frege's thesis that truth values are objects which are signified by certain sentences is an assumption which was unjustified even for Frege. In this paper I wish to show that Frege's thesis was one of several assumptions which led Frege to a complex semantic theory for the first order predicate calculus which is surpassed only by Tarski's truth and satisfaction definitions. As such, this thesis receives its justification by being an essential part (...)
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  49. II. Frege as Idealist and Then Realist.Michael D. Resnik - 1979 - Inquiry: An Interdisciplinary Journal of Philosophy 22 (1-4):350-357.
    Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated (...)
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  50. Frege's Realism.Gregory Currie - 1978 - Inquiry: An Interdisciplinary Journal of Philosophy 21 (1-4):218-221.
    In this note the claim is defended that Frege was a realist in the sense that he attributed causal efficacy to certain abstract objects. The arguments of Dummett and Sluga (cf. Inquiry, Vols. 18, 19, and 20 [1975–77]) to the contrary are criticized.
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