Philosophy Gottlob Frege
by
Michael Beaney
  • LAST REVIEWED: 08 October 2015
  • LAST MODIFIED: 29 September 2014
  • DOI: 10.1093/obo/9780195396577-0209

Introduction

Gottlob Frege (b. 1848–d. 1925) was a German mathematician, logician, and philosopher who is generally regarded as one of the founders of the analytic tradition in philosophy—together with Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Frege’s main project was to demonstrate the logicist thesis that arithmetic can be reduced to logic. In attempting to do so, he revolutionized logical theory, creating the first system of modern predicate logic in his first book, Begriffsschrift (1879; the term is often left untranslated: see Main Works). In The Foundations of Arithmetic (Die Grundlagen der Arithmetik, 1884), he offered an informal account of his logicist project, showing how the natural numbers could be defined as extensions of (logically definable) concepts—roughly, what we would now call sets or classes. In Basic Laws of Arithmetic (Grundgesetze der Arithmetik, Vol. 1 [1893], Vol. 2 [1903]), he then set out to demonstrate formally, using his logical system, that arithmetic could be reduced to logic. Between the Foundations and Basic Laws he thought through—and revised—his underlying philosophical ideas, explaining them in three of his most influential essays: “Function and Concept” (1891), “On Sense and Reference” (1892), and “On Concept and Object” (1892). In 1902, however, as the second volume of Basic Laws was in press, Russell wrote to Frege informing him of a contradiction that he had discovered in Frege’s system—now known as Russell’s paradox. Frege attempted to resolve the paradox in a hastily written appendix, but he soon realized that the attempt failed and he abandoned his logicist project. He continued to work on his philosophical and logical ideas, though, planning but never completing a textbook on logic; what survived was eventually published posthumously. In the last years of his life he wrote three essays in a series called “Logical Investigations,” the first of which—“Thought”—has also been much discussed and cited. Frege influenced Russell, Rudolf Carnap (who attended two of his lecture courses), and especially Wittgenstein; however, it was only after his death that the significance of his work began to be widely recognized, and it was not until after the Second World War that his writings began to be translated into English (the only exception being the opening thirty pages of Basic Laws, which had appeared in 1915–1917). Today Frege’s place in the history of philosophy is secure, and interest in his work is still blossoming, not just in Anglo-American analytic philosophy, but also right across the world. (Acknowledgments: I would like to thank Gottfried Gabriel, Robert May, and Kai Wehmeier for comments on the first draft of this article and suggestions for additions.)

General Overviews

Overviews of Frege’s philosophy have been divided into Introductory Books, Introductory Essays, Entries in Reference Works, and More Advanced Works.

Introductory Books

This section is subdivided into Introductory Books in English and Introductory Books in Other Languages.

Introductory Books in English

There are several introductory books on the market. For the beginner, Weiner 2004 is recommended, followed by Kenny 1995 and Noonan 2001. Currie 1982 was the first introductory book published.

  • Currie, Gregory. Frege: An Introduction to His Philosophy. Brighton, UK: Harvester, 1982.

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    This was the first introductory book on Frege, emphasizing his epistemological rather than ontological or semantic concerns.

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    • Kenny, Anthony. Frege. London: Penguin, 1995.

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      This is lucidly written. Kenny sticks quite closely to Frege’s own words so that what he offers is, in effect, a précis of Frege’s main writings. This has the disadvantage, though, that Kenny does not always identify or examine the problematic moves in Frege’s thinking. So the book must be supplemented by more critical accounts.

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      • Noonan, Harold W. Frege: A Critical Introduction. Cambridge, UK: Polity Press, 2001.

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        This book is especially good on Frege’s philosophical logic, clarifying his fundamental distinctions between function and object and between sense and reference.

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        • Weiner, Joan. Frege Explained. Chicago: Open Court, 2004.

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          This is a slightly expanded version of a book that was originally published by Oxford University Press in their old Past Masters series (Joan Weiner, Frege [Oxford: Oxford University Press, 1999]). It focuses on Frege’s logicist project and explains his philosophical ideas in the context of this project.

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          Introductory Books in Other Languages

          Recommended for readers of German are Wille 2013 or Stepanians 2001, followed by Mayer 1996 and Kutschera 1989. Readers of Italian can be recommended Penco 2010 and those who read Chinese Wang 2008.

          • Kutschera, Franz von. Gottlob Frege: Eine Einführung in sein Werk. Berlin: de Gruyter, 1989.

            DOI: 10.1515/9783110853933Save Citation »Export Citation »E-mail Citation »

            For the German-language reader, this is a more advanced introduction than Mayer 1996 and Stepanians 2001. It is about the same length but presupposes knowledge of elementary logic and is written in a more technical style.

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            • Mayer, Verena. Gottlob Frege. Munich: Beck, 1996.

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              This provides a good introduction for the German-language reader, focusing on Frege’s logic and philosophical logic rather than his philosophy of mathematics.

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              • Penco, Carlo. Frege. Rome: Carocci, 2010.

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                This is the best introductory book in Italian, by one of the leading Italian Frege scholars. There are three main chapters, on Frege’s concept of function and the new logic, epistemology and the philosophy of mathematics, and ontology and the philosophy of language. It also includes a useful bibliography, which includes further works in Italian.

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                • Stepanians, Markus S. Gottlob Frege zur Einführung. Hamburg, Germany: Junius, 2001.

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                  For the German-language reader, this provides an alternative to Mayer 1996. They are similar in length and coverage.

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                  • Wang, Lu. 弗雷格思想研究. Shanghai: Commercial Press, 2008.

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                    This is the best account in Chinese of Frege’s philosophy by one of the top Chinese scholars and translators of Frege’s work. The title is translated as “A study in Frege’s thought.”

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                    • Wille, Matthias. Frege: Einführung und Texte. Paderborn, Germany: Wilhelm Fink, 2013.

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                      This is the most recent introductory book in German.

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                      Introductory Essays

                      The pieces selected here offer introductions in a variety of different contexts. Beaney 1997 provides an overview in introducing the selections of Frege’s writings translated in Frege 1997 (cited under Collections of English Translations). Dummett 2001 gives an account of Frege’s main ideas in a companion to analytic philosophy. Potter 2010 provides a biographical sketch of Frege’s life and works in introducing his coedited collection of essays on Frege (see Multiauthored Single-Volume Collections). Beaney 2011 outlines the development of those of Frege’s ideas that are now seen as fundamental in the philosophy of language. Burge 2013 explains Frege’s influence on subsequent philosophy. Beaney, et al. 2010 offers an introduction for the Chinese-language reader. The encyclopedia articles cited under Entries in Reference Works can also be recommended.

                      • Beaney, Michael. “Introduction.” In The Frege Reader. Edited by Michael Beaney, 1–46. Oxford: Blackwell, 1997.

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                        This material contains sections on Frege’s life and works, Frege’s achievement, issues of interpretation, and the translation of “Bedeutung.”

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                        • Beaney, Michael. “Gottlob Frege.” In Philosophy of Language: The Key Thinkers. Edited by Barry Lee, 33–55. London: Continuum, 2011.

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                          Beaney here outlines how Frege’s use of function-argument analysis gave rise to some of his key ideas, such as his distinction between concept and object and between sense and reference.

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                          • Beaney, Michael, Chen Bo, and Koji Nakatogawa. “弗雷格,他的逻辑和他的哲学.” World Philosophy 2 (2010): 64–82.

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                            For the Chinese-language reader, this offers an introduction to Frege’s main ideas in the form of a dialogue. The translation of the title is “Frege: His logic and his philosophy.”

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                            • Burge, Tyler. “Gottlob Frege: Some Forms of Influence.” In The Oxford Handbook of the History of Analytic Philosophy. Edited by Michael Beaney, 355–382. Oxford: Oxford University Press, 2013.

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                              Burge here discusses seven ways in which Frege influenced subsequent philosophy, from his development of logic to his rationalism.

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                              • Dummett, Michael. “Gottlob Frege.” In A Companion to Analytic Philosophy. Edited by A. P. Martinich and David Sosa, 6–20. Oxford: Blackwell, 2001.

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                                Dummett here outlines some of the main ideas of Frege’s philosophy of language and philosophy of mathematics.

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                                • Potter, Michael. “Introduction.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 1–31. Cambridge, UK: Cambridge University Press, 2010.

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                                  Potter here introduces Frege’s work through a biographical sketch.

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                                  Entries in Reference Works

                                  Several encyclopedia articles offer reliable, though brief, outlines of Frege’s ideas. George and Heck 1998, Wehmeier 2006, and Zalta 2012 focus more on his philosophy of mathematics; Klement 2014 offers a more balanced account. Barone and Penco 2006 is in Italian.

                                  • Barone, Francesco, and Carlo Penco. “Frege, Gottlob, 1848–1925.” In Enciclopedia filosofica. Vol. 5. Edited by Fondazione centro studi di filosofici di Gallarate, 4470–4478. Milan: Bompiani, 2006.

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                                    This entry in Italian, originally written by Barone, was updated by Penco in 2006.

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                                    • George, Alexander, and Richard Heck. “Frege, Gottlob, 1848–1925.” In Routledge Encyclopedia of Philosophy. Vol. 3. Edited by Edward Craig, 765–778. London: Routledge, 1998.

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                                      This outlines some of Frege’s main ideas, with five of the ten sections on his logic and philosophy of mathematics. It is also available online.

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                                      • Klement, Kevin C. “Gottlob Frege, 1848–1925.” Internet Encyclopedia of Philosophy. 2014.

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                                        This offers a brief account of Frege’s life and works, logic, philosophy of mathematics, and theory of sense and reference.

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                                        • Wehmeier, Kai. “Frege, Gottlob.” In The Encyclopedia of Philosophy. 2d ed. Edited by Donald Borchert, 725–736. Detroit: Macmillan, 2006.

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                                          Wehmeier briefly outlines Frege’s ideas, with more on his philosophy of mathematics than on the rest of his philosophy.

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                                          • Zalta, Edward N. “Gottlob Frege.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University Press, 2012.

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                                            First published in 1995, and updated in 2012, this contains sections on Frege’s life and influences, logic and philosophy of mathematics, and philosophy of language. It also contains a bibliography and, as a supplement, a complete list of Frege’s writings.

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                                            More Advanced Works

                                            A variety of more advanced works offer different approaches and interpretations. Dummett 1981a (first published in 1973) is the book that finally placed Frege’s thought at the center of debates in analytic philosophy. An influential philosophical text in its own right, but perhaps inevitably as a pioneering work, it gives a one-sided and controversial interpretation of Frege’s philosophy. Frege is seen as a philosopher of language engaged in the project that had emerged in the 1970s as fundamental to philosophy, namely, the construction of a theory of meaning for natural languages. This led to the appearance of several books that took issue with Dummett’s interpretation, most notably Sluga 1980 and Baker and Hacker 1984. Dummett 1981b responds to some of the criticisms that had been made of his first book, and Dummett 1991 is the sequel to this first book in which the author turns to the philosophy of mathematics and, hence, finally corrects the imbalance in the view of Frege that his first book had fostered. Other books, such as Weiner 1990 and Beaney 1996, stress the importance of understanding Frege’s logicist project in explaining his philosophical ideas. Books on Frege that focus on particular aspects of Frege’s work, such as his distinction between sense and reference, are cited in the relevant sections of this article.

                                            • Baker, G. P., and P. M. S. Hacker. Frege: Logical Excavations. Oxford: Blackwell, 1984.

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                                              Written in reaction to Dummett 1981a, (which was originally published in 1973) and from a Wittgensteinian perspective, this does much to correct some of the distortions in Dummett’s interpretation but arguably goes too far in the other direction in seeing much of what Frege thought as “conceptual confusion.” It is especially good, though, on the importance of function-argument analysis in Frege’s philosophy.

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                                              • Beaney, Michael. Frege: Making Sense. London: Duckworth, 1996.

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                                                This work provides an account of the development of Frege’s philosophy from his earliest to his latest works. While focusing on the evolution of his conception of sense, Beaney also locates this evolution in the context of Frege’s logicist project, which is what inspired his philosophical thinking.

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                                                • Dummett, Michael. Frege: Philosophy of Language. 2d ed. London: Duckworth, 1981a.

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                                                  Originally published in 1973. This book pioneered serious work on Frege, although its reading of Frege as a philosopher of language is arguably anachronistic. The book has been included in this subsection of General Overviews, however, because, taken with Dummett 1991, it does indeed provide an overview of most of Frege’s philosophical ideas, even if some of Dummett’s interpretations have been fiercely disputed.

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                                                  • Dummett, Michael. The Interpretation of Frege’s Philosophy. London: Duckworth, 1981b.

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                                                    Dummett reports that he wrote this book “without meaning to” (p. vii) when writing what was originally intended as an introduction to the second edition of his Frege: Philosophy of Language. It evolved, instead, into another book of more than six hundred pages in which Dummett responds to criticisms of his earlier interpretation of Frege and modifies and further develops his account.

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                                                    • Dummett, Michael. Frege: Philosophy of Mathematics. London: Duckworth, 1991.

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                                                      Unlike his first book, this work is much more sensitive to the actual historical development of Frege’s thinking. It is difficult and (semi-)technical in places, but there is no better book on Frege’s philosophy of mathematics. It has contributed enormously to the renaissance of interest in Frege’s logicism that has taken place since the 1980s.

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                                                      • Sluga, Hans. Gottlob Frege. London: Routledge, 1980.

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                                                        This was the first book on Frege that was written in direct opposition to Dummett 1981a (which was originally published in 1973). It seeks to set Frege’s philosophy in historical context, stressing the influences on Frege of earlier German philosophers such as Hermann Lotze. The book was translated into Chinese by Jiang Yi (Beijing: Chinese Social Science Press, 1989).

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                                                        • Weiner, Joan. Frege in Perspective. Ithaca, NY: Cornell University Press, 1990.

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                                                          Like her later introduction to Frege (Weiner 2004, cited under Introductory Books), this book stresses the centrality of Frege’s logicist project to the development of his philosophical ideas. The final chapter, “Elucidations,” is especially recommended in emphasizing the important role that “elucidation” plays in Frege’s philosophy.

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                                                          Anthologies

                                                          This section has been divided into four subsections. The first three concern collections devoted solely to Frege: major (multivolume) collections, single-volume but multiauthored collections, and single-authored collections. The fourth offers a selection of collections on the history of (early) analytic philosophy more generally but which include important papers on Frege.

                                                          Multivolume Collections

                                                          There have been three major collections of papers on Frege’s philosophy: Schirn 1976, Sluga 1993, and Beaney and Reck 2005.

                                                          • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers. 4 vols. London: Routledge, 2005.

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                                                            This contains the most important papers published on Frege between 1986 and 2005, divided into four volumes: Vol. 1 Frege’s Philosophy in Context; Vol. 2, Frege’s Philosophy of Logic; Vol. 3, Frege’s Philosophy of Mathematics; and Vol. 4, Frege’s Philosophy of Thought and Language. Each volume comes with an introduction by the editors, and a general introduction in the first volume explains the selection.

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                                                            • Schirn, Matthias, ed. Studien zu Frege. 3 vols. Stuttgart: Frommann, 1976.

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                                                              This collection brings together papers in both English and German, most of them published for the first time, on all aspects of Frege’s philosophy by most of the key scholars of the time. The three volumes are on Frege’s logic and philosophy of mathematics, his theory of functions and concept of logic, and his distinction between sense and reference.

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                                                              • Sluga, Hans, ed. The Philosophy of Frege. 4 vols. New York: Garland, 1993.

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                                                                This contains papers published up to 1988, including many of the classics from the earliest years of commentary on Frege. It is divided into the following four volumes: 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; and Vol. 4, Sense and Reference in Frege’s Philosophy.

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                                                                Multiauthored Single-Volume Collections

                                                                A number of collections on Frege’s philosophy have been published. Some are on specific aspects of his philosophy, such as his philosophy of mathematics, and these are listed in the relevant sections of this article. Klemke 1968 was the first collection, and Wright 1984 and Haaparanta and Hintikka 1986 were influential collections published in the 1980s. Schirn 1996 marks the point at which Frege’s philosophy of mathematics comes to be generally seen as central to his philosophy as a whole. Potter and Ricketts 2010 was long in production. Most of the chapters were commissioned in the early 1990s by Ricketts. However, more than fifteen years later the book was still advertised as forthcoming, although some of the papers had been published elsewhere and most had been available to other scholars for some time so that responses to those papers were being published before the original papers themselves. Eventually, Potter was asked to coedit the volume and further chapters were commissioned. It is strongly recommended as the best single-volume collection on Frege.

                                                                • Haaparanta, Leila, and Jaakko Hintikka, eds. Frege Synthesized. Dordrecht, The Netherlands: D. Reidel, 1986.

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                                                                  This contains several papers that were quite influential on subsequent interpretations of Frege, most notably, Ricketts’s “Objectivity and Objecthood: Frege’s Metaphysics of Judgment” and Burge’s “Frege on Truth.”

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                                                                  • Klemke, E. D., ed. Essays on Frege. Urbana: University of Illinois Press, 1968.

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                                                                    This was the first collection published, and it is interesting now mainly for historical reasons. It includes translations of three of Frege’s essays: the first and third of his “Logical Investigations” and “On the Foundations of Geometry.”

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                                                                    • Potter, Michael, and Tom Ricketts, eds. The Cambridge Companion to Frege. Cambridge, UK: Cambridge University Press, 2010.

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                                                                      Almost all the papers in this volume can be recommended on the topic they treat, and they are cited in the relevant sections of this article. The different dates of composition need to be kept in mind, however (see the comments made in introducing this section).

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                                                                      • Schirn, Matthias, ed. Frege: Importance and Legacy. Berlin: de Gruyter, 1996.

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                                                                        This contains papers on Frege’s logic and philosophy of mathematics, epistemology, and philosophy of language, though most of them fall into the first category (ten of the sixteen papers). Some of them are cited in the relevant sections of this article.

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                                                                        • Wright, Crispin, ed. Frege: Tradition and Influence. Oxford: Blackwell, 1984.

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                                                                          This contains several papers that were influential in subsequent debates about the interpretation of Frege, most notably, Diamond, “What Does a Concept Script Do?” (see Philosophy of Thought and Language). Originally published as a special issue of Philosophical Quarterly on Frege edited by Wright (Philosophical Quarterly 34.136 [July 1984]; available online by subscription.).

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                                                                          Single-Authored Collections

                                                                          Two of the most influential commentators—Burge and Dummett—have published collections of their papers on Frege (Burge 2005 and Dummett 1991). Their key papers are cited in the relevant sections of this article. Picardi 1994 is a collection in Italian by one of the leading Italian scholars of Frege.

                                                                          • Burge, Tyler. Truth, Thought, Reason: Essays on Frege. Oxford: Clarendon, 2005.

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                                                                            Burge collects all of his previously published papers on Frege in this volume and provides a substantial introduction that offers a useful overview of his interpretations.

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                                                                            • Dummett, Michael. Frege and Other Philosophers. Oxford: Oxford University Press, 1991.

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                                                                              This contains papers that Dummett wrote on Frege between 1976 and 1990, some of which were previously unpublished and most of which make at least some comparison with the work of other philosophers, such as Bolzano, Lotze, Husserl, and Wittgenstein.

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                                                                              • Picardi, Eva. La chimica dei concetti: Linguaggio, logica, psicologia, 1879–1927. Bologna, Italy: Il Mulino, 1994.

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                                                                                Picardi is one of the leading Italian scholars of Frege’s work, and this book includes her early papers in Italian on topics such as Frege’s anti-psychologism, concept and object, and sense and reference. Other, more recent papers, in English or German, are cited in the relevant sections of this article.

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                                                                                Collections on the History of (Early) Analytic Philosophy

                                                                                Beaney 2013 is the most substantial collection on the history of analytic philosophy. Reck 2002 contains several papers not only on Frege, but also on the relationship between Frege and Wittgenstein. Tait 1997 and Floyd and Shieh 2001 also include papers on Frege. The key papers are cited in the relevant sections of this article.

                                                                                • Beaney, Michael, ed. The Oxford Handbook of the History of Analytic Philosophy. Oxford: Oxford University Press, 2013.

                                                                                  DOI: 10.1093/oxfordhb/9780199238842.001.0001Save Citation »Export Citation »E-mail Citation »

                                                                                  This contains several chapters on Frege by Gabriel, Burge, and Heck and May. Other chapters also discuss Frege to some extent, most notably, the chapters by Miller and Diamond.

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                                                                                  • Floyd, Juliet, and Sanford Shieh, eds. Future Pasts: The Analytic Tradition in Twentieth-Century Philosophy. New York: Oxford University Press, 2001.

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                                                                                    This contains two papers on Frege: Goldfarb’s “Frege’s Conception of Logic” and Weiner’s “Theory and Elucidation.”

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                                                                                    • Reck, Erich H., ed. From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. New York: Oxford University Press, 2002.

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                                                                                      Part 1 of this volume contains an essay by Reck on the influence of Frege on Wittgenstein, and the relationship between the ideas of the two philosophers is further explored in Part 3 with essays by Goldfarb, Macbeth, Ricketts, and Diamond. Part 2 contains essays more specifically on Frege, including two on truth by Sluga and Shieh.

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                                                                                      • Reck, Erich H., ed. The Historical Turn in Analytic Philosophy. Basingstoke, UK: Palgrave Macmillan, 2013.

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                                                                                        This includes three essays that contain discussions of Frege: by Heis on Frege, Lotze, and Boole, by Reck on Frege and Dedekind, and by Beaney on the idea of rational reconstruction.

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                                                                                        • Tait, William W., ed. Early Analytic Philosophy: Frege, Russell, Wittgenstein. Chicago: Open Court, 1997.

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                                                                                          This has five papers on Frege, including Burge’s “Frege on Knowing the Third Realm,” Reck’s “Frege’s Influence on Wittgenstein,” Tait’s “Frege versus Cantor and Dedekind,” and Weiner’s “Has Frege a Philosophy of Language?”

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                                                                                          Biographies

                                                                                          A full-length biography of Frege is currently available only in German: Kreiser 2001. The longest account in English is Bynum 1972. Potter 2010 provides a biographical sketch, and Thiel and Beaney 2005 provides a chronology of the main events in Frege’s life. Wehmeier and Schmidt am Busch 2005 tells the tragic tale of Frege’s Nachlass, which may yet have a happy ending . . .

                                                                                          • Bynum, Terrell Ward. “On the Life and Work of Gottlob Frege.” In Conceptual Notation and Related Articles. Edited by Terrell Ward Bynum, 1–54. Oxford: Oxford University Press, 1972.

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                                                                                            Published more than forty years ago, this remains the most detailed account of Frege’s life in English. It was reprinted in 2000. Unfortunately, however, the errors in the account (understandable at the time it was written) were not corrected.

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                                                                                            • Kreiser, Lothar. Gottlob Frege: Leben—Werk—Zeit. Hamburg, Germany: Felix Meiner, 2001.

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                                                                                              This contains a wealth of details about Frege’s life, not all of which are philosophically relevant, and the account is long (more than six hundred pages), sometimes rambling, and poorly organized. Treated as a biographical resource rather than a biography, however, it is indispensable. Kreiser spent a lifetime collecting the data, mostly in the oppressive academic climate of the former East Germany.

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                                                                                              • Potter, Michael. “Introduction.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 1–31. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                Potter outlines Frege’s life and work in this introduction.

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                                                                                                • Thiel, Christian, and Michael Beaney. “Frege’s Life and Work: Chronology and Bibliography.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. Edited by Michael Beaney and Erich H. Reck, 23–39. London: Routledge, 2005.

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                                                                                                  This contains both a chronology of the main events in Frege’s life (correcting Bynum’s account) and a complete list of Frege’s publications.

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                                                                                                  • Wehmeier, Kai F., and Hans-Christoph Schmidt am Busch. “The Quest for Frege’s Nachlass.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. Edited by Michael Beaney and Erich H. Reck, 54–68. London: Routledge, 2005.

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                                                                                                    It has long been assumed that Frege’s Nachlass was destroyed by an Allied bombing raid during the Second World War. The evidence for this is reassessed. Translation by Kai Wehmeier. The German text is “Auf der Suche nach Freges Nachlass,” in Gottlob Frege: Werk und Wirkung, edited by Gottfried Gabriel and Uwe Dathe (Paderborn, Germany: Mentis, 2000), pp. 267–81.

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                                                                                                    Bibliographies

                                                                                                    Bibliographies of Frege’s own works can be found in Bynum and Bynum 1972, Gabriel 1983, Thiel and Beaney 2005, and Zalta 2012. Bibliographies of secondary literature can be found in Bynum and Bynum 1972, Beaney and Reck 2005, and Potter and Ricketts 2010.

                                                                                                    • Beaney, Michael, and Erich H. Reck. “Introduction.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. Edited by Michael Beaney and Erich H. Reck, 5–19. London: Routledge, 2005.

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                                                                                                      This contains a bibliography of all books (monographs and collections) published on Frege in English or German and a selection of those in Italian.

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                                                                                                      • Bynum, Terrell Ward, and Aline W. Bynum. “A Frege Bibliography, 1873–1966.” In Conceptual Notation and Related Articles. Edited by Terrell Ward Bynum, 239–287. Oxford: Oxford University Press, 1972.

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                                                                                                        This bibliography, covering the period from Frege’s doctoral dissertation of 1873 to 1966, is divided into three sections on Frege’s works, secondary sources, and additional sources.

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                                                                                                        • Gabriel, Gottfried. “Bibliographie der Werke Freges.” In Nachgelassene Schriften. 2d ed. Edited by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach, 303–314. Hamburg, Germany: Felix Meiner, 1983.

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                                                                                                          This contains a complete list of Frege’s works, including translations, from 1873 to 1980.

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                                                                                                          • Potter, Michael, and Tom Ricketts. “Bibliography.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 602–627. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                            This bibliography contains works by Frege and other works.

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                                                                                                            • Thiel, Christian, and Michael Beaney. “Frege’s Life and Work: Chronology and Bibliography.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. Edited by Michael Beaney and Erich H. Reck, 23–39. London: Routledge, 2005.

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                                                                                                              This contains a complete list of Frege’s publications and of the collections in German and English in which they appear.

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                                                                                                              • Zalta, Edward N. “Chronological Catalog of Frege’s Work.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University Press, 2012.

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                                                                                                                Included as a supplement to Zalta 2012 (cited under Entries in Reference Works), this gives a list of all Frege’s works.

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                                                                                                                Primary Literature

                                                                                                                This section has been divided into three subsections on Frege’s three Main Works, on his four Seminal Essays, and on the various Collections of Frege’s Works.

                                                                                                                Main Works

                                                                                                                Frege published three main works in his lifetime: Begriffsschrift (1879), Die Grundlagen der Arithmetik (1884), and Grundgesetze der Arithmetik (1893, 1903).

                                                                                                                Begriffsschrift

                                                                                                                Begriffsschrift was Frege’s first book, published in 1879. “Begriffsschrift” (literally, “concept-script”) is the name that Frege gave to his logical symbolism. His book is generally regarded as inaugurating modern logic. Inventing a notation for quantification, Frege presents the first system of predicate logic and also offers an axiomatization of propositional logic, thereby integrating the two traditional parts of logic, syllogistic theory and propositional logic, into one comprehensive theory. In Part 3 he uses his logical system to provide the first logical analysis of mathematical induction. Frege’s achievements in Begriffsschrift opened up the possibility of demonstrating the logicist claim that arithmetic is reducible to logic. There are two complete translations of Begriffsschrift: the one by Bynum (Frege 1972) comes with substantial editorial material, and it can be recommended over the one by Bauer-Mengelberg (Frege 1967). There are two translations of (most of) Part 1, by Geach (Frege 1980; originally published in 1952) and Beaney (Frege 1997). The latter comes with a translation of the preface as well, together with a summary of Part 3 and helpful editorial material.

                                                                                                                • Frege, Gottlob. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle, Germany: L. Nebert, 1879.

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                                                                                                                  This is the original German edition. It is reprinted in Begriffsschrift und andere Aufsätze, edited by Ignacio Angellelli (see German Collections).

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                                                                                                                  • Frege, Gottlob. “Begriffsschrift.”. In From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Translated by S. Bauer-Mengelberg Edited by Jean van Heijenoort, 5–82. Cambridge, MA: Harvard University Press, 1967.

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                                                                                                                    This was the first complete translation.

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                                                                                                                    • Frege, Gottlob. “Conceptual Notation.” In Conceptual Notation and Related Articles. Translated by Terrell Ward Bynum. Edited by Terrell Ward Bynum, 101–203. Oxford: Oxford University Press, 1972.

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                                                                                                                      This translation is accompanied by substantial editorial material, the translation of three short pieces that Frege wrote shortly after Begriffsschrift, and the reviews of the book. It was reprinted, unrevised, in 2000.

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                                                                                                                      • Frege, Gottlob. “Begriffsschrift.” In Translations from the Philosophical Writings of Gottlob Frege. 3d ed. Translated by P. T. Geach. Edited by Peter Geach and Max Black, 1–20. Oxford: Blackwell, 1980.

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                                                                                                                        Originally published in 1952. Includes most of Part 1 (§§1–12). This was the first translation of any substantial part of Begriffsschrift.

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                                                                                                                        • Frege, Gottlob. “Begriffsschrift.” In The Frege Reader. Translated by Michael Beaney. Edited by Michael Beaney, 47–78. Oxford: Blackwell, 1997.

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                                                                                                                          This translation of the preface and Part 1 comes with a summary of Part 3 and editorial material. It supersedes the 1952 translation by Geach (Frege 1980).

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                                                                                                                          The Foundations of Arithmetic

                                                                                                                          Die Grundlagen der Arithmetik (The foundations of arithmetic), published in 1884, is now widely recognized as a masterpiece of analytic philosophy. Frege here offers an informal account of his logicist project. In the first half he provides a critique of earlier views of arithmetic, and in the second half he presents his own positive account, based on his claim that number statements involve assertions about concepts. There are two complete English translations, of which only the one by Austin (Frege 1953) can be recommended. A partial translation is provided by Beaney (Frege 1997).

                                                                                                                          • Frege, Gottlob. Die Grundlagen der Arithmetik. Breslau, Germany: W. Koebner, 1884.

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                                                                                                                            This is the original German edition. Reprinted in a centenary critical edition, edited by Christian Thiel (Hamburg, Germany: Felix Meiner, 1986).

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                                                                                                                            • Frege, Gottlob. The Foundations of Arithmetic. 2d ed. Translated by J. L. Austin. Oxford: Blackwell, 1953.

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                                                                                                                              Originally published in 1950. This was the first translation of Frege’s work. Although it renders some of Frege’s sentences too freely, it is still the only complete translation that can be recommended. There is a more recent translation by Dale Jacquette, but this is unreliable; see the review by Kremer in the Notre Dame Philosophical Reviewsonline.

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                                                                                                                              • Frege, Gottlob. “The Foundations of Arithmetic.” In The Frege Reader. Translated by Michael Beaney. Edited by Michael Beaney, 84–129. Oxford: Blackwell, 1997.

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                                                                                                                                This provides a more accurate translation than Austin’s, but of only part of the text: the introduction, §§ 1–4, 45–69, 87–91, 104–109. Beaney provides summaries of the rest of the text, however.

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                                                                                                                                Basic Laws of Arithmetic

                                                                                                                                Grundgesetze der Arithmetik (Frege 1893–1903) is Frege’s magnum opus, seeking to demonstrate formally what he had attempted to show, informally, in the Foundations. Volume 1 was published in 1893, Volume 2 in 1903. A short selection from this work was the first of Frege’s writings to be published in English translation (in 1915–1917) (see Frege 1915), and other selections appeared subsequently in 1952 (Frege 1952), 1964 (Frege 1964), and 1997 (Frege 1997). But it was only in 2013 that a complete translation was published, by Ebert and Rossberg (Frege 2013). This will be the definitive translation for the foreseeable future.

                                                                                                                                • Frege, Gottlob. Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet. 2 vols. Jena, Germany: H. Pohle, 1893–1903.

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                                                                                                                                  This was the original German edition, in two volumes. They were reprinted together in 1962 (Hildesheim, Germany: Georg Olms), and this edition was reprinted in 1998 with corrigenda by C. Thiel.

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                                                                                                                                  • Frege, Gottlob. “The Fundamental Laws of Arithmetic.” Translated by P. E. B. Jourdain and J. Stachelroth. The Monist 25 (1915): 481–494.

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                                                                                                                                    Published in three instalments in The Monist (continued in Vol. 26 [1916]: 182–199 and Vol. 27 [1917]: 114–127), this was the first translation of any of Frege’s writings, and contains the preface, introduction, and §§ 1–7 of Volume 1. Most of it was subsequently reprinted in Frege 1952, pp. 137–158.

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                                                                                                                                    • Frege, Gottlob. “Translation of Parts of Frege’s Grundgesetze der Arithmetik.” In Translations from the Philosophical Writings of Gottlob Frege. Edited by Peter Geach and Max Black, 137–244. Oxford: Blackwell, 1952.

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                                                                                                                                      As well as most of Jourdain and Stachelroth’s translation of the opening pages of Volume 1 (Frege 1915), this also includes, from Volume 2, material on definitions (§§ 56–67, 139–144, 146–147; translated by P. T. Geach), Frege’s critique of formalism (§§ 86–137; translated by Max Black), and the appendix seeking to respond to Russell’s paradox (translated by P. T. Geach).

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                                                                                                                                      • Frege, Gottlob. The Basic Laws of Arithmetic: Exposition of the System. Translated and edited by Montgomery Furth. Los Angeles: University of California Press, 1964.

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                                                                                                                                        This contains a translation of the preface, introduction, and §§ 1–52 of Volume 1, and the appendix to Volume 2. It also includes a substantial introduction by Furth.

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                                                                                                                                        • Frege, Gottlob. “Grundgesetze der Arithmetik: Selections.” In The Frege Reader. Edited by Michael Beaney, 194–223, 258–289. Oxford: Blackwell, 1997.

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                                                                                                                                          This contains most of the preface; introduction; and §§ 1–7, 26–29, 32–33 from Volume 1 (translated by M. Beaney) and §§ 55–67, 138–147, and the appendix from Volume 2 (translated by P. T. Geach) together with helpful editorial material.

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                                                                                                                                          • Frege, Gottlob. Basic Laws of Arithmetic. Translated and edited by Philip A. Ebert and Marcus Rossberg, with Crispin Wright. Oxford: Oxford University Press, 2013.

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                                                                                                                                            This is the first complete translation of Frege’s Grundgesetze, with substantial editorial material. The translation was a major undertaking that took a decade of work under the direction of Wright and with an international team of consultants advising on the project.

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                                                                                                                                            Seminal Essays

                                                                                                                                            As well as his three books, Frege published a number of important essays, of which the four most influential are “Funktion und Begriff” (Frege 1891), “Über Sinn und Bedeutung” (Frege 1892a), “Über Begriff und Gegenstand” (Frege 1892b), and “Der Gedanke: Eine logische Untersuchung” (Frege 1918). All four essays are available in English translation. The first three explain the philosophical ideas that underlie his logic and philosophy of mathematics, and the fourth elucidates his conception of truth and thought. The translation of “Über Sinn und Bedeutung” has varied. “Sinn” is uncontroversially rendered as “sense,” but the translation of “Bedeutung” has been highly controversial: it has been rendered as “reference,” “meaning,” “denotation,” “nominatum,” and “indication,” in approximate order of popularity. “Reference” is used in this article. For a discussion of the problem of translating “Bedeutung,” see Beaney 1997 (cited under Sense and Reference).

                                                                                                                                            Collections of Frege’s Works

                                                                                                                                            Various collections of Frege’s works are available. They are divided into German Collections and Collections of English Translations.

                                                                                                                                            German Collections

                                                                                                                                            Most of the writings that Frege published in his lifetime, other than his three books (for which see Main Works), are collected in Frege 1967, with additional pieces (as well as Begriffsschrift) in Frege 1964. A selection of five of these papers can be found in Frege 1962 and Frege 2007. What survived of Frege’s Nachlass appears in Frege 1983 (originally published in 1969), from which a selection was made in Frege 2001 (originally published in 1971). His correspondence was published in Frege 1976 and a selection made in Frege 1980.

                                                                                                                                            • Frege, Gottlob. Funktion, Begriff, Bedeutung: Fünf logische Studien. Edited by G. Patzig. Göttingen, Germany: Vandenhoeck & Ruprecht, 1962.

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                                                                                                                                              This includes “Funktion und Begriff,” “Über Sinn und Bedeutung,” and “Über Begriff und Gegenstand.” Though still available, this has now been superseded by Frege 2007.

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                                                                                                                                              • Frege, Gottlob. Begriffsschrift und andere Aufsätze. Edited by Ignacio Angelelli. Hildesheim, Germany: Georg Olms, 1964.

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                                                                                                                                                This contains Frege’s Begriffsschrift together with some shorter pieces that Frege wrote explaining his logical notation and its use.

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                                                                                                                                                • Frege, Gottlob. Kleine Schriften. Edited by Ignacio Angelelli. Hildesheim, Germany: Georg Olms, 1967.

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                                                                                                                                                  This contains most of the writings (excluding his books) published by Frege in his lifetime. Translated as Frege 1984 (cited under Collections of English Translations).

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                                                                                                                                                  • Frege, Gottlob. Wissenschaftlicher Briefwechsel. Edited by G. Gabriel, H. Hermes, F. Kambartel, C. Thiel, and A. Veraart. Hamburg, Germany: Felix Meiner, 1976.

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                                                                                                                                                    This collects together all the correspondence known at the time. Other correspondence has been discovered and published subsequently. Selection in Frege 1980. Abridged and translated as Frege 1980a (cited under Collections of English Translations).

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                                                                                                                                                    • Frege, Gottlob. Gottlob Freges Briefwechsel. Edited by G. Gabriel, F. Kambartel, and C. Thiel. Hamburg, Germany: Felix Meiner, 1980.

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                                                                                                                                                      This selection, from Frege 1976, mainly contains the correspondence with Hilbert, Liebmann, Husserl, and Russell.

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                                                                                                                                                      • Frege, Gottlob. Nachgelassene Schriften. 2d ed. Edited by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach. Hamburg, Germany: Felix Meiner, 1983.

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                                                                                                                                                        First published in 1969, this contains all of Frege’s Nachlass that survived after the Second World War. The editors provide an account of this in their introductory material. The second edition, revised and enlarged, includes correspondence subsequently discovered. The first edition was translated as Frege 1979 (cited under Collections of English Translations). Selection in Frege 2001.

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                                                                                                                                                        • Frege, Gottlob. Schriften zur Logik und Sprachphilosophie: Aus dem Nachlaß. 4th ed. Edited by G. Gabriel. Hamburg, Germany: Felix Meiner, 2001.

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                                                                                                                                                          This is a selection from the first (1969) edition of Frege 1983, with emphasis on his writings on logic and philosophy of language. Originally published in 1971.

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                                                                                                                                                          • Frege, Gottlob. Funktion—Begriff—Bedeutung. 2d ed. Edited by Mark Textor. Göttingen, Germany: Vandenhoeck & Ruprecht, 2007.

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                                                                                                                                                            This includes “Funktion und Begriff,” “Über Sinn und Bedeutung,” and “Über Begriff und Gegenstand.” This replaces Frege 1962 and can be recommended instead for the German-language reader, with more up-to-date editorial material.

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                                                                                                                                                            Collections of English Translations

                                                                                                                                                            The first collection of Frege’s writings in English translation was published in 1952 (Frege 1980b). This has now been superseded by Frege 1997, which contains a far greater range of material selected. Frege 1977 is now contained in Frege 1984, which collects together almost all of the writings published in his lifetime, other than his three books. Frege’s Nachlass was published in English translation in 1979 (Frege 1979) and his correspondence in 1980 (Frege 1980a).

                                                                                                                                                            • Frege, Gottlob. Logical Investigations. Edited by P. T. Geach. Translated by P. T. Geach and R. H. Stoothoff. Oxford: Blackwell, 1977.

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                                                                                                                                                              This contains “Thoughts,” “Negation,” and “Compound Thoughts,” all of which were subsequently included in Frege 1984.

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                                                                                                                                                              • Frege, Gottlob. Posthumous Writings. Translated by P. Long and R. White. Oxford: Blackwell, 1979.

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                                                                                                                                                                This is the translation of the first (1969) edition of Frege 1983 (cited under German Collections), though, regrettably, it omits many of the original German editors’ footnotes and other editorial material.

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                                                                                                                                                                • Frege, Gottlob. Philosophical and Mathematical Correspondence. Edited by B. McGuinness. Translated by H. Kaal. Oxford: Blackwell, 1980a.

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                                                                                                                                                                  This is the translation of Frege 1976 (cited under German Collections).

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                                                                                                                                                                  • Frege, Gottlob. Translations from the Philosophical Writings of Gottlob Frege. 3d ed. Translated and edited by Peter Geach and Max Black. Oxford: Blackwell, 1980b.

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                                                                                                                                                                    Originally published in 1952, second edition in 1960. This includes selections from Frege’s Begriffsschrift and Basic Laws of Arithmetic as well as his three essays, “Function and Concept,” “On Concept and Object,” and “On Sense and Reference.” The first and second editions also contained “Negation,” the second of Frege’s “Logical Investigations,” but this was deleted in the third edition since, by then, it had appeared in Frege 1977.

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                                                                                                                                                                    • Frege, Gottlob. Collected Papers on Mathematics, Logic, and Philosophy. Edited by Brian McGuinness. Translated by Max Black, et al. Oxford: Blackwell, 1984.

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                                                                                                                                                                      This is the translation of Frege 1967 (cited under German Collections).

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                                                                                                                                                                      • Frege, Gottlob. The Frege Reader. Edited and with an introduction by Michael Beaney. Oxford: Blackwell, 1997.

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                                                                                                                                                                        This includes selections from Frege’s Begriffsschrift, The Foundations of Arithmetic, and Basic Laws of Arithmetic as well as his four seminal essays, “Function and Concept,” “On Concept and Object,” “On Sense and Reference,” and “Thought,” among other pieces and selections from his Nachlass and correspondence.

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                                                                                                                                                                        Historical Context

                                                                                                                                                                        Since the 1980s interest has grown in the historical context of Frege’s work, and scholars have explored the influences on Frege, the evolution of his thinking, and the influence that he, in turn, had on subsequent philosophy. Sluga 1980 was the first substantial work to place Frege in historical context. The best collection of papers on this is contained in Beaney and Reck 2005, many of which are cited in what follows. Gabriel and Kienzler 1997 and Gabriel and Dathe 2000 contain papers in German on Frege’s life in Jena and his ideas in broader context. Beaney 1996 provides a detailed account of the development of Frege’s philosophy, focusing on his conception of sense, while Kienzler 2009 offers a complementary account, focusing on his distinction between concept and object. Dummett 1991 contains his own papers on some of the relationships between Frege and other philosophers. Beaney 2013 is the most substantial collection of papers on the history of analytic philosophy, in which Frege played such a significant role. This section also contains eight subsections, on particular relationships that Frege had to other mathematicians, logicians, and philosophers and, more specifically, to Husserl, Hilbert, Russell, Wittgenstein, and Carnap. Further information can also be found in the works cited in Biographies.

                                                                                                                                                                        • Beaney, Michael. Frege: Making Sense. London: Duckworth, 1996.

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                                                                                                                                                                          This places the development of Frege’s conception of sense in the context of his logicist project. The first two chapters discuss the logical context and the following two chapters the mathematical context.

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                                                                                                                                                                          • Beaney, Michael, ed. The Oxford Handbook of the History of Analytic Philosophy. Oxford: Oxford University Press, 2013.

                                                                                                                                                                            DOI: 10.1093/oxfordhb/9780199238842.001.0001Save Citation »Export Citation »E-mail Citation »

                                                                                                                                                                            This contains several chapters on Frege and his place in the history of analytic philosophy, which are cited in the relevant sections of this article. This volume is also cited in Collections on the History of (Early) Analytic Philosophy, where further works are recommended.

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                                                                                                                                                                            • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. London: Routledge, 2005.

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                                                                                                                                                                              This is the first of the four-volume collection that includes the most important papers published on Frege between 1986 and 2005 (cited under Anthologies). This volume is divided into three parts: on Frege’s life and work, on Frege and other philosophers, and on Frege’s epistemology and metaphysics (see Epistemology and Metaphysics).

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                                                                                                                                                                              • Dummett, Michael. Frege and Other Philosophers. Oxford: Oxford University Press, 1991.

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                                                                                                                                                                                As noted in Single-Authored Collections, this contains papers that Dummett wrote between 1976 and 1990 comparing Frege’s ideas with the work of other philosophers, such as Bolzano, Lotze, Husserl, and Wittgenstein.

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                                                                                                                                                                                • Gabriel, Gottfried, and Uwe Dathe, eds. Gottlob Frege: Werk und Wirkung. Paderborn, Germany: Mentis, 2000.

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                                                                                                                                                                                  Following on from Gabriel and Kienzler 1997, this contains a range of papers (all in German) on Frege’s ideas and their relationships to the work of others. Some of the key papers in this volume are cited in other sections.

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                                                                                                                                                                                  • Gabriel, Gottfried, and Wolfgang Kienzler, eds. Frege in Jena: Beiträge zur Spurensicherung. Würzburg, Germany: Königshausen & Neumann, 1997.

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                                                                                                                                                                                    This contains various papers, all in German, on Frege’s life in Jena and his relationships with colleagues such as Ernst Abbe, Rudolf Eucken, and Johannes Thomae.

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                                                                                                                                                                                    • Kienzler, Wolfgang. Begriff und Gegenstand: Eine historische und systematische Studie zur Entwicklung von Gottlob Freges Denken. Frankfurt: Vittorio Klostermann, 2009.

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                                                                                                                                                                                      This monograph provides a detailed account (in German) of the historical development of Frege’s thought from his early writings to the publication of the first volume of his Basic Laws in 1893.

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                                                                                                                                                                                      • Sluga, Hans. Gottlob Frege. London: Routledge, 1980.

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                                                                                                                                                                                        The first three chapters of this book, in particular, offer an account of the historical background to Frege’s work and the philosophical influences upon him.

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                                                                                                                                                                                        Frege in Mathematical Context

                                                                                                                                                                                        In the early years of Frege scholarship, Frege’s logicism tended to be seen as driven primarily by philosophical concerns—to secure the foundations of mathematics by showing that arithmetic is essentially logic. As the historical context of Frege’s work began to be appreciated, however, it became clear just how rooted Frege was in the mathematics of his time, and since the 1990s, this has come to be explored with ever greater sophistication. Demopoulos 1995 and Beaney and Reck 2005 both contain parts devoted to the mathematical context of Frege’s logicism, which include the papers cited below: Demopoulos 1994, Tait 1997, and Tappenden 1995. More recent collections also include papers on Frege’s engagement with his mathematical contemporaries and the mathematical background to his work, most notably, Wilson 2010 and Reck 2013. For more on Frege’s relationship to Hilbert, in particular, see Frege and Hilbert.

                                                                                                                                                                                        • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 3, Frege’s Philosophy of Mathematics. London: Routledge, 2005.

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                                                                                                                                                                                          This is the third of the four-volume collection that includes the most important papers published on Frege between 1986 and 2005 (Beaney and Reck 2005, cited under Anthologies). The first part of this volume is titled “Frege and the History and Philosophy of Mathematics,” and it contains papers by Mark Wilson, William Demopoulos, Jamie Tappenden, and W. W. Tait. All are cited in this section.

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                                                                                                                                                                                          • Demopoulos, William. “Frege and the Rigorization of Analysis.” Journal of Philosophical Logic 23 (1994): 225–246.

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                                                                                                                                                                                            Demopoulos here places Frege’s logicism in the context of 19th-century mathematical analysis. Reprinted in Demopoulos 1995, pp. 68–88. Also reprinted in Beaney and Reck 2005 (cited under Frege in Mathematical Context), pp. 50–66.

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                                                                                                                                                                                            • Demopoulos, William, ed. Frege’s Philosophy of Mathematics. Cambridge, MA: Harvard University Press, 1995.

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                                                                                                                                                                                              Part 1 of this collection is titled “The Intellectual Background to Frege’s Logicism,” and it includes Demopoulos 1994.

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                                                                                                                                                                                              • Reck, Erich H. “Frege or Dedekind? Towards a Reevaluation of Their Legacies.” In The Historical Turn in Analytic Philosophy. Edited by Erich H. Reck, 139–170. Basingstoke, UK: Palgrave Macmillan, 2013.

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                                                                                                                                                                                                Frege and Dedekind were both “logicists” in some sense, but Frege is generally regarded as far more philosophically sophisticated. Reck offers a reevaluation.

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                                                                                                                                                                                                • Tait, W. W. “Frege versus Cantor and Dedekind.” In Early Analytic Philosophy: Frege, Russell, Wittgenstein. Edited by William W. Tait, 213–248. Chicago: Open Court, 1997.

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                                                                                                                                                                                                  In this paper, Tait compares Frege’s views on the concept of number with those of Cantor and Dedekind. Reprinted in Frege: Importance and Legacy, edited by Matthias Schirn (Berlin: Walter de Gruyter, 1996), pp. 70–113. Also reprinted in Beaney and Reck 2005 (cited under Frege in Mathematical Context), pp. 115–156.

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                                                                                                                                                                                                  • Tappenden, Jamie. “Extending Knowledge and ‘Fruitful Concepts’: Fregean Themes in the Foundations of Mathematics.” Noûs 29 (1995): 427–467.

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                                                                                                                                                                                                    Tappenden here argues that Frege’s philosophical work on the foundations of mathematics must be understood in its mathematical context, focusing on Frege’s conception of “fruitful” definitions. Reprinted in Beaney and Reck 2005 (cited under Frege in Mathematical Context), pp. 67–114.

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                                                                                                                                                                                                    • Wilson, Mark. “Frege’s Mathematical Setting.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 379–412. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                      Wilson here explores the 19th-century geometrical context of what he calls Frege’s “absolute” logicism, focusing on mathematical debates concerning the role and justification of extension elements in geometry. See also Wilson 2005 (cited under Context Principle).

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                                                                                                                                                                                                      Frege in Logical Context

                                                                                                                                                                                                      Dummett once wrote that Frege’s logical theory “is astonishing because it has no predecessors: it appears to have been born from Frege’s brain unfertilized by external influences” (Dummett 1981a, p. xxxv, cited under More Advanced Works). Frege’s logic was indeed revolutionary, but it was far from unfertilized by external influences. It crucially depended on the development of function theory in mathematics, as Baker and Hacker 1984 and Beaney 1996 show. We can also understand Frege’s logic better when we see it in the broader context of the history of logic. MacFarlane 2002 compares Frege and Kant on their conception of logic; Gabriel 2005 considers the influence of Herbart on Frege; Heis 2013 elucidates Frege’s critique of Boolean logic and his relationship to Lotze; Peckhaus 2004 discusses Frege and Schröder; and Woleński 2004 outlines Frege’s influence on Polish logic and philosophy. Thiel 2005 examines the two main versions of Frege’s logical system, as presented in 1879 and 1893.

                                                                                                                                                                                                      • Baker, Gordon P., and P. M. S. Hacker. Frege: Logical Excavations. Oxford: Blackwell, 1984.

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                                                                                                                                                                                                        Baker and Hacker emphasize how Frege’s logic resulted from extending the notion of a function that had been developed in 19th-century mathematics; see especially chapter 6 and chapter 9.

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                                                                                                                                                                                                        • Beaney, Michael. Frege: Making Sense. London: Duckworth, 1996.

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                                                                                                                                                                                                          Chapter 1 of this book sketches the logical background to Frege’s work, and chapter 2 explains how Frege’s “Begriffsschrift” improved on both Aristotelian and Boolean logic.

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                                                                                                                                                                                                          • Gabriel, Gottfried. “Existential and Number Statements: Herbart and Frege.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. Edited by Michael Beaney and Erich H. Reck, 109–123. London: Routledge, 2005.

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                                                                                                                                                                                                            Gabriel compares Frege’s analysis of existential and number statements with Herbart’s, arguing that Herbart showed Frege the way to this analysis. Translation by Christian Kästner of “Existenz- und Zahlaussage: Herbart und Frege,” in Herbarts Kultursystem: Perspektiven der Transdisziplinarität im 19. Jahrhundert, edited by A. Hoeschen and L. Schneider (Würzburg, Germany: Königshausen & Neumann, 2001), pp. 149–162.

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                                                                                                                                                                                                            • Heis, Jeremy. “Frege, Lotze, and Boole.” In The Historical Turn in Analytic Philosophy. Edited by Erich H. Reck, 113–138. Basingstoke, UK: Palgrave Macmillan, 2013.

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                                                                                                                                                                                                              In this paper, Heis examines Frege’s critique of Boolean logic and the advance he made over Lotze.

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                                                                                                                                                                                                              • MacFarlane, John. “Frege, Kant, and the Logic in Logicism.” Philosophical Review 111 (2002): 25–65.

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                                                                                                                                                                                                                MacFarlane explores the issue of whether Frege and Kant had the same conception of logic, so that they can be taken to be addressing the same question as to whether arithmetic is reducible to logic. Reprinted in Beaney and Reck 2005 (cited under Historical Context), pp. 71–108.

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                                                                                                                                                                                                                • Peckhaus, Volker. “Calculus Ratiocinator versus Characteristica Universalis? The Two Traditions in Logic, Revisited.” History and Philosophy of Logic 25 (2004): 3–14.

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                                                                                                                                                                                                                  Beginning from Jean van Heijenoort’s influential distinction between logic as calculus and logic as language (see van Heijenoort 1967, cited under Philosophy of Logic), Peckhaus briefly considers the relationship between Frege and Schröder. Reprinted in Beaney and Reck 2005 (cited under Historical Context), pp. 176–190.

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                                                                                                                                                                                                                  • Thiel, Christian. “‘Not Arbitrarily and Out of a Craze for Novelty’: The Begriffsschrift, 1879 and 1893.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 2, Frege’s Philosophy of Logic. Edited by Michael Beaney and Erich H. Reck, 13–28. London: Routledge, 2005.

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                                                                                                                                                                                                                    After a brief comment about the origins of the term “Begriffsschrift,” Thiel compares the two forms of Frege’s logical notation that he presented in 1879 and 1893. Translation of “‘Nicht aufs Gerathewohl und aus Neuerungssucht’: Die Begriffsschrift, 1879–1893” by Michael Beaney, in Logik und Mathematik: Frege-Kolloquium Jena 1993, edited by Ingolf Max and Werner Stelzner (Berlin: de Gruyter, 1995), pp. 20–37.

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                                                                                                                                                                                                                    • Woleński, Jan. “The Reception of Frege in Poland.” History and Philosophy of Logic 25 (2004): 37–51.

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                                                                                                                                                                                                                      The Polish contribution to analytic philosophy is all too often ignored. Woleński here elucidates Frege’s influence on the development of Polish logic and philosophy. Reprinted in Beaney and Reck 2005 (cited under Historical Context), pp. 290–309.

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                                                                                                                                                                                                                      Frege in Philosophical Context

                                                                                                                                                                                                                      In recent years much light has been shed on the German philosophical background to Frege’s work: see especially the writings by Gabriel, of which Gabriel 2002 and Gabriel 2013 can be recommended first. Dummett 1982 discusses Frege and Lotze. For Frege’s relationship to neo-Kantianism, in particular, see Gabriel 1986, Peckhaus 2000, and Schlotter and Wehmeier 2013. Schlotter 2006 shows how Frege’s late essay on “Negation” was a response to Bauch. Works on Frege’s relationship to Husserl, Hilbert, Russell, Wittgenstein, and Carnap are given in the separate subsections that follow. See also the works cited under Historical Context.

                                                                                                                                                                                                                      Frege and Husserl

                                                                                                                                                                                                                      Frege and Husserl are often regarded as the founders of the analytic and phenomenological traditions of philosophy, respectively; yet, as many have pointed out, they were both trained as mathematicians and were both concerned with the foundations of mathematics. Their relationship has been explored in a number of books, most notably, Mohanty 1982, Haaparanta 1994, Dummett 1993, Stepanians 1998, and Hill and Haddock 2003. Dummett 1991 and Smith 2013 offer further accounts on specific issues.

                                                                                                                                                                                                                      • Dummett, Michael. “Thought and Perception: The Views of Two Philosophical Innovators.” In The Analytic Tradition. Edited by David Bell and Neil Cooper, 83–103. Oxford: Blackwell, 1991.

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                                                                                                                                                                                                                        Beginning with the problem of intentionality bequeathed by Brentano, Dummett compares Frege’s and Husserl’s responses to this problem. Reprinted in Dummett 1991, pp. 263–288 (cited under Single-Authored Collections). Also reprinted in Beaney and Reck 2005 (cited under Historical Context), pp. 191–212.

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                                                                                                                                                                                                                        • Dummett, Michael. Origins of Analytical Philosophy. London: Duckworth, 1993.

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                                                                                                                                                                                                                          Originally published in German translation in 1988, and then in Italian in 1990 and French in 1991, this book explores the relationship between Frege and Husserl, with some discussion also of Brentano. The title is misleading in that Russell’s and Moore’s roles in the emergence of analytic philosophy are not considered.

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                                                                                                                                                                                                                          • Haaparanta, Leila, ed. Mind, Meaning and Mathematics: Essays on the Philosophical Views of Husserl and Frege. Dordrecht, The Netherlands: Kluwer, 1994.

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                                                                                                                                                                                                                            This collection contains contributions from many of the scholars who have concerned themselves with the relationship between Frege and Husserl, including Dagfinn Føllesdal, Martin Kusch, Richard Tieszen, Claire Ortiz Hill, J. N. Mohanty, Barry Smith, David Bell, and Leila Haaparanta.

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                                                                                                                                                                                                                            • Hill, Claire Ortiz, and Guillermo E. Rosado Haddock. Husserl or Frege? Meaning, Objectivity, and Mathematics. La Salle, IL: Open Court, 2003.

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                                                                                                                                                                                                                              This is a collection of papers written by either Hill or Rosado Haddock, some of which directly compare Frege and Husserl on certain topics, such as sense and reference.

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                                                                                                                                                                                                                              • Mohanty, J. N. Husserl and Frege. Bloomington: Indiana University Press, 1982.

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                                                                                                                                                                                                                                This was the first book-length account of the relationship between Frege and Husserl, written from a more Husserlian then Fregean orientation.

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                                                                                                                                                                                                                                • Smith, David Woodruff. “The Role of Phenomenology in Analytic Philosophy.” In The Oxford Handbook of the History of Analytic Philosophy. Edited by Michael Beaney, 1117–1142. Oxford: Oxford University Press, 2013.

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                                                                                                                                                                                                                                  This compares the ideas of Frege and Husserl in the broader context of the relationship between the analytic and phenomenological traditions.

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                                                                                                                                                                                                                                  • Stepanians, Markus S. Frege und Husserl über Urteilen und Denken. Paderborn, Germany: Schöningh, 1998.

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                                                                                                                                                                                                                                    For the German-language reader, this monograph offers a detailed account of Frege’s and Husserl’s views on judgment and thought. Part 1 is devoted to Frege’s views; Part 2 discusses Husserl’s views, including his criticisms of Frege’s analysis of judgment.

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                                                                                                                                                                                                                                    Frege and Hilbert

                                                                                                                                                                                                                                    Frege’s dispute with Hilbert over the foundations of geometry is one of the most instructive in understanding developments in the philosophy of mathematics and logic around the turn of the 20th century. They corresponded between 1895 and 1903 (see Frege 1980a, cited under Collections of English Translations), and Frege criticized Hilbert in two papers on the foundations of geometry published in 1903 and 1906 (included in Frege 1984, cited under Collections of English Translations). Good accounts of this dispute are given in Blanchette 2012 and Hallett 2010, and more specific aspects are considered in Resnik 1980 and Wehmeier 1997. One central issue has been Frege’s appreciation of metatheory: This is discussed in Demopoulos 1994, Blanchette 1996, and Tappenden 2000. (See also the works cited under Metalogic, especially Antonelli and May 2000).

                                                                                                                                                                                                                                    • Blanchette, Patricia A. “Frege and Hilbert on Consistency.” Journal of Philosophy 93 (1996): 317–336.

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                                                                                                                                                                                                                                      Blanchette aims to show just how different Frege’s conception of logic is from the model-theoretic conception associated with Hilbert. For a much fuller account, see Blanchette 2012 (cited under Philosophy of Logic). Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 29–49.

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                                                                                                                                                                                                                                      • Blanchette, Patricia. “The Frege-Hilbert Controversy.” The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University Press, 2012.

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                                                                                                                                                                                                                                        First published in 2007 and updated in 2012, this article provides a useful overview of Frege’s and Hilbert’s dispute over the foundations of geometry.

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                                                                                                                                                                                                                                        • Demopoulos, William. “Frege, Hilbert and the Conceptual Structure of Model Theory.” History and Philosophy of Logic 15 (1994): 211–225.

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                                                                                                                                                                                                                                          Demopoulos here offers an explanation of what prevented Frege, unlike Hilbert, from appreciating the model-theoretic point of view.

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                                                                                                                                                                                                                                          • Hallett, Michael. “Frege and Hilbert.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 413–464. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                            Hallett discusses the dispute between Frege and Hilbert on the foundations of geometry, focusing on the question of reference-fixing.

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                                                                                                                                                                                                                                            • Resnik, Michael. Frege and the Philosophy of Mathematics. Ithaca, NY: Cornell University Press, 1980.

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                                                                                                                                                                                                                                              In chapter 2, on formalism, and chapter 3, on deductivism, Resnik examines several key features of Frege’s critique of Hilbert’s views.

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                                                                                                                                                                                                                                              • Tappenden, Jamie. “Frege on Axioms, Indirect Proofs, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments?” Notre Dame Journal of Formal Logic 41 (2000): 271–315.

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                                                                                                                                                                                                                                                By distinguishing two approaches to independence arguments in geometry, Tappenden sets out to show that Frege did not reject all such independence arguments, and so he was not as hostile to metatheory as some have supposed.

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                                                                                                                                                                                                                                                • Wehmeier, Kai. “Aspekte der Frege-Hilbert-Korrespondenz.” History and Philosophy of Logic 18 (1997): 201–209.

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                                                                                                                                                                                                                                                  Wehmeier examines Frege’s criticisms of Hilbert’s formalism, as revealed in correspondence they had in 1899–1900.

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                                                                                                                                                                                                                                                  Frege and Russell

                                                                                                                                                                                                                                                  Much has been written on the relationship between Frege and Bertrand Russell, often embedded in broader accounts of the history of analytic philosophy or of the development of Frege’s or Russell’s philosophies. Particular papers that focus on their relationship, however, are Levine 2002, Beaney 2003, Demopoulos and Clark 2005, and Hylton 2005. Russell 1903 gives Russell’s own early account of Frege’s ideas.

                                                                                                                                                                                                                                                  • Beaney, Michael. “Russell and Frege.” In The Cambridge Companion to Bertrand Russell. Edited by Nicholas Griffin, 128–170. Cambridge, UK: Cambridge University Press, 2003.

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                                                                                                                                                                                                                                                    This explores the relationship between Frege and Russell with particular focus on their logicism and their different conceptions of analysis. Reprinted, without the final section on analysis, as “Frege, Russell and Logicism” in Beaney and Reck 2005 (cited under Historical Context), pp. 213–240.

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                                                                                                                                                                                                                                                    • Demopoulos, William, and Peter Clark. “The Logicism of Frege, Dedekind, and Russell.” In The Oxford Handbook of Philosophy of Mathematics and Logic. Edited by Stewart Shapiro, 129–165. Oxford: Oxford University Press, 2005.

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                                                                                                                                                                                                                                                      This paper compares Frege’s and Russell’s logicism, with further brief discussion of Dedekind.

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                                                                                                                                                                                                                                                      • Hylton, Peter. “Frege and Russell.” In Propositions, Functions, and Analysis: Selected Essays on Russell’s Philosophy. Edited by Peter Hylton, 153–184. Oxford: Oxford University Press, 2005.

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                                                                                                                                                                                                                                                        Hylton elucidates the key differences between the views of Frege and Russell on meaning/sense/reference and function-argument analysis. Reprinted in The Cambridge Companion to Frege, edited by Michael Potter and Tom Ricketts (Cambridge, UK: Cambridge University Press, 2010), pp. 509–549.

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                                                                                                                                                                                                                                                        • Levine, James. “Analysis and Decomposition in Frege and Russell.” Philosophical Quarterly 52 (2002): 195–216.

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                                                                                                                                                                                                                                                          Beginning with a distinction drawn by Michael Dummett between analysis and decomposition, Levine argues that while Russell accepts this distinction, Frege does not. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 392–413.

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                                                                                                                                                                                                                                                          • Russell, Bertrand. The Principles of Mathematics. Cambridge, UK: Cambridge University Press, 1903.

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                                                                                                                                                                                                                                                            In Appendix A of this book, Russell gives his own account of Frege’s logical and arithmetical views, which introduced those views to the English-speaking world. Wittgenstein may have first learnt about Frege through this book.

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                                                                                                                                                                                                                                                            Frege and Wittgenstein

                                                                                                                                                                                                                                                            More has been written on the relationship between Frege and Wittgenstein than on his relationship with any other philosopher. Frege had an enormous influence on Wittgenstein, though the precise nature of this influence has been highly controversial. Commentators such as Baker and Hacker (e.g., Baker 1988, Hacker 2001, both cited under Books) have stressed how Wittgenstein was concerned to repudiate much of what Frege thought, while others, such as Diamond (Diamond 2010 and Diamond 2013, both cited under Essays) and Conant (in Reck 2002, cited under Books), have emphasized just how deeply Wittgenstein engaged in Frege’s thinking and the problems it raised. Dummett 1981 (cited under Essays), by contrast, argues that Wittgenstein goes wrong when he departs from Frege. There has also been argument about the relative influence on Wittgenstein of Frege and Russell; see, for example, the debate between Ricketts and Goldfarb in Reck 2002. Most commentators tend to focus on Frege’s influence on the Tractatus (see, e.g., Potter 2009 [cited under Books], Floyd 2011 and Kienzler 2011 [both cited under Essays]), but his influence on Wittgenstein’s later work is also significant (see, e.g., Travis 2006 [cited under Books] and Künne 2009 [cited under Essays]). Reck 1997 (cited under Essays) and Reck 2002 emphasize both. This section is divided into two subsections, covering Books and Essays.

                                                                                                                                                                                                                                                            Books

                                                                                                                                                                                                                                                            Baker 1988 and Potter 2009 are monographs in which the relationship between Frege and Wittgenstein is central, and Reck 2002 contains various papers on the topic. Travis 2006 explores Frege’s influence on Wittgenstein’s later work. Hacker 2001 contains two papers of his on the relationship.

                                                                                                                                                                                                                                                            • Baker, Gordon P. Wittgenstein, Frege and the Vienna Circle. Oxford: Blackwell, 1988.

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                                                                                                                                                                                                                                                              Baker focuses in this book on the philosophy of logic, arguing that Wittgenstein’s views of logic are fundamentally different from those of both Frege and the Vienna Circle.

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                                                                                                                                                                                                                                                              • Hacker, P. M. S. Wittgenstein: Connections and Controversies. Oxford: Clarendon, 2001.

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                                                                                                                                                                                                                                                                This contains two papers, “Frege and the Early Wittgenstein” and “Frege and the Later Wittgenstein,” which summarize Hacker’s view of their relationship. That view is presented in more detail in other works, some of them co-authored with Baker, such as Baker and Hacker 1984 (cited under More Advanced Works).

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                                                                                                                                                                                                                                                                • Potter, Michael, Wittgenstein’s Notes on Logic. Oxford: Oxford University Press, 2009.

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                                                                                                                                                                                                                                                                  Wittgenstein engages most explicitly with Frege’s ideas in his “Notes on Logic” (1913), making criticisms that inform the views that eventually found their way into his Tractatus. Potter gives a very clear and detailed account of these notes in this book.

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                                                                                                                                                                                                                                                                  • Reck, Erich H., ed. From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. New York: Oxford University Press, 2002.

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                                                                                                                                                                                                                                                                    Also cited under Collections on the History of (Early) Analytic Philosophy, this volume contains many essays on the relationship between Frege and Wittgenstein. It begins with a biographical overview of their relationship by the editor and contains useful papers, in particular, by Goldfarb, Ricketts, and Conant.

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                                                                                                                                                                                                                                                                    • Travis, Charles. Thought’s Footing: A Theme in Wittgenstein’s Philosophical Investigations. Oxford: Oxford University Press, 2006.

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                                                                                                                                                                                                                                                                      As his introduction makes clear, the guiding thought of this book is that Wittgenstein’s later Philosophical Investigations can be seen as a deep response to Frege’s work.

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                                                                                                                                                                                                                                                                      Essays

                                                                                                                                                                                                                                                                      Drawing inspiration from Geach 1976, Diamond has done most to stress the significance of Frege’s influence on Wittgenstein; for her most recent views, see Diamond 2010 and Diamond 2013. See also Conant’s essay in Reck 2002 (cited under the subsection Books above), a collection that contains other papers on the relationship between Frege and Wittgenstein. For other views, see Dummett 1981, Reck 1997, Künne 2009, and Kienzler 2011. Floyd 2011 offers an account of the correspondence between Frege and Wittgenstein.

                                                                                                                                                                                                                                                                      • Diamond, Cora. “Inheriting from Frege: The Work of Reception, as Wittgenstein Did It.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 550–601. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                                                        In this rich paper (the first draft of which was written in the 1990s), Diamond explores several ways in which Wittgenstein thinks through some of the tensions in Frege’s philosophy in coming to his own views, a process that she calls “overcoming by taking seriously.”

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                                                                                                                                                                                                                                                                        • Diamond, Cora. “Reading the Tractatus with G. E. M. Anscombe.” In The Oxford Handbook of the History of Analytic Philosophy. Edited by Michael Beaney, 870–905. Oxford: Oxford University Press, 2013.

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                                                                                                                                                                                                                                                                          Anscombe played an important role in convincing people that Wittgenstein’s Tractatus can be understood only by recognizing the influence of Frege, and Diamond explains and develops Anscombe’s views, and Diamond’s own earlier views, in this essay.

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                                                                                                                                                                                                                                                                          • Dummett, Michael. “Frege and Wittgenstein.” In Perspectives on the Philosophy of Wittgenstein. Edited by Irving Block, 31–42. Oxford: Blackwell, 1981.

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                                                                                                                                                                                                                                                                            Dummett here argues—controversially—that Wittgenstein is at his best when he builds on Frege’s work. Reprinted in Dummett 1991, pp. 237–248 (cited under Single-Authored Collections).

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                                                                                                                                                                                                                                                                            • Floyd, Juliet. “The Frege-Wittgenstein Correspondence: Interpretive Themes.” In Interactive Wittgenstein: Essays in Memory of Georg Henrik von Wright. Edited by E. De Pellegrin, 75–107. Dordrecht, The Netherlands: Springer, 2011.

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                                                                                                                                                                                                                                                                              Dreben and Floyd published a translation of the Frege-Wittgenstein correspondence in this same collection. Floyd’s essay is appended to this translation.

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                                                                                                                                                                                                                                                                              • Geach, Peter. “Saying and Showing in Frege and Wittgenstein.” In Essays on Wittgenstein in Honour of G. H. von Wright. Edited by Jaakko Hintikka, 54–70. Acta Philosophica Fennica 28. Amsterdam: North-Holland, 1976.

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                                                                                                                                                                                                                                                                                This classic paper is the inspiration behind the “new Wittgensteinian” readings of the Tractatus spearheaded by Diamond and Conant. Geach argues that Wittgenstein’s distinction between saying and showing has its roots in Frege’s problems in articulating his distinction between concept and object.

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                                                                                                                                                                                                                                                                                • Kienzler, Wolfgang. “Wittgenstein and Frege.” In The Oxford Handbook of Wittgenstein. Edited by Oskari Kuusela and Marie McGinn, 79–104. Oxford: Oxford University Press, 2011.

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                                                                                                                                                                                                                                                                                  Kienzler here focuses on the criticisms of Frege that Wittgenstein makes in the Tractatus.

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                                                                                                                                                                                                                                                                                  • Künne, Wolfgang. “Wittgenstein and Frege’s Logical Investigations.” In Wittgenstein and Analytic Philosophy. Edited by Hans-Johann Glock and John Hyman, 26–62. Oxford: Oxford University Press, 2009.

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                                                                                                                                                                                                                                                                                    Frege and Wittgenstein met three times in the early 1910s and corresponded until 1920, during the period when Frege was writing his “Logical Investigations.” Künne considers their correspondence and the criticisms that Wittgenstein made of Frege’s ideas.

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                                                                                                                                                                                                                                                                                    • Reck, Erich H. “Frege’s Influence on Wittgenstein: Reversing Metaphysics via the Context Principle.” In Early Analytic Philosophy: Frege, Russell, Wittgenstein. Edited by William W. Tait, 123–185. Chicago: Open Court, 1997.

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                                                                                                                                                                                                                                                                                      Focusing on the role of the context principle in their thinking, Reck stresses the positive connection between Frege and Wittgenstein, arguing that Frege should be seen as a “contextual” rather than a “metaphysical” Platonist. Reprinted, shortened and revised, in Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. 1, Frege’s Philosophy in Context, edited by Michael Beaney and Erich H. Reck (London: Routledge, 2005), pp. 241–289.

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                                                                                                                                                                                                                                                                                      Frege and Carnap

                                                                                                                                                                                                                                                                                      Carnap attended three lecture courses that Frege gave at Jena in 1910–1911, 1913, and 1914, which have now been published (Frege 2004). Beaney 2004, Reck 2004, and Ricketts 2004 all contain discussions of Frege’s influence on Carnap. Gabriel 2007 offers a useful overview.

                                                                                                                                                                                                                                                                                      • Beaney, Michael. “Carnap’s Conception of Explication: From Frege to Husserl?” In Carnap Brought Home: The View from Jena. Edited by Steve Awodey and Carstein Klein, 117–150. Chicago: Open Court, 2004.

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                                                                                                                                                                                                                                                                                        Beaney here explores the roots of Carnap’s conception of explication in Frege’s methodology, especially as revealed in Frege’s lectures on “Logic in Mathematics,” which Carnap attended.

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                                                                                                                                                                                                                                                                                        • Frege, Gottlob. Frege’s Lectures on Logic: Carnap’s Student Notes, 1910–1914. Chicago: Open Court, 2004.

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                                                                                                                                                                                                                                                                                          Carnap’s notes on Frege’s lectures are transcribed and translated (by Erich H. Reck and Steve Awodey) in this volume, with introductory material by Gottfried Gabriel, Reck and Awodey.

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                                                                                                                                                                                                                                                                                          • Gabriel, Gottfried. “Carnap and Frege.” In The Cambridge Companion to Carnap. Edited by Michael Friedman and Richard Creath, 65–80. Cambridge, UK: Cambridge University Press, 2007.

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                                                                                                                                                                                                                                                                                            Gabriel provides a useful overview of the relationship between Frege and Carnap in this essay.

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                                                                                                                                                                                                                                                                                            • Reck, Erich H. “From Frege and Russell to Carnap: Logic and Logicism in the 1920s.” In Carnap Brought Home: The View from Jena. Edited by Steve Awodey and Carstein Klein, 151–180. Chicago: Open Court, 2004.

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                                                                                                                                                                                                                                                                                              Reck discusses the influence of both Frege and Russell on Carnap.

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                                                                                                                                                                                                                                                                                              • Ricketts, Thomas. “Frege, Carnap, and Quine: Continuities and Discontinuities.” In Carnap Brought Home: The View from Jena. Edited by Steve Awodey and Carstein Klein, 181–202. Chicago: Open Court, 2004.

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                                                                                                                                                                                                                                                                                                Ricketts compares the views of Frege, Carnap, and Quine on logic and its application to philosophy.

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                                                                                                                                                                                                                                                                                                Philosophy of Mathematics

                                                                                                                                                                                                                                                                                                In the early years of Frege scholarship, his philosophy of mathematics was generally ignored, the assumption being that Russell’s paradox had been fatal to his logicism. In recent years, with the discovery of what is now known as Frege’s theorem (see Frege’s Theorem and Neo-Logicism), interest has blossomed. Wright 1983 and Boolos 1998 have been especially influential in this respect. The work of these authors has been developed, most notably, by Heck (Heck 2011, cited under Frege’s Theorem and Neo-Logicism). The two most useful collections of papers on Frege’s philosophy of mathematics generally are Demopoulos 1995 and Beaney and Reck 2005. Resnik 1980 was the first book on Frege’s philosophy of mathematics. Dummett 1991 is the best single book on the subject, and Burgess 2005 reviews the attempts to repair Frege’s system. This section contains two subsections: Russell’s Paradox and Responses and Frege’s Theorem and Neo-Logicism, both of which, but especially the first, cites material that is quite technical.

                                                                                                                                                                                                                                                                                                • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 3, Frege’s Philosophy of Mathematics. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                  This is the third of the four-volume collection that includes the most important papers published on Frege between 1986 and 2005 (cited under Anthologies). This volume is divided into three parts, on the historical context (cited under Frege in Mathematical Context), on numbers and value-ranges, and on consistency, Frege’s theorem, and neo-logicism.

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                                                                                                                                                                                                                                                                                                  • Boolos, George. Logic, Logic, and Logic. Edited by J. Burgess and R. Jeffrey. Cambridge, MA: Harvard University Press, 1998.

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                                                                                                                                                                                                                                                                                                    This collects together Boolos’s various papers on logic, many of which concern Frege’s logicist project.

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                                                                                                                                                                                                                                                                                                    • Burgess, John. Fixing Frege. Princeton, NJ: Princeton University Press, 2005.

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                                                                                                                                                                                                                                                                                                      Burgess considers the various suggestions that have been made to repair Frege’s system in the aftermath of Russell’s paradox.

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                                                                                                                                                                                                                                                                                                      • Demopoulos, William, ed. Frege’s Philosophy of Mathematics. Cambridge, MA: Harvard University Press, 1995.

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                                                                                                                                                                                                                                                                                                        This was the first collection of papers on Frege’s philosophy of mathematics. It is divided into three parts, on the intellectual background to Frege’s logicism (see Frege in Mathematical Context), the mathematical content of Begriffsschrift and Foundations, and the Basic Laws. Contributors include Boolos, Parsons, Heck, and Dummett.

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                                                                                                                                                                                                                                                                                                        • Dummett, Michael. Frege: Philosophy of Mathematics. London: Duckworth, 1991.

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                                                                                                                                                                                                                                                                                                          This is the best single book on Frege’s philosophy of mathematics, tracing the development of Frege’s thought from the Foundations of Arithmetic to the Basic Laws. It covers all the main elements of Frege’s positive account as well as his main criticisms of other views, such as those of Dedekind, Cantor, and the formalists.

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                                                                                                                                                                                                                                                                                                          • Heck, Richard G. Reading Frege’s Grundgesetze. Oxford: Oxford University Press, 2012.

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                                                                                                                                                                                                                                                                                                            This book reassesses Frege’s logicism, the first part focusing on the underlying logic and the second part on the underlying mathematics.

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                                                                                                                                                                                                                                                                                                            • Resnik, Michael. Frege and the Philosophy of Mathematics. Ithaca, NY: Cornell University Press, 1980.

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                                                                                                                                                                                                                                                                                                              Now somewhat dated in its positive account of Frege’s philosophy of mathematics (the topic of the final chapter), this book nevertheless contains useful chapters on psychologism, formalism, deductivism, and Mill’s empiricism.

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                                                                                                                                                                                                                                                                                                              • Wright, Crispin. Frege’s Conception of Numbers as Objects. Aberdeen, Scotland: Aberdeen University Press, 1983.

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                                                                                                                                                                                                                                                                                                                This was the pioneering work that inspired the renaissance of interest in Frege’s logicism.

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                                                                                                                                                                                                                                                                                                                Russell’s Paradox and Responses

                                                                                                                                                                                                                                                                                                                Russell’s paradox is the contradiction that arises from considering the class of all classes that are not members of themselves and asking if this class is a member of itself or not: if it is, then it is not; and if it is not, then it is. Russell wrote to Frege in 1902 informing him of this contradiction, and it devastated Frege. Frege tried to respond to the paradox in a hastily written appendix to the second volume of his Basic Laws, which was then in press, but he soon realized that his response did not work and gave up his logicist project. In recent years, however, much work has been done investigating what fragments of Frege’s logical system are immune to Russell’s paradox. The development of our understanding of what parts are consistent can be traced in the following papers: Boolos 1987, Parsons 1987, Burgess 1998, Heck 1996, Wehmeier 1999, and Ferreira and Wehmeier 2002. See also the works cited under Frege’s Theorem and Neo-Logicism.

                                                                                                                                                                                                                                                                                                                Frege’s Theorem and Neo-Logicism

                                                                                                                                                                                                                                                                                                                Frege’s theorem is the theorem that the Dedekind-Peano axioms for arithmetic can be derived in second-order logic from Hume’s principle, which asserts that for any concepts F and G, the number of Fs is equal to the number of Gs if and only if there is a one–one correlation between the Fs and the Gs. (This principle has also been called the “Cantor–Hume Principle” to do justice to Cantor’s use of it.) The work of Wright, Boolos, and Heck has been especially influential—see, for example, Boolos 1987, Heck 1993, and Wright 1997. Heck’s papers are collected in Heck 2011. Boolos’s papers are collected in Boolos 1998 (cited under Philosophy of Mathematics), and Wright’s papers, together with additional papers on neo-logicism (as the reconstruction of Frege’s logicism is called) by Hale, are collected in Hale and Wright 2001. Zalta 2013 explains the theorem in modern notation.

                                                                                                                                                                                                                                                                                                                Philosophy of Logic

                                                                                                                                                                                                                                                                                                                Frege created the first system of modern quantificational logic, and his own use of, and reflection on, this logic has informed all subsequent philosophy of logic. Blanchette 2012 provides an especially rich book-length treatment of his conception of logic, while Macbeth 2005 and Landini 2012 offer alternative, if controversial, readings of Frege’s “Begriffsschrift.” For a useful account intermediate in length between book and article, Sullivan 2004 can be recommended. Much of the debate about Frege’s conception of logic has been inspired by the distinction that van Heijenoort 1967 drew between logic as calculus and logic as language. Goldfarb 2001 gives clear expression to one influential view in this debate, the view that interprets Frege as holding a “universalist” conception of logic. This section contains three subsections: Metalogic, Permutation Argument, and Truth, and many of the papers cited are contained in Beaney and Reck 2005.

                                                                                                                                                                                                                                                                                                                • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 2, Frege’s Philosophy of Logic. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                  This is the second of the four-volume collection that includes the most important papers published on Frege between 1986 and 2005 (cited under Anthologies). This volume is divided into four parts: on Frege’s logic, on Frege and metalogic, on logic and truth, and on logic and epistemology (on the latter, see Epistemology and Metaphysics).

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                                                                                                                                                                                                                                                                                                                  • Blanchette, Patricia A. Frege’s Conception of Logic. Oxford: Oxford University Press, 2012.

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                                                                                                                                                                                                                                                                                                                    In this book Blanchette explores the relationship between Frege’s conception of logic and his use and understanding of conceptual analysis. She looks, in particular, at Frege’s use of analysis in his logicist project.

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                                                                                                                                                                                                                                                                                                                    • Goldfarb, Warren. “Frege’s Conception of Logic.” In Future Pasts. Edited by Juliet Floyd and Sanford Shieh, 25–41. Oxford: Oxford University Press, 2001.

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                                                                                                                                                                                                                                                                                                                      Goldfarb explains his influential view that Frege held a “universalist” conception of logic. Reprinted in Beaney and Reck 2005, pp. 50–68. Also reprinted in The Cambridge Companion to Frege, edited by Michael Potter and Tom Ricketts (Cambridge, UK: Cambridge University Press, 2010), pp. 63–85.

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                                                                                                                                                                                                                                                                                                                      • Landini, Gregory. Frege’s Notations: What They Are and How They Mean. Basingstoke, UK: Palgrave Macmillan, 2012.

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                                                                                                                                                                                                                                                                                                                        Landini here argues that Frege’s logic must be seen as a function calculus, not a predicate calculus as we know it today, and he draws out the implications of this view for the interpretation of some of Frege’s most characteristic doctrines.

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                                                                                                                                                                                                                                                                                                                        • Macbeth, Danielle. Frege’s Logic, Cambridge, MA: Harvard University Press, 2005.

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                                                                                                                                                                                                                                                                                                                          Taking seriously its two-dimensional character, Macbeth offers a novel reading of Frege’s “Begriffsschrift.”

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                                                                                                                                                                                                                                                                                                                          • Sullivan, Peter. “Frege’s Logic.” In Handbook of the History of Logic. Vol. 3, The Rise of Modern Logic: From Leibniz to Frege. Edited by Dov M. Gabbay and John Woods, 671–762. Amsterdam: Elsevier, 2004.

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                                                                                                                                                                                                                                                                                                                            This long article explains Frege’s “Begriffsschrift” and the associated philosophical ideas, such as those of function-argument analysis, truth, judgment, and the distinction between sense and reference.

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                                                                                                                                                                                                                                                                                                                            • van Heijenoort, Jean. “Logic as Calculus and Logic as Language.” Synthese 17 (1967): 324–330.

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                                                                                                                                                                                                                                                                                                                              This is the classic source of the distinction between two views of logic that has informed much subsequent discussion of Frege’s conception.

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                                                                                                                                                                                                                                                                                                                              Metalogic

                                                                                                                                                                                                                                                                                                                              The question of whether Frege had a metatheory of logic, especially in his Basic Laws, has been much debated since the 1990s. Ricketts (see, e.g., Ricketts 1998) has been the foremost advocate of the “no metatheory” interpretation, and this view has been opposed most strongly in the following works: Stanley 1996, Antonelli and May 2000, and Heck 2007. Tappenden 1997, Shieh 2002, and Sullivan 2005 offer more nuanced accounts.

                                                                                                                                                                                                                                                                                                                              • Antonelli, Aldo, and Robert May. “Frege’s New Science.” Notre Dame Journal of Formal Logic 41 (2000): 242–270.

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                                                                                                                                                                                                                                                                                                                                Frege’s dispute with Hilbert is often taken to show that Frege had no metatheoretical approach to logic. Antonelli and May argue that while Frege criticized Hilbert’s approach, he did have his own metatheory—his “New Science.” Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 156–189.

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                                                                                                                                                                                                                                                                                                                                • Heck, Richard. “Frege and Semantics.” In Essays on Frege’s Conception of Truth. Edited by Dirk Greimann, 27–63. Grazer Philosophische Studien 75. Amsterdam: Rodopi, 2007.

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                                                                                                                                                                                                                                                                                                                                  Heck here argues, against some commentators, that Frege did make use of semantic concepts in his informal mathematical arguments for semantic claims. Reprinted in The Cambridge Companion to Frege, edited by Michael Potter and Tom Ricketts (Cambridge, UK: Cambridge University Press, 2010), pp. 342–378.

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                                                                                                                                                                                                                                                                                                                                  • Ricketts, Thomas. “Frege’s 1906 Foray into Metalogic.” Philosophical Topics 25 (1998): 169–188.

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                                                                                                                                                                                                                                                                                                                                    In “On the Foundations of Arithmetic” (1906), Frege seems to make use of metalogical reasoning. According to Ricketts, however, this is the exception that proves the general rule that Frege’s view of logic precludes metalogic. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 136–155.

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                                                                                                                                                                                                                                                                                                                                    • Shieh, Sanford. “On Interpreting Frege on Truth and Logic.” In From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Edited by Erich H. Reck, 96–124. New York: Oxford University Press, 2002.

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                                                                                                                                                                                                                                                                                                                                      Distinguishing “semantical” from “antisemantical” interpretations of Frege’s philosophy of logic, Shieh examines both in arguing that the disagreement is not what it is often taken to be.

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                                                                                                                                                                                                                                                                                                                                      • Stanley, Jason. “Truth and Metatheory in Frege.” Pacific Philosophical Quarterly 77 (1996): 45–70.

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                                                                                                                                                                                                                                                                                                                                        Stanley here argues, against the view of Ricketts and others, that Frege did have a semantic metatheory in his Basic Laws. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 109–135.

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                                                                                                                                                                                                                                                                                                                                        • Sullivan, Peter. “Metaperspectives and Internalism in Frege.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 2, Frege’s Philosophy of Logic. Edited by Michael Beaney and Erich H. Reck, 85–105. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                          This paper offers an “internalist” reading of Frege’s philosophy of logic that still allows room for metatheoretical perspectives. Extracted and revised from “Frege’s Logic,” in Handbook of the History of Logic, Vol. 3, The Rise of Modern Logic: From Leibniz to Frege, edited by Dov M. Gabbay and John Woods (Amsterdam: Elsevier, 2004), pp. 671–762.

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                                                                                                                                                                                                                                                                                                                                          • Tappenden, Jamie. “Metatheory and Mathematical Practice in Frege.” Philosophical Topics 25 (1997): 213–264.

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                                                                                                                                                                                                                                                                                                                                            Tappenden here distinguishes different senses of “metatheory” in exploring just what Frege did and did not do in his logical and mathematical work. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 190–228.

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                                                                                                                                                                                                                                                                                                                                            The Permutation Argument

                                                                                                                                                                                                                                                                                                                                            §10 of Volume 1 of the Basic Laws has generated much controversy, especially in relation to the question of whether Frege had a metatheoretical approach to logic (see Metalogic). Frege here claims that his Basic Law V leaves it undetermined exactly what the references (Bedeutungen) of terms for value-ranges (Werthverläufe) are, and he offers what has come to be called his permutation argument, aimed at establishing the thesis that it is always possible to identify the two truth-values (the True and the False) with two arbitrary but different value-ranges—the identifiability thesis, as Schroeder-Heister 1987 termed it. As well as Schroeder-Heister 1987, early accounts include Moore and Rein 1986 and Moore and Rein 1987. Fuller, but differing, accounts are provided in Ricketts 1997 and Heck 1999; and for a technical study, see Wehmeier and Schroeder-Heister 2005. More accessible discussions, which bring out its significance in the wider context of Frege’s philosophy of mathematics, can be found in Dummett 1991 and Ruffino 2002. (See also §2 of Hallett 2010, cited under Frege and Hilbert, where Frege’s permutation argument is also considered in addressing the question of reference-fixing.)

                                                                                                                                                                                                                                                                                                                                            • Dummett, Michael. Frege: Philosophy of Mathematics. London: Duckworth, 1991.

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                                                                                                                                                                                                                                                                                                                                              Dummett discusses the permutation argument in chapter 17 in considering the role of the context principle in the Basic Laws. (Dummett first introduced the term permutation argument in discussing the context principle in chapter 19 (p. 408) of The Interpretation of Frege’s Philosophy [Dummett 1981, cited under Context Principle]).

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                                                                                                                                                                                                                                                                                                                                              • Heck, Richard. “Grundgesetze der Arithmetik I, §10.” Philosophia Mathematica 7 (1999): 258–292.

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                                                                                                                                                                                                                                                                                                                                                Heck offers a detailed account of §10, placing it in the wider context of Frege’s argumentation and, in particular, seeing it as preparing the way for the (fallacious) proof Frege offers in §31 that every expression of his formal language has reference (Bedeutung).

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                                                                                                                                                                                                                                                                                                                                                • Moore, Adrian, and Andrew Rein. “Grundgesetze, Section 10.” In Frege Synthesized. Edited by Leila Haaparanta and Jaakko Hintikka, 375–384. Dordrecht, The Netherlands: D. Reidel, 1986.

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                                                                                                                                                                                                                                                                                                                                                  Moore and Rein discuss how Frege solves the problem of indeterminacy he notes in §10 by identifying each truth-value with its unit class.

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                                                                                                                                                                                                                                                                                                                                                  • Moore, Adrian, and Andrew Rein. “Frege’s Permutation Argument.” Notre Dame Journal of Formal Logic 28 (1987): 51–54.

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                                                                                                                                                                                                                                                                                                                                                    Moore and Rein here respond to Schroeder-Heister 1987, seeking to show that Frege’s permutation argument does indeed establish the identifiability thesis.

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                                                                                                                                                                                                                                                                                                                                                    • Ricketts, Thomas. “Truth-Values and Courses-of-Value in Frege’s Grundgesetze.” In Early Analytic Philosophy: Frege, Russell, Wittgenstein. Edited by William W. Tait, 187–211. Chicago: Open Court, 1997.

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                                                                                                                                                                                                                                                                                                                                                      Focusing on §10 of Volume 1 of the Basic Laws, Ricketts argues that Frege’s concern with determining more precisely the references of terms for value-ranges (which Ricketts calls “courses-of-value”) is incompatible with what he regards as Frege’s universalist conception of logic. Reprinted in Beaney and Reck 2005 (cited under Frege in Mathematical Context), pp. 218–244.

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                                                                                                                                                                                                                                                                                                                                                      • Ruffino, Marco. “Logical Objects in Frege’s Grundgesetze, Section 10.” In From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Edited by Erich H. Reck, 125–148. New York: Oxford University Press, 2002.

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                                                                                                                                                                                                                                                                                                                                                        Ruffino discusses §10 in the wider context of the Platonism about logical objects that he sees Frege as advocating.

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                                                                                                                                                                                                                                                                                                                                                        • Schroeder-Heister, Peter. “A Model-Theoretic Reconstruction of Frege’s Permutation Argument.” Notre Dame Journal of Formal Logic 28 (1987): 69–79.

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                                                                                                                                                                                                                                                                                                                                                          Schroeder-Heister offers a model-theoretic reconstruction of the permutation argument according to which it is correct but does not establish the identifiability thesis.

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                                                                                                                                                                                                                                                                                                                                                          • Wehmeier, Kai F., and Peter Schroeder-Heister. “Frege’s Permutation Argument Revisited.” Synthese 147 (2005): 43–61.

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                                                                                                                                                                                                                                                                                                                                                            Wehmeier and Schroeder consider, in a technical study, how to interpret both the permutation argument and the identifiability thesis.

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                                                                                                                                                                                                                                                                                                                                                            Truth

                                                                                                                                                                                                                                                                                                                                                            Frege’s views on truth are fundamental to his conception of logic, but these views have been no less debated than his general conception of logic, as illustrated by the 1996 symposium between Ricketts and Levine (see Ricketts 1996 and Levine 1996, cited under Essays). Greimann has made a major contribution to the debate, both in his own book (Greimann 2003a, in German) and in two collections he has edited, one in German (Greimann 2003b), from which his own chapter has been translated (Greimann 2005), and one in English (Greimann 2007). Other important works include Sluga 2002, Burge 2005, and Taschek 2008. Pardey 2004 and Pardey 2012 offer a very detailed analysis of Frege’s arguments concerning truth in his late essay “Thoughts.”

                                                                                                                                                                                                                                                                                                                                                            Books

                                                                                                                                                                                                                                                                                                                                                            Greimann has published two collections of papers on truth, one in German (Greimann 2003a) and one in English (Greimann 2007). In 2003 he also published his own monograph on truth, in German (Greimann 2003b). Another good book in German on truth is Pardey 2004, expanded and translated into English as Pardey 2012. Burge 2005 contains three of the author’s own papers on truth.

                                                                                                                                                                                                                                                                                                                                                            • Burge, Tyler. Truth, Thought, Reason: Essays on Frege. Oxford: Clarendon, 2005.

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                                                                                                                                                                                                                                                                                                                                                              Part 1 of this book is titled “Truth, Structure and Method,” and brings together three of Burge’s papers on truth, with postscripts provided to two of them.

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                                                                                                                                                                                                                                                                                                                                                              • Greimann, Dirk. Freges Konzeption der Wahrheit. Hildesheim, Germany: Georg Olms, 2003a.

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                                                                                                                                                                                                                                                                                                                                                                For the German-language reader, this offers a full-length treatment of Frege’s conception of truth.

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                                                                                                                                                                                                                                                                                                                                                                • Greimann, Dirk, ed. Das Wahre und das Falsche. Hildesheim, Germany: Georg Olms, 2003b.

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                                                                                                                                                                                                                                                                                                                                                                  Complementing his own account, this collects together papers on Frege’s views on truth by most of the main German scholars of Frege’s philosophy.

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                                                                                                                                                                                                                                                                                                                                                                  • Greimann, Dirk, ed. Essays on Frege’s Conception of Truth. Grazer Philosophische Studien 75. Amsterdam: Rodopi, 2007.

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                                                                                                                                                                                                                                                                                                                                                                    This collects together papers by Hans Sluga, Richard Heck, Danielle Macbeth, Michael Beaney, Dirk Greimann, Erich H. Reck, Verena Mayer, Oswaldo Chateaubriand, and Marco Ruffino.

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                                                                                                                                                                                                                                                                                                                                                                    • Pardey, Ulrich. Freges Kritik an der Korrespondenztheorie der Wahrheit. Paderborn, Germany: Mentis, 2004.

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                                                                                                                                                                                                                                                                                                                                                                      This is the original German version of Pardey 2012.

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                                                                                                                                                                                                                                                                                                                                                                      • Pardey, Ulrich. Frege on Absolute and Relative Truth. Basingstoke, UK: Palgrave Macmillan, 2012.

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                                                                                                                                                                                                                                                                                                                                                                        In this book Pardey offers a detailed textual and philosophical analysis of Frege’s argument in “Thoughts” against the correspondence theory of truth and in favor of the indefinability of truth. The book is a revision, expansion, and translation of Pardey 2004.

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                                                                                                                                                                                                                                                                                                                                                                        Essays

                                                                                                                                                                                                                                                                                                                                                                        A good starting place is the debate between Ricketts and Levine (Ricketts 1996 and Levine 1996). Sluga 2002, Greimann 2005, and Taschek 2008 can then be usefully read in this order.

                                                                                                                                                                                                                                                                                                                                                                        • Greimann, Dirk. “Frege’s Understanding of Truth.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 2, Frege’s Philosophy of Logic. Edited by Michael Beaney and Erich H. Reck, 295–314. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                                                          This is a translation of Greimann’s contribution to the collection of papers on Frege’s conception of truth that he published in 2003 (cited under Truth: Books) in which he offers an interpretation of Frege as an “assertion theorist” of truth.

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                                                                                                                                                                                                                                                                                                                                                                          • Levine, James. “Logic and Truth in Frege.” Proceedings of the Aristotelian Society 70, suppl., (1996): 141–175.

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                                                                                                                                                                                                                                                                                                                                                                            Levine responds to Ricketts 1996, arguing that Frege not only rejected the view that truth could be defined, but also ruled out any correspondence “elucidation” of truth. Reprinted in a revised and shortened form in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 248–269.

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                                                                                                                                                                                                                                                                                                                                                                            • Ricketts, Thomas. “Logic and Truth in Frege.” Proceedings of the Aristotelian Society 70, suppl., (1996): 121–140.

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                                                                                                                                                                                                                                                                                                                                                                              Ricketts has been one of the main advocates of the view that Frege held a “universalist” conception of logic. Here he argues that this conception is grounded in a view of truth as “immanent” in judgment-making. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 231–247.

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                                                                                                                                                                                                                                                                                                                                                                              • Sluga, Hans. “Frege on the Indefinability of Truth.” In From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Edited by Erich H. Reck, 75–95. New York: Oxford University Press, 2002.

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                                                                                                                                                                                                                                                                                                                                                                                Sluga here traces the development of Frege’s views on truth. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Logic), pp. 270–294.

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                                                                                                                                                                                                                                                                                                                                                                                • Taschek, William W. “Truth, Assertion, and the Horizontal: Frege on ‘the Essence of Logic.’” Mind 117 (2008): 375–401.

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                                                                                                                                                                                                                                                                                                                                                                                  This paper sheds light on Frege’s conception of logic by exploring the relationship between judgment, truth, and assertion. Taschek argues, however, that a tension remains in Frege’s conception between the “descriptive” and the “normative” aspects of logic.

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                                                                                                                                                                                                                                                                                                                                                                                  Philosophy of Thought and Language

                                                                                                                                                                                                                                                                                                                                                                                  Frege has often been regarded as the founder of modern (analytic) philosophy of language, a view represented most notably in Dummett’s first book, Frege: Philosophy of Language (Dummett 1981a, first published in 1973). This book provoked a great deal of criticism, one of the main objections being that such a view is anachronistic; see, for example, as cited in the following subsections Books and Essays: Baker and Hacker 1984, Burge 1979 and Burge 1990 (both reprinted in Burge 2005), Ricketts 1986, and Weiner 1997. Dummett responded to his critics in his subsequent works (Dummett 1981b, Dummett 1993), arguing that Frege was a philosopher of thought, but one for whom the analysis of thought proceeds only through the analysis of language. Heck and May 2006 can be recommended as a recent account of Frege’s role in the development of modern philosophy of language. The debate has now ramified into all aspects of what might be called Frege’s philosophy of thought and language, to emphasize the interconnection of thought and language here. Beaney and Reck 2005 provides a collection of papers on the relevant topics. This section contains seven subsections, the first two covering Books and Essays on the general topic (providing full citations of the items just mentioned), and the other five on more specific topics, namely, Concept and Object, Sense and Reference, Thought and Indexicality, Analysis and Elucidation, and Analysis and Decomposition.

                                                                                                                                                                                                                                                                                                                                                                                  Books

                                                                                                                                                                                                                                                                                                                                                                                  Dummett has been the most influential commentator: see especially Dummett 1981a, Dummett 1981b, and Dummett 1993. Baker and Hacker 1984 offers the strongest critique. Burge’s collection of his own papers (Burge 2005) also contains criticisms of Dummett’s view. Beaney and Reck 2005 is the most substantial collection of papers on Frege’s philosophy of thought and language.

                                                                                                                                                                                                                                                                                                                                                                                  • Baker, G. P., and P. M. S. Hacker. Frege: Logical Excavations. Oxford: Blackwell, 1984.

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                                                                                                                                                                                                                                                                                                                                                                                    Emphasizing Frege’s roots in 19th-century mathematics, and especially in function theory, Baker and Hacker argue strongly against Dummett’s view that Frege was a philosopher of language concerned to construct a theory of meaning for natural language.

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                                                                                                                                                                                                                                                                                                                                                                                    • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. 4, Frege’s Philosophy of Thought and Language. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                      This is the fourth of the four-volume collection that includes the most important papers published on Frege between 1986 and 2005 (cited under Anthologies). This volume is divided into four parts: the first titled “Frege and the Philosophy of Language,” the second “Concepts and Predication,” the third “Sinn and Bedeutung,” and the fourth “The Analysis of Thoughts.”

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                                                                                                                                                                                                                                                                                                                                                                                      • Burge, Tyler. Truth, Thought, Reason: Essays on Frege. Oxford: Clarendon, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                        Part 2 of this book is titled “Sense and Cognitive Value,” which comprises Burge’s two most influential papers on Frege’s notion of sense: Burge 1979 and Burge 1990 (see Philosophy of Thought and Language: Essays).

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                                                                                                                                                                                                                                                                                                                                                                                        • Dummett, Michael. Frege: Philosophy of Language. 2d ed. London: Duckworth, 1981a.

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                                                                                                                                                                                                                                                                                                                                                                                          This pioneering book interpreted Frege as the founder of modern philosophy of language. The first edition was published in 1973, but inexplicably left out the references to Frege’s writings. These were added in the second edition, which is therefore the edition to use.

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                                                                                                                                                                                                                                                                                                                                                                                          • Dummett, Michael. The Interpretation of Frege’s Philosophy. London: Duckworth, 1981b.

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                                                                                                                                                                                                                                                                                                                                                                                            In this book Dummett responds to the criticisms made of his first book and discusses further topics. Chapter 3 is titled “Was Frege a Philosopher of Language?”

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                                                                                                                                                                                                                                                                                                                                                                                            • Dummett, Michael. Origins of Analytical Philosophy. London: Duckworth, 1993.

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                                                                                                                                                                                                                                                                                                                                                                                              In the longest (and last main) chapter of this book, titled “Thought and Language,” Dummett argues that it is to Frege we owe the “fundamental axiom of analytical philosophy—that the only route to the analysis of thought goes through the analysis of language” (p. 128).

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                                                                                                                                                                                                                                                                                                                                                                                              Essays

                                                                                                                                                                                                                                                                                                                                                                                              Burge 1979 was the first important paper taking issue with Dummett’s interpretation of Frege as a philosopher of language. See also Ricketts 1986, Burge 1990, and Weiner 1997. Heck and May 2006 offers an account more sympathetic to Dummett’s concerns.

                                                                                                                                                                                                                                                                                                                                                                                              Concept and Object

                                                                                                                                                                                                                                                                                                                                                                                              The distinction between objects and functions, of which concepts are one kind (functions that map objects onto truth-values) is the most fundamental distinction in Frege’s philosophy. Yet, notoriously, it is a distinction that cannot be expressed in Frege’s own ‘Begriffsschrift.’ This, together with Frege’s characterization of objects as “unsaturated” and functions as “unsaturated” and the resultant “paradox of the concept horse,” as it has been called, has generated enormous controversy among commentators. The paradox has inspired the work of Diamond and Conant (see Frege and Wittgenstein), and an excellent recent account of the distinction and paradox is provided in Ricketts 2010. The paradox is also discussed in Wright 1998, Gaskin 2008, and Proops 2013. Rumfitt 1994 and Oliver 2010 offer further elucidation of Frege’s theory of predication, and Heck and May 2013 carefully traces the evolution of Frege’s notion of function. Frege also insisted that concepts must be defined for all objects: the problems that this raises are discussed in Kemp 1996.

                                                                                                                                                                                                                                                                                                                                                                                              • Gaskin, Richard. The Unity of the Proposition. Oxford: Oxford University Press, 2008.

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                                                                                                                                                                                                                                                                                                                                                                                                Gaskin discusses the paradox of the concept horse in the context of considering Frege’s views on the unity of the proposition, an issue that loomed large in Russell’s philosophy (but which Russell never solved).

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                                                                                                                                                                                                                                                                                                                                                                                                • Heck, Richard G., and Robert May. “The Function is Unsaturated.” In The Oxford Handbook of the History of Analytic Philosophy. Edited by Michael Beaney, 825–850. Oxford: Oxford University Press, 2013.

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                                                                                                                                                                                                                                                                                                                                                                                                  This provides a detailed account of the development of Frege’s conception of the “unsaturatedness” of functions, which is what he saw as distinguishing them from objects.

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                                                                                                                                                                                                                                                                                                                                                                                                  • Kemp, Gary. “Frege’s Sharpness Requirement.” Philosophical Quarterly 45 (1996): 168–184.

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                                                                                                                                                                                                                                                                                                                                                                                                    Concepts, according to Frege, must be defined for all objects. Kemp investigates this requirement and draws out its implications for our understanding of ordinary language. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 160–176.

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                                                                                                                                                                                                                                                                                                                                                                                                    • Oliver, Alex. “What Is a Predicate?” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 118–148. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                                                                                                                                                                                      Oliver explores the question of what Frege meant by “predicate.”

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                                                                                                                                                                                                                                                                                                                                                                                                      • Proops, Ian. “What is Frege’s ‘concept horse problem’?” In Wittgenstein’s Tractatus: History and Interpretation. Edited by Peter Sullivan and Michael Potter, 76–96. Oxford: Oxford University Press, 2013.

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                                                                                                                                                                                                                                                                                                                                                                                                        Proops distinguishes four sub-problems that fall under the general rubric “Frege’s concept horse problem.”

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                                                                                                                                                                                                                                                                                                                                                                                                        • Ricketts, Thomas. “Concepts, Objects and the Context Principle.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 149–219. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                                                                                                                                                                                          In this long and rich paper, Ricketts discusses Frege’s fundamental distinction between concept and object, the paradox (which Ricketts calls the “Kerry paradox,” otherwise known as the paradox of the concept horse) that Frege’s understanding of that distinction generates, and the role that the context principle plays alongside the distinction in his logicist project.

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                                                                                                                                                                                                                                                                                                                                                                                                          • Rumfitt, Ian. “Frege’s Theory of Predication: An Elaboration and Defense, with Some New Applications.” Philosophical Review 103 (1994): 599–637.

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                                                                                                                                                                                                                                                                                                                                                                                                            Rumfitt explains and refines Frege’s use of function-argument analysis in developing his theory of predication. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 127–159.

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                                                                                                                                                                                                                                                                                                                                                                                                            • Wright, Crispin. “Why Frege Does Not Deserve His Grain of Salt: A Note on the Paradox of ‘the Concept Horse’ and the Ascription of Bedeutungen to Predicates.” In New Essays on the Philosophy of Michael Dummett. Edited by J. Brandl and P. Sullivan, 239–263. Grazer Philosophische Studien 55. Amsterdam: Rodopi, 1998.

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                                                                                                                                                                                                                                                                                                                                                                                                              Wright discusses the paradox of the concept horse and argues that Frege was wrong to have extended his distinction between sense and reference to the case of predicates. Reprinted in Hale and Wright 2001, pp. 72–90 (cited under Frege’s Theorem and Neo-Logicism). Also reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 349–386.

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                                                                                                                                                                                                                                                                                                                                                                                                              Sense and Reference

                                                                                                                                                                                                                                                                                                                                                                                                              Frege’s distinction between Sinn and Bedeutung is his most well-known and influential doctrine. “Sinn” is uncontroversially translated as “sense,” but the translation of “Bedeutung” has been much disputed; see Beaney 1997 for discussion. “Reference,” “denotation,” and “meaning” have been most commonly used; “reference” is used here. This section is divided into two subsections: Books and Essays.

                                                                                                                                                                                                                                                                                                                                                                                                              • Beaney, Michael. “Introduction.” In The Frege Reader. Edited by Michael Beaney, 1–46. Oxford: Blackwell, 1997.

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                                                                                                                                                                                                                                                                                                                                                                                                                §4 of this introduction is titled “The Translation of ‘Bedeutung,’” and discusses the controversy over the translation of this key term in Frege’s writings. In The Frege Reader, the term is left untranslated.

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                                                                                                                                                                                                                                                                                                                                                                                                                Books

                                                                                                                                                                                                                                                                                                                                                                                                                Book-length treatments of Frege’s conception of sense include Carl 1994, Beaney 1996, Mendelsohn 2005, and Textor 2011. The latter can be recommended as the most up-to-date treatment.

                                                                                                                                                                                                                                                                                                                                                                                                                • Beaney, Michael. Frege: Making Sense. London: Duckworth, 1996.

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                                                                                                                                                                                                                                                                                                                                                                                                                  This book traces the development of Frege’s conception of sense in the context of his logicist project. The last three chapters discuss a number of issues that arise in understanding that conception.

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                                                                                                                                                                                                                                                                                                                                                                                                                  • Carl, Wolfgang. Frege’s Theory of Sense and Reference. Cambridge, UK: Cambridge University Press, 1994.

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                                                                                                                                                                                                                                                                                                                                                                                                                    Carl places Frege’s theory of sense and reference in the broader context of the Kantian tradition of epistemology.

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                                                                                                                                                                                                                                                                                                                                                                                                                    • Mendelsohn, Richard L. The Philosophy of Gottlob Frege. Cambridge, UK: Cambridge University Press, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                      The title of this book is misleading: It gives no account of Frege’s philosophy of mathematics or his logicist project, out of which his philosophical ideas developed. But it offers a detailed analysis of the arguments in Frege’s famous essay on sense and reference and of the philosophical issues raised.

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                                                                                                                                                                                                                                                                                                                                                                                                                      • Textor, Mark. Frege on Sense and Reference. London: Routledge, 2011.

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                                                                                                                                                                                                                                                                                                                                                                                                                        This book provides one of the fullest treatments to date of Frege’s distinction between sense and reference. After setting the scene in the first three chapters, Textor explains in chapter 4 how Frege’s early notion of content split into the notions of sense and reference. The remaining three chapters concern the application of the distinction to singular terms, sentences, and concept-words, respectively.

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                                                                                                                                                                                                                                                                                                                                                                                                                        Essays

                                                                                                                                                                                                                                                                                                                                                                                                                        The best (though long) article on the distinction is Kremer 2010. A reading of this could then be supplemented by Taschek 2010 (and see also his earlier paper, Taschek 1992). Kripke has offered his own account of Frege’s distinction (Kripke 2008); for responses, see Künne 2010 and Yourgrau 2012.

                                                                                                                                                                                                                                                                                                                                                                                                                        • Kremer, Michael. “Sense and Reference: The Origins and Development of the Distinction.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 220–292. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                                                                                                                                                                                                          In this long article, Kremer offers a detailed account of the origins of the distinction in Frege’s early account of “content” and his arguments in “On Sense and Reference.”

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                                                                                                                                                                                                                                                                                                                                                                                                                          • Kripke, Saul. “Frege’s Theory of Sense and Reference: Some Exegetical Notes.” Theoria 74 (2008): 181–218.

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                                                                                                                                                                                                                                                                                                                                                                                                                            Considering the shift of sense and reference in indirect contexts, Kripke argues that we must ascribe a doctrine of acquaintance to Frege. Reprinted in Saul Kripke, Philosophical Troubles, Collected Papers, Vol. 1 (Oxford: Oxford University Press, 2011), pp. 254–291.

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                                                                                                                                                                                                                                                                                                                                                                                                                            • Künne, Wolfgang. “Sense, Reference and Hybridity: Reflections on Kripke’s Recent Reading of Frege.” Dialectica 64 (2010): 529–551.

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                                                                                                                                                                                                                                                                                                                                                                                                                              Künne here responds to Kripke 2008.

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                                                                                                                                                                                                                                                                                                                                                                                                                              • Taschek, William. “Frege’s Puzzle, Sense, and Information Content.” Mind 101 (1992): 767–791.

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                                                                                                                                                                                                                                                                                                                                                                                                                                What has been called “Frege’s puzzle” concerns how two sentences can possess the same referential truth conditions but differ in cognitive value. Taschek discusses this puzzle and argues that Russellian accounts fail. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 217–244.

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                                                                                                                                                                                                                                                                                                                                                                                                                                • Taschek, William. “On Sense and Reference: A Critical Reception.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 293–339. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                                                                                                                                                                                                                  In considering the reception of Frege’s distinction in 20th-century philosophy of language, Taschek focuses on the debate as to whether an adequate theory of meaning requires a Fregean notion of sense.

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                                                                                                                                                                                                                                                                                                                                                                                                                                  • Yourgrau, Palle. “Kripke’s Frege.” Thought 1 (2012): 100–107.

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                                                                                                                                                                                                                                                                                                                                                                                                                                    Yourgrau offers a response to Kripke 2008.

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                                                                                                                                                                                                                                                                                                                                                                                                                                    Thought and Indexicality

                                                                                                                                                                                                                                                                                                                                                                                                                                    Indexicals are expressions, such as “I,” “here,” “now,” and “this,” whose reference depends systematically on the context of utterance. They pose a serious problem for Frege’s conception of thought (understood as the sense expressed by a sentence), threatening what many have taken as his criterion for sameness of thought. The problem was first raised by Perry (Perry 1977, Perry 1979), and an attempt to reconstruct Frege’s views to answer it was made by Evans (Evans 1981). Harcourt 1999 argues that a tension remains in Frege’s philosophy, since his interests were different from ours today. May 2006 offers a different solution, developing Frege’s views by distinguishing two kinds of sense. The problem also raises issues about the compositionality of thought, which has also been much debated in Frege scholarship, as indeed in analytic philosophy more generally. The best paper on this is Heck and May 2011.

                                                                                                                                                                                                                                                                                                                                                                                                                                    • Evans, Gareth. “Understanding Demonstratives.” In Meaning and Understanding. Edited by Herman Parret and Jacques Bouveresse, 280–303. Berlin: Walter de Gruyter, 1981.

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                                                                                                                                                                                                                                                                                                                                                                                                                                      Evans attempts to develop Frege’s theory of sense to accommodate demonstratives and other indexicals, arguing that the “way of thinking” of the referent of an indexical should be construed as a “way of keeping track” of it. Reprinted in Gareth Evans, Collected Papers (Oxford: Oxford University Press, 1985), pp. 291–321.

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                                                                                                                                                                                                                                                                                                                                                                                                                                      • Harcourt, Edward. “Frege on ‘I,’ ‘Now,’ ‘Today,’ and Some Other Linguistic Devices.” Synthese 121 (1999): 329–356.

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                                                                                                                                                                                                                                                                                                                                                                                                                                        Opposing the views of Perry and Evans, among others, Harcourt argues that Frege did not recognize the apparent irreducibility of indexicals and hence the problem they posed for his criterion for sameness of thought. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 262–287.

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                                                                                                                                                                                                                                                                                                                                                                                                                                        • Heck, Richard G., and Robert May. “The Composition of Thoughts.” Noûs 45 (2011): 126–166.

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                                                                                                                                                                                                                                                                                                                                                                                                                                          Heck and May offer a sophisticated account of compositionality according to which, as they put it: “Thoughts are coherently organized not because there is some organizing principle that binds the senses themselves together, but because senses are related to references that compose via function-application” (p. 153).

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                                                                                                                                                                                                                                                                                                                                                                                                                                          • May, Robert. “Frege on Indexicals.” Philosophical Review 115 (2006): 487–516.

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                                                                                                                                                                                                                                                                                                                                                                                                                                            Distinguishing senses that constrain reference from senses that present reference, May argues that the senses of indexicals are constraining senses, not presenting senses.

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                                                                                                                                                                                                                                                                                                                                                                                                                                            • Perry, John. “Frege on Demonstratives.” Philosophical Review 86 (1977): 474–497.

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                                                                                                                                                                                                                                                                                                                                                                                                                                              This was the first paper to discuss the problem that demonstratives pose for Frege’s conception of sense. Reprinted in John Perry, The Problem of the Essential Indexical and Other Essays (Oxford: Oxford University Press, 1993), pp. 3–25.

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                                                                                                                                                                                                                                                                                                                                                                                                                                              • Perry, John. “The Problem of the Essential Indexical.” Noûs 13 (1979): 3–21.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                What Perry calls “the problem of the essential indexical” suggests that some thoughts, at least, are essentially dependent on the indexicals that are used in giving expression to them, threatening Frege’s apparent assumption that all thoughts are objective. Reprinted in John Perry, The Problem of the Essential Indexical and Other Essays (Oxford: Oxford University Press, 1993), pp. 26–49.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                Analysis and Elucidation

                                                                                                                                                                                                                                                                                                                                                                                                                                                Frege is rightly taken as one of the founders of analytic philosophy, given the important role that logical analysis played in his own work. But this is not to say that there is agreement on exactly what Frege understood by analysis or on the kinds of analysis that can be found in his work. For an overview of the historical background to Frege’s conception and practice of analysis, see Beaney 2014. Levine 2007 and Reck 2007 show how dependent Frege’s logicist project (and indeed Russell’s logicist project) is on the underlying analytic methodology. Fundamental to all debates about analysis is the so-called paradox of analysis, which Frege himself formulated in responding to objections that Husserl had raised to his logicist analyses in the Foundations. For discussion, see Dummett 1991 and Beaney 2005. Other aspects of his methodology are also relevant here. Diamond 1984, a classic paper on the purpose of a “Begriffsschrift,” is still worth reading, and it is essential to understand the importance of “elucidation” (Erläuterung) in Frege’s philosophy; on this, see especially Weiner 2005 and Beaney 2006. See also Analysis and Decomposition.

                                                                                                                                                                                                                                                                                                                                                                                                                                                • Beaney, Michael. “Sinn, Bedeutung and the Paradox of Analysis.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 4, Frege’s Philosophy of Thought and Language. Edited by Michael Beaney and Erich H. Reck, 288–310. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                  Beaney stresses the role that the distinction between sense and reference played in justifying Frege’s logicist project, and discusses three responses to the paradox of analysis that can be discerned in Frege’s writings.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Beaney, Michael. “Frege and the Role of Historical Elucidation: Methodology and the Foundations of Mathematics.” In The Architecture of Modern Mathematics: Essays in History and Philosophy. Edited by José Ferreirós and Jeremy Gray, 49–71. Oxford: Oxford University Press, 2006.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                    Beaney here argues that “elucidation,” as offered by Frege himself in motivating his logicist project, has an essentially historical dimension.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Beaney, Michael. “Analysis.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University Press, 2014.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                      First published in 2003, and last revised in 2014, this entry provides an overview of the development of conceptions and practices of analysis in the history of philosophy from ancient Greek geometry onward. It also contains an extensive bibliography.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Diamond, Cora. “What Does a Concept Script Do?” In Frege: Tradition and Influence. Edited by Crispin Wright, 158–183. Oxford: Blackwell, 1984.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                        Diamond argues that one of the purposes of a “Begriffsschrift” is to allow us to see that certain philosophical claims simply drop away as mere nonsense when thought through.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                        • Dummett, Michael. “Frege and the Paradox of Analysis.” In Frege and Other Philosophers. Edited by Michael Dummett, 17–52. Oxford: Oxford University Press, 1991.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                          Dummett discusses the paradox of analysis as it is illustrated in questions about the status of Frege’s logicist definitions.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                          • Levine, James. “Analysis and Abstraction Principles in Russell and Frege.” In The Analytic Turn: Analysis in Early Analytic Philosophy and Phenomenology. Edited by Michael Beaney, 51–74. London: Routledge, 2007.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                            Levine shows how the differences in Frege’s and Russell’s logicist projects, reflected in their use and understanding of abstraction principles, such as Hume’s Principle, are based on their different conceptions of analysis.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                            • Reck, Erich H. “Frege-Russell Numbers: Analysis or Explication?” In The Analytic Turn: Analysis in Early Analytic Philosophy and Phenomenology. Edited by Michael Beaney, 33–50. London: Routledge, 2007.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                              Reck addresses the question of whether Frege’s logicist definitions of the natural numbers were intended as an “analysis,” revealing what the numbers “really” are, or an “explication,” reconstructing them in a more powerful theory.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                              • Weiner, Joan. “On Fregean Elucidation.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 4, Frege’s Philosophy of Thought and Language. Edited by Michael Beaney and Erich H. Reck, 197–214. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                Developing the account in the final chapter of her 1990 book (see More Advanced Works), Weiner emphasizes the important role played by “elucidation” in Frege’s philosophy. This is a revised version of “Theory and Elucidation: The End of the Age of Innocence,” in Future Pasts, edited by Juliet Floyd and Sanford Shieh (Oxford: Oxford University Press, 2001), pp. 43–65.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                Analysis and Decomposition

                                                                                                                                                                                                                                                                                                                                                                                                                                                                One fundamental question about Frege’s conception of analysis is whether he allowed that there can be alternative analyses. This was disputed between Bell (Bell 1987) and Dummett (Dummett 1989), drawing on his earlier account (Dummett 1981). Landini 1996 and Levine 2002 give opposed responses to this debate.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                Epistemology and Metaphysics

                                                                                                                                                                                                                                                                                                                                                                                                                                                                Frege’s revolutionary work on logic and the philosophy of mathematics, and the enormous influence that his ideas have had in philosophy of language, have made it easy to overlook or play down his epistemological interests and metaphysical views. Yet the epistemological dimension of Frege’s logicism is obvious: in the Foundations Frege locates his own view in a Kantian epistemological framework, as has been emphasized in Kitcher 1979. Sluga 1980 and Gabriel 1996 also see Frege as rooted in German epistemology. Burge has perhaps done most to clarify Frege’s epistemology; his essays are collected in Burge 2005. As to his metaphysics, this dimension of Frege’s philosophy is most obvious in the distinction he draws between concepts and objects (see Concept and Object). But it also comes out, especially in his later work, in regarding thoughts and other abstract objects as inhabitants of a “third realm,” neither mental nor physical. Beaney and Reck 2005 contains papers on Frege’s epistemology and metaphysics. This section contains four subsections: Epistemology and Logic, Context Principle, Thought and Judgment, and Thought and Objectivity.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                • Beaney, Michael, and Erich H. Reck, eds. Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 1, Frege’s Philosophy in Context. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                  This is the first of the four-volume collection that includes the most important papers published on Frege between 1986 and 2005 (cited under Anthologies). The third part is on Frege’s epistemology and metaphysics, with papers by Ricketts, Picardi, Gabriel, Kremer, and Carl.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Burge, Tyler. Truth, Thought, Reason: Essays on Frege. Oxford: Clarendon, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Part 3 is titled “Rationalism” and contains Burge’s essays on Frege’s epistemology. Burge remarks in the preface to this book that “Frege’s epistemology—his attempt to understand the nature of mathematical knowledge—lies at the philosophical heart of all his work, including his philosophy of language” (p. v).

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Gabriel, Gottfried. “Frege’s ‘Epistemology in Disguise.’” In Frege: Importance and Legacy. Edited by Matthias Schirn, 330–346. Berlin: Walter de Gruyter, 1996.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Gabriel argues that Frege was more an epistemologist than philosopher of language and that we should recognize the distinction between “justification” and “proof” in appreciating his epistemology. Reprinted in Beaney and Reck 2005 (cited under Historical Context), pp. 359–374.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Kitcher, Philip. “Frege’s Epistemology.” Philosophical Review 88 (1979): 235–262.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Kitcher argues that throughout his life, Frege worked within a Kantian epistemological framework.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                        • Sluga, Hans. Gottlob Frege. London: Routledge, 1980.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Reacting against Dummett’s view of Frege as a philosopher of language, Sluga places Frege firmly in the broad Kantian epistemological tradition that was dominant in Germany at the time.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Epistemology and Logic

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Beaney and Reck 2005 contains papers on this topic, to be read in this order: Burge 1998, Jeshion 2001, Weiner 2004, Jeshion 2004.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          The Context Principle

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          The context principle is only explicitly formulated by Frege in the Foundations of Arithmetic, and the question of whether Frege held it before but especially after the Foundations has been highly controversial, involving as it does the deepest issues in his philosophy. Dummett changed his mind on this several times; see Dummett 1981, Dummett 1991, and Dummett 1995. Ricketts 2010 gives an account of the principle in connection with Frege’s distinction between concept and object, and Wilson 2005 argues that Frege’s use of it in the Foundations needs to be seen in context itself. Reck 1997 emphasizes the importance of the context principle not only in Frege’s philosophy, but also in appreciating Frege’s influence on Wittgenstein.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          • Dummett, Michael. The Interpretation of Frege’s Philosophy. London: Duckworth, 1981.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Dummett discusses the context principle at length in chapter 19.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                            • Dummett, Michael. Frege: Philosophy of Mathematics. London: Duckworth, 1991.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Dummett discusses the context principle in the central chapters of this book (chapters 9–18), in explaining its role in Frege’s logicist project.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                              • Dummett, Michael. “The Context Principle: Centre of Frege’s Philosophy.” In Logik und Mathematik: Frege-Kolloquium Jena 1993. Edited by Ingolf Max and Werner Stetzner, 3–19. Berlin: de Gruyter, 1995.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Rejecting some of his own earlier views, Dummett here argues that Frege continued to hold the context principle after the Foundations. Reprinted in Beaney and Reck 2005 (cited under Philosophy of Thought and Language: Books), pp. 245–261.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                • Reck, Erich H. “Frege’s Influence on Wittgenstein: Reversing Metaphysics via the Context Principle.” In Early Analytic Philosophy: Frege, Russell, Wittgenstein. Edited by William W. Tait, 123–185. Chicago: Open Court, 1997.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  In exploring Frege’s influence on Wittgenstein, Reck argues that Frege should be seen as a “contextual” rather than “metaphysical” Platonist, with the context principle at the center of his philosophy. Reprinted in a shortened and revised version in Beaney and Reck 2005 (cited under Historical Context), pp. 241–289.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Ricketts, Thomas. “Concepts, Objects and the Context Principle.” In The Cambridge Companion to Frege. Edited by Michael Potter and Tom Ricketts, 149–219. Cambridge, UK: Cambridge University Press, 2010.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Ricketts discusses the context principle in the last two sections of this paper.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Wilson, Mark. “Ghost World: A Context for Frege’s Context Principle.” In Gottlob Frege: Critical Assessments of Leading Philosophers. Vol. 3, Frege’s Philosophy of Mathematics. Edited by Michael Beaney and Erich H. Reck, 157–175. London: Routledge, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Wilson argues that Frege’s context principle must be understood in the context of concern in 19th-century geometry with the introduction of extension elements. By taking the particular case study of Frege’s context principle, Wilson thus illustrates his earlier claims in Wilson 2010 (cited under Frege in Mathematical Context).

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Thought and Judgment

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      According to Frege, as he explains it in his late essay “Thought,” judgment is the acknowledgment of the truth of a thought, so elucidation of his notion of judgment requires understanding its connection to his notions of thought and truth. The best and fullest treatment of all this is provided by Künne in his commentary in German on the essays that compose Frege’s “Logical Investigations” (Künne 2010). See Künne 2013 for a much briefer account in English. Both Kremer 2000 and Gabriel 2013 shed further light on Frege’s theory of judgment by considering it in historical context, and Reck 2007 and Textor 2010 offer further philosophical elucidation.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Gabriel, Gottfried. “Truth, Value, and Truth Value: Frege’s Theory of Judgement and its Historical Background.” In Judgement and Truth in Early Analytic Philosophy and Phenomenology. Edited by Mark Textor, 36–51. Basingstoke, UK: Palgrave Macmillan, 2013.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Gabriel locates Frege’s theory of judgment against the background of neo-Kantianism, especially that of the Southwest School.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        • Kremer, Michael. “Judgment and Truth in Frege.” Journal of the History of Philosophy 38 (2000): 549–581.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Responding to several of Ricketts’ papers (e.g., Ricketts 1986, cited under Thought and Objectivity), Kremer argues that the connection Frege saw between judgment and truth depends on his conception of “holding-true.” Reprinted in Beaney and Reck 2005 (cited under Historical Context), pp. 375–408.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          • Künne, Wolfgang. Die Philosophische Logik Gottlob Freges: Ein Kommentar. Frankfurt: Vittorio Klostermann, 2010.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            For the German-language reader, this is the best work on Frege’s “Logical Investigations,” which is where Frege discusses thought, judgment, and truth in most detail.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            • Künne, Wolfgang. “Merely Entertaining a Thought, Judging and Asserting: Notes on a Passage in Frege’s ‘The Thought.’” In Judgement and Truth in Early Analytic Philosophy and Phenomenology. Edited by Mark Textor, 52–73. Basingstoke, UK: Palgrave Macmillan, 2013.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Künne explores the relationship between Frege’s conceptions of entertaining thoughts, judging, and asserting, as they emerge in Frege’s late essay “Thought.”

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              • Reck, Erich H. “Frege on Truth, Judgment, and Objectivity.” In Essays on Frege’s Conception of Truth. Edited by Dirk Greimann, 149–173. Grazer Philosophische Studien 75. Amsterdam: Rodopi, 2007.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Reck argues that Frege’s notions of truth, judgment, and objectivity, as well as related notions, can be understood only in their interconnections.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                • Textor, Mark. “Frege on Judging as Acknowledging the Truth.” Mind 119 (2010): 615–655.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  In this paper, Textor expounds and defends Frege’s conception of judgment as the acknowledgment of truth.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Thought and Objectivity

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Throughout his life Frege stressed the objectivity of thoughts, though quite what this amounted to has been debated. In his late essay “Thought,” he argues that thoughts—and other abstract objects—are objects inhabiting a “third realm” that is neither physical nor mental. Dummett 1986 attacks this “myth of the third realm,” and most commentators have felt obliged to reconstruct Frege’s views in defending the objectivity of thought. Dummett 1981 discusses Frege’s realism, Burge 1992 interprets Frege as a rationalist and Platonist, while Ricketts 1986 rejects the Platonist reading, and Carl 2001 argues that Frege is neither a Platonist nor a neo-Kantian. The issue connects with Frege’s lifelong hostility to psychologism; see Picardi 1996 and May 2006 for two different angles on this.

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