Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the (...) analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research. (shrink)

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been (...) proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured. (shrink)

George Boolos; IX*—Saving Frege from Contradiction, Proceedings of the Aristotelian Society, Volume 87, Issue 1, 1 June 1987, Pages 137–152, https://doi.org/10.

Michael DUMMETT: Frege: Philosophy of Language, London: Duckworth second edition 1981; and Michael DUMMETT: The Interpretation of Frege's Philosophy, London: Duckworth 1981.

I wish to express, first of all, my profound gratitude to Professor J. M. Bochenski, without whose assistance the present work would have not been possible. To be concise, I would like to state that his contribution to this book may be viewed at three levels: (1) that of the general spirit, (2) that of the specific ideas, theses or approaches which are expressed in its pages, (3) that of this work qua doctoral dissertation. The general spirit which has guided (...) my research coincides with that underlying Professor :Oochenski's own works, in particular his Formale Logik (Munchen 1956). Moreover, the particular occasion which suggested my investigation was a statement included in that book according to which the literature in the field still lacked a detailed work on Frege (p. 317). I wish, likewise, to express my gratitude to other professors of the University of Fribourg for their generous help. I mention especially Professors P. Wyser, M. D. Philippe, N. Luyten, and V. Kuiper. I have also benefited from Professor E. Specker's lectures at the Eidge nossische Technische Hochschule (ZUrich) and from Professor Olof Gigon's lectures at the University of Bern. From an earlier period I wish to express my gratitude to the professors of the philosophy department of the Universidad Nacional de Buenos Aires, especially the late Professor Francisco Romero. The Swiss National Library (Bern) has greatly facilitated access to bibliographical sources, and the library of the University of Munster (Westphalien) has kindly provided microfilms of Frege's Nachlap. (shrink)

In this paper, the authors discuss Frege's theory of "logical objects" and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for (...) Logical Objects and banishes encoding formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: the theory of extensions, the theory of directions and shapes, and the theory of truth values. (shrink)

In this extended essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed (...) evidence that there are numerous (over a hundred) and extensive parallels both in formulation and --more importantly-- in content between the Stoics and Frege, parallels so plentiful that one would be hard pressed to brush them off as coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope. -/- (Corrigendum: At school, Frege likely had seven, not ten, years of intensive Latin and four years of intensive ancient Greek courses.). (shrink)

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1973.

Gottlob Frege (1848-1925) und Ludwig Wittgenstein gelten als die geistigen Väter der analytischen Philosophie. Das wissenschaftliche Schaffen Gottlob Freges hat wie kein anderes nach Aristoteles die Logik in ihrer theoretischen Erscheinungsform und in ihrer praktischen Relevanz grundlegend verändert. Seine logisch-semantischen Untersuchungen haben noch immer auf Philosophie und Sprachwissenschaft großen Einfluß. Doch wer war dieser Mann, der die Geistesgeschichte des 20. Jahrhunderts mitgestaltete, dessen Rückführung logischen Schließens auf mechanisch kontrollierte Elementarschritte den Weg zur Logik der elektronischen Datenverarbeitung eröffnete? Zwar gibt es (...) Arbeiten, die sich mit besonderen Seiten oder speziellen Zeiten von Freges Leben beschäftigen, eine umfassende Biographie über ihn gab es jedoch bislang nicht. Diese Lücke schließt Lothar Kreisers Buch. Freges Leben wird biographisch zunächst in dem Kontext der Stadt und Stadtschule Wismar, dann in dem der Stadt und der Universität Jena eingebettet rekonstruiert. Regional übergreifende politische und wissenschaftliche Vorgänge werden einbezogen, um verbürgten konkreten Ereignissen aus Freges Leben einen für das Verstehen tieferen und festeren Rahmen zu geben. Seine Mitwirkung in Kommisionen und Gesellschaften kommt ebenso zur Sprache wie die Wurzeln seines wissenschaftlichen Lebenswerkes, seine Beziehungen zu anderen Persönlichkeiten und deren Bestrebungen, aber auch der Wandel in seinen politischen Überzeugungen. Die Biographie setzt keine speziellen Fachkenntnisse, nur Interesse an einem spannenden Abschnitt der Wissenschaftsgeschichte, fokussiert auf die Person Gottlob Frege, voraus. "Gottlob Frege: Leben - Werk - Zeit" ist Biographie und Millieustudie zugleich. (shrink)

Dieses Buch enthält in einer historisch-kritischen Edition die Texte, die es in seinem Hauptteil kommentiert: Das Vorwort (1893) zu Gottlob Freges Hauptwerk, den "Grundgesetzen der Arithmetik", in dem er seine fulminante Psychologismus-Kritik vorträgt; die drei von Frege selbst veröffentlichten "Logischen Untersuchungen" (1918-1923), in denen er "die Ernte [s]eines Lebens heimbringen" wollte; und schließlich ein Fragment aus seinem Nachlass, das der Entwurf zu einer vierten LU ist.

In this investigation into Frege's philosophical views as a whole, the central focus is on his notion of sense, the conception that has proved most influential in the development of analytical philosophy, and around which the main problems of interpretation revolve.

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic and hence with the (...) notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (shrink)

Demonstratives seem to have posed a severe difficulty for Frege’s philosophy of language, to which his doctrine of incommunicable senses was a reaction. In “The Thought,” Frege briefly discusses sentences containing such demonstratives as “today,” “here,” and “yesterday,” and then turns to certain questions that he says are raised by the occurrence of “I” in sentences (T, 24-26). He is led to say that, when one thinks about oneself, one grasps thoughts that others cannot grasp, that cannot be communicated. However, (...) nothing could be more out of the spirit of Frege’s account of sense and thought than an incommunicable, private thought. In the first part of the paper, I explain the problem demonstratives pose for Frege, and explore three ways he might have dealt with it. I argue that none of these ways provides Frege with a solution to his problem consistent with his philosophy of language. The first two are plausible as solutions, but contradict his identification of the sense expressed by a sentence with a thought. The third preserves the identification, but is implausible. In the second part, I suggest that Frege was led to his doctrine of incommunicable senses as a result of some appreciation of the difficulties his account of demonstratives faces, for these come quickly to the surface when we think about “I.” I argue that incommunicable senses won’t help. I end by trying to identify the central problem with Frege’s approach, and sketching an alternative. (shrink)

How many senses can a given name have, with its reference held fixed? One, more than one? One answer that most would agree to is that sense is unique for each utterance of a name, that is, that a name can have no more than one sense on any given occasion. But is sense unique in any stronger sense than this? The answer that is typically attributed to Frege is that there is not, that, as Tyler Burge puts it, 1 (...) Frege “treats proper names as having different senses while applying to the same person.” There are a number of possibilities for the locus of this multiplicity of sense; the following remark by Ruth Marcus indicates the possibilities: “the sense of a term is whatever is grasped or understood by a speaker on a particular occasion of use and may vary from occasion to occasion as well as from speaker to speaker.”2 Of the views canvassed by Marcus, we can draw out a more conservative one, and one more extreme. On the more conservative view, Frege is holding that sense may vary from speaker to speaker; on the more extreme view, Frege holds not only this, but that sense may vary from context to context. Endorsements of the two views are not hard to find. For example, typical sorts of endorsement of the conservative view are found in Harold Noonan’s remark that “different senses [are] associated with the name ‘Aris-. (shrink)

It is a characteristically Fregean thesis that the sense expressed by an expression is the linguistic meaning of that expression. Sense can play this role for Frege since it meets fundamental desiderata for meaning, that it be universal and invariantly expressed and objectively the same for everyone who knows the language. It has been argued,1 however, that, as a general thesis about natural languages, the identi cation of sense and meaning cannot be sustained since it is in con ict with (...) another characteristically Fregean thesis, that sense uniquely determines reference. The argument is quite simple and can be outlined as follows. Assume the two theses we have just stated. (shrink)

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...) every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. (shrink)

überall einen richtigen Gebrauch der reinen Vernunft giebt, in welchem Fall es auch einen Canon derselben geben muß, so wird dieser nicht den speculativen, sondernden pr.ntischen Vernunftgebrauch betreffen, den wir also iezt ...

Husserls »Logische Untersuchungen« sind eines der folgenreichsten Werke der neueren Philosophiegeschichte. Mit dem ersten Erscheinen in den Jahren 1900 und 1901 (Max Niemeyer Verlag, Halle/Saale) nimmt jene Schule ihren Anfang, deren Name im Untertitel des zweiten Bandes zum ersten Mal sinnfällig wird: die Phänomenologie. Husserl sah damals in diesem Werk »Versuche zur Neubegründung der reinen Logik und Erkenntnistheorie«, die den Grund zu einem größeren Gedankengebäude zu legen imstande waren. Sie wollten freilich kein bloßes Programm sein, sondern »Fundamentalarbeit an den unmittelbar (...) erschauten und ergriffenen Sachen« darstellen. Die weitere Arbeit an der Ausprägung der phänomenologischen Philosophie führte schon nach wenigen Jahren zu neuen Problemen, zu vertieften Erkenntnissen und zu schärferen Formulierungen. Ihnen trägt die zweite, zum Teil tiefgreifend umgearbeitete Auflage Rechnung, deren Text seither in unveränderter Form immer wieder nachgedruckt wurde. (shrink)

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)

It has been noted before in the history of logic that some of Frege's logical and semantic views were anticipated in Stoicism. In particular, there seems to be a parallel between Frege's Gedanke (thought) and Stoic lekton; and the distinction between complete and incomplete lekta has an equivalent in Frege's logic. However, nobody has so far claimed that Frege was actually influenced by Stoic logic; and there has until now been no indication of such a causal connection. In this essay, (...) we attempt, for the first time, to provide detailed evidence for the existence of this connection. In the course of our argumentation, further analogies between the positions of Frege and the Stoics will be revealed. The classical philologist Rudolf Hirzel will be brought into play as the one who links Frege with Stoicism. The renowned expert on Stoic philosophy was Frege's tenant and lived in the same house as the logician for many years. In der Geschichte der Logik ist häufig bemerkt worden, dass einige der logischen und semantischen Auffassungen Freges in der Stoa antizipiert worden sind. Genannt wurden insbesondere die Parallelen zwischen dem Fregeschen Gedanken und dem stoischen Lekton sowie die Unterscheidung zwischen vollständigen und unvollständigen Lekta, die bei Frege ihre Entsprechung hat. Ein Wirkungszusammenhang ist allerdings nicht behauptet worden. Dazu gab es bislang auch keinen Anlass. Der vorliegende Beitrag versucht erstmalig, einen detaillierten Indizienbeweis für das Bestehen eines solchen Zusammenhangs vorzulegen. Dabei werden weitere charakteristische Übereinstimmungen zwischen Frege und der Stoa aufgewiesen. Als Mittelsmann wird der Altphilologe Rudolf Hirzel vorgestellt. Er wohnte lange Jahre als Mieter zusammen mit Frege im selben Haus und war ein anerkannter Experte der stoischen Philosophie. (shrink)

Translation of Frege's 'Über Begriff und Gegenstand' (1892). Translation by Peter Geach, revised by Max Black.

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

This analysis of Frege's views on language and metaphysics in On Sense and Reference, arguably one of the most important philosophical essays of the past hundred years, provides a thorough introduction to the function/argument analysis and applies Frege's technique to the central notions of predication, identity, existence and truth. Of particular interest is the analysis of the Paradox of Identity and a discussion of three solutions: the little-known Begriffsschrift solution, the sense/reference solution, and Russell's 'On Denoting' solution. Russell's views wend (...) their way through the work, serving as a foil to Frege. Appendices give the proofs of the first 68 propositions of Begriffsschrift in modern notation. This book will be of interest to students and professionals in philosophy and linguistics. (shrink)