Frege: Intellectual Context

Frege and Peano started in 1896 a debate where they contrasted the respective conceptions on the theory and practice of mathematical definitions. Which was (if any) the influence of the Frege-Peano debate on the conceptions by the two authors on the theme of defining in mathematics and which was the role played by this debate in the broader context of their scientific interaction?

Kant's claim that arithmetical truths are synthetic is famously contradicted by Frege, who considers them to be analytical. It may seem that this is a mere dispute about linguistic labels, since both Kant and Frege agree that arithmetical truths are a priori and informative, and, therefore, it is only a matter of how one chooses to call them. I argue that the choice between calling arithmetic “synthetic” or “analytic” has a deeper significance. I claim that the dispute is not a (...) merely linguistic one, but one involving the status of arithmetic as a science. Namely, it is a dispute about what truths are appropriate to use in grounding a scientific discipline. I interpret Frege's critique of Kant as being mainly about the lack of distinction between the context of justification and the context of discovery. (shrink)

In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.

In 1919, when his Logisch-Philosophische Abhandlung (Tractatus Logico-Phi-losophicus), was finished but still unpublished, Wittgenstein sent the manuscript to Frege, and, as a consequence of that, they exchanged several fairly polemic letters in 1919 – 1920. Only Frege’s letters were preserved. The letters are highly compressed in content, and offer an interesting insight in how, mostly critically, one of the authors of whom Wittgenstein held highest esteem, thought about the content, style, and organisation of the manuscript. At the same time, we (...) can get some impression from Frege’s letters how Wittgenstein reacted to his initial letter addressing the Tractatus, and how the subsequent exchange went. In this paper, I offer several observations concerning their exchange, and I compare it to the parallel exchange on the same matter between Wittgenstein and Russell. (shrink)

Há muitos pontos de concordância entre Frege e os neokantianos. Isso vale especialmente para os representantes do neokantismo da teoria do valor ou do Sudoeste alemão na tradição de Hermann Lotze. Não discutiremos aqui todos os aspectos dessa proximidade; de acordo com o tema que propomos, ficaremos restritos à filosofia da matemática. A primeira parte do artigo tratará da relação entre aritmética e geometria, mostrando surpreendentes semelhanças entre Frege e o neokantiano Otto Liebmann. A segunda parte discutirá as diferentes recepções (...) do logicismo de Frege por Jonas Cohn, Paul Natorp, Heinrich Rickert, Ernst Cassirer e Bruno Bauch. (shrink)

The similarity between logic and semantics of the Stoics and Frege has long been known, and it can be explained in various ways. In 2021, Susane Bobzien published a work in which she explains this similarity rather surprisingly: she hypothesizes that Frege generously helped himself with the foundations of Stoic logic as it was published in the first volume of History of Logic in the West by Carl Prantl. However, this hypothesis encounters various problems. The key point of the whole (...) accusation is founded on the formulation of a general propo-sition in language using implication and anaphora, which Frege supposedly took from the Stoics, although in Prantl’s text there is only one example of a sentence with this structure. On the contrary, there are many examples of such sentences in contemporary professional (e.g. legal) texts. Many examples of semantic simi-larities that Bobzien presents are based only on the similarities between isolated concepts; however, that is regularly the case for such concepts with the same conceptual basis. Bobzien presents a significant number of matches only on the basis of results that could allegedly be inferred from the texts. However, this cannot be considered a proof of plagiarism. Bobzien does not consider many sources for the continuity of interpretation such as the so-called hypothetical syllogism found in available textbooks of logic. Last but not least, her claims do not consider many differences between Stoic and Frege’s logic. All this leads us to the conclusion that Bobzien does not present sufficient facts and connections between them that would confirm her hypothesis about Frege’s plagiarism of the Stoic logic: Frege simply was not a plagiarist. (shrink)

The paper discusses Husserl’s criticism of Frege in Philosophy of Arithmetic (1891) and then his later attitude towards logicism as expressed in Logical Investigations (1900-01). In Philosophy of Arithmetic Husserl holds that logicists offer needless and artificial definitions of notions such as equivalence and number. Frege criticized Husserl’s approach in Philosophy of Arithmetic as psychological, thus shifting the focus of the debate away from logicism. However, Frege’s criticism could be seen to lead Husserl to his later transcendental phenomenological concept of (...) correlation and, with it, to a more developed criticism of logicism. In this regard the division of labor between mathematics and philosophy established in Prolegomena to the Logical Investigations (1900) is central. It implies that in Husserl’s view formal methods fail to shed philosophical insight into the essence of mathematics. In his picture the central notions in need of philosophical clarification are, instead of number and quantity, the notions that are central to abstract structural mathematics. Contrary to Frege who can only elucidate the primitive concepts, Husserl engages in detailed description of their constitution. (shrink)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim that (...) his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 988-1009, December 2021.

Il s’agit dans cet article de proposer une interprétation du projet logique à travers une discussion entre Hegel et Frege. Au-delà des divergences bien connues concernant, entre autres, la formalisation du langage et le rapport aux mathématiques, et après avoir souligné quelques points de convergences parfois remarqués, notamment la critique du psychologisme, nous voulons montrer ici comment la logique se construit, et comment cette construction implique une certaine productivité de la forme logique. Le fait que la forme logique ne puisse (...) pas être abordée de manière immédiate, dans une évidence, conduit à une conception de celle-ci comme développement. Derrière cette présentation « organique » de la logique se joue en réalité une certaine compréhension de la forme dans laquelle celle-ci se produit elle-même dans son explicitation. Cette exigence d’autonomie est comprise à partir d’une analyse, chez Frege, de l’autonomie du nombre. Mais la réponse hégélienne sur le statut de celui-ci nous permet de souligner la contradiction que le nombre abrite. C’est à ce titre que nous pouvons rendre compte, de manière plus détaillée, non seulement du processus d’élaboration de la logique, mais également de la production des contenus : en comprenant le rapport réflexif de la forme comme instauration de la contradiction. (shrink)

By way of a close reading of Boole and Frege’s solutions to the same logical problem, we highlight an underappreciated aspect of Boole’s work—and of its difference with Frege’s better-known approach—which we believe sheds light on the concepts of ‘calculus’ and ‘mechanization’ and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege’s Begriffsschrift, on the other hand, (...) is a visual tool to scrutinize concepts and inferences, and is a calculus only in the thin sense that every possible transition between sentences is fully and unambiguously specified in advance. While Frege’s outlook has dominated much of philosophical thinking about logical symbolism, we believe there is value—particularly in light of recent interest in the role of notations in mathematics and logic—in reviving Boole’s idea of an intrinsic link between, as he put it, a ‘calculus’ and a ‘directive method’ to solve problems. (shrink)

In this paper I examine two substantial interpretations of Wittgenstein’s criticisms of Frege’s conception of logic. One is based on Frege’s rejection of psychologism and alleges that this rejection engenders a tension that is resolved in the Tractatus. The other is based on the claim that there are patterns of inference involving what are now known as propositional attitude ascriptions that Frege’s conception of logic is not equipped to handle. I show that neither of these interpretations present a compelling criticism (...) of Frege. I then argue that Wittgenstein inherited from Frege the ideas of affirmation, denial, and the “opposite” of a thought, but came to see that these conflict with Frege’s conception of negation as a truth-function. This leads to the Grundgedanke of the Tractatus: neither negation nor any other “logical constant” is a representative in our picturing of the world. (shrink)

In this article I explore some implications of the correspondence that went on between Ludwig Wittgenstein and the logician and mathematician Gottlob Frege. Part of this exchange was focused on the envisaged publication of Wittgenstein’s Tractatus Logico-Philosophicus, and on the philosophical or literary character of that work. The problem discussed concerned the question of whether the Tractatus should be seen not as a scientific but as an artistic achievement. My first goal is to present what, given Frege’s writings, his phrase (...) “an artistic rather than a scientific achievement” could be understood to mean in terms of the Tractatus itself. Secondly, I seek to determine the extent to which traces of Frege’s understanding of such terms as “mock thoughts,” “fiction,” “elucidation,” “paintings” and “colouring” are to be found in the language of the Tractatus. This should then make it possible to show how Wittgenstein’s work, viewed from a Fregean perspective, can be seen as furnishing a logic and semantics not only for the languages of logic and natural science, but also for something that is “an artistic rather than a scientific achievement”, while also indicating that the content of the Tractatus as a whole could not have been captured independently of the unified form Wittgenstein himself gave it. (shrink)

This paper argues for the centrality of expression for the project of phenomenology. It shows, first, that the concept of expression grows out of the debate with Frege concerning meaning that led to Husserl’s distinct phenomenological project. Specifically, expression is Husserl’s first attempt to more rigorously define ‘sense’ as the essential connection between subjective acts of meaning and ‘objective’ meanings. This account of expression is then taken up in Husserl’s later work on spirit, which thereby makes expression central to Husserl’s (...) entire analysis of the lifeworld. Insofar as Husserl saw phenomenology growing out of his dispute with Frege on meaning, and working toward the ability to clarify the sense of all scientific knowledge, expression names the promise inherent to phenomenology itself, that which defines the very project of phenomenology. (shrink)

ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...) between structurally identical but importantly distinct mathematical objects, such as the complex roots of $-1$. (shrink)

Volume 40, Issue 4, November 2019, Page 403-406.

Wittgenstein’s attitude to writing philosophy is an important part of his complex legacy from Frege. Even the frequently misconstrued phrase, “Philosophie dürfte man eigentlich nur dichten”, is part of that legacy. How should we actually render that sentence in English? How is the idea that Dichtung is a necessary aspect of philosophical method rooted in thoughts that ultimately find their way back to Frege? Where do we find Dichtung in the so-called private language argument? How is Wittgenstein’s view of the (...) role of Dichtung in philosophy related to his appreciation of humor in philosophizing? What is the role of humor in Frege’s work? How does Wilhelm Busch in Eduards Traum illustrate the philosophical significance of humorous Dichtung? What is the link between Dichtung and craftsmanship in writing philosophy for Wittgenstein? These are the central issues that the article addresses. (shrink)

ABSTRACT A review of the book by Gottfried Gabriel and Sven Schlotter Frege und die kontinentalen Ursprünge der analytischen Philosophie (Münster, Mentis, 2017).

In this book, Michael Potter offers a fresh and compelling portrait of the birth and first several decades of analytic philosophy, one of the most important periods in philosophy’s long history. He focuses on the period between the publication of Gottlob Frege’s _Begriffsschrift _in 1879 and Frank Ramsey’s death in 1930. Potter--one of the most influential writers on late 19 th and early 20 th century philosophy--presents a deep but accessible account of the break with Absolute Idealism and Neo-Kantianism, specifically, (...) and more generally with many of the metaphysical preoccupations of philosophy’s preceding history. Potter’s focus is on philosophical logic and philosophy of mathematics, but he also relies heavily on important issues in metaphysics and meta-ethics to complete his story. The book provides an essential starting point for any student or philosopher attempting to understand Frege, Russell, Wittgenstein, and Ramsey as well as their interactions and their intellectual milieux. It will also be of interest to a great many philosophers today who want to illuminate the problems they work on by better knowing their origins. KEY FEATURES: 1. Discusses the interconnections of Frege, Russell and Wittgenstein—founding thinkers in the history of analytic philosophy—and also brings the neglected Frank Ramsey into this conversation, providing a unique focus and depth to an introductory text 2. Increases the general awareness of the importance of the history of analytic philosophy for today’s non-historical debates, giving the book appeal in all areas of analytic philosophy 3. Written by one of the most influential philosophers of logic and writers in the history of analytic philosophy 4. Written for upper-level undergraduates, guaranteeing widespread accessibility 5. Includes coverage of topics and issues neglected in competing publications, including Russell’s _Principles_, solipsism in the _Tractatus_, and the contributions of Frank Ramsey 6. Emphasizes the chronological development of authors’ views so as to provide a better understanding of their motivation. (shrink)

In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...) is an unsatisfactory way of reading Lotze’s Platonism and that the Ricketts-Reck reading of Frege is in fact the correct way of thinking about Lotze’s Platonism. (shrink)

This article presents and compares Frege’s and Husserl’s conceptions of sense, also taking into account their 1891 and 1906 correspondence. It is argued that while the similarities between their views speak in favour of a Fregean interpretation of Husserl’s notion of noematic sense, there are also important differences. With regard to the latter, it is argued that Husserl’s view yields a more general criterion of propositional difference and also provides a more detailed conception of the use of indexicals and non-descriptive (...) singular terms, and of their reference. In this context, Husserl’s conceptions of constitution and genetic constitution analysis, respectively, are invoked and interpreted in terms of the epistemic notion of processing mental files or individual “concepts”. (shrink)

Während die Bedeutung Freges für die Philosophie der Gegenwart, soweit sich diese der analytischen Philosophie verpflichtet fühlt, allgemeine Anerkennung gefunden hat, ist seine Stellung innerhalb der eigenen Zeit noch weitgehend unaufgeklärt geblieben. So herrscht die Auffassung vor, Frege habe seine Ideen ganz aus sich selbst oder geradezu im Gegensatz zur deutschen philosophischen Tradition seiner Zeit gewonnen. Bei genauerer Textanalyse weisen Freges Schriften dagegen vielfältige Beziehungen zur zeitgenössischen Logik, Erkenntnistheorie, Sprachphilosophie und Philosophie der Mathematik auf, so dass bei ihm von einem (...) Bruch mit der kontinentalen Philosophie nicht die Rede sein kann. Weil die historischen Voraussetzungen unberücksichtigt geblieben sind, ist ein unzutreffendes Bild von Freges Einsichten entstanden. Dieses Bild wird durch die Entfaltung des historischen Kontextes korrigiert. Bestimmend ist dabei ein problemorientierter Zugang, der sich systematischer Bewertungen und Weiterführungen nicht enthält. (shrink)

Abstract: Groundwork is lain for answering questions as to how to situate Husserl’s theory of functions in relation to Frege’s. I examine Husserl’s ideas about analyticity and mathematics, logic and mathematics, formalization, calculating with concepts and propositions, the foundations of arithmetic, extensions to show that, although he knew, studied and lauded Frege’s ideas about functions and concepts, each man approached the issues from different angles. Seduced by the siren of transcendental phenomenology Husserl did not pursue the issues, implications, and consequences (...) of his ideas about functions. I ask whether so doing could provide new insight into, or even solutions to, the problems involving functions that beset Frege, Russell and have beset their successors. (shrink)

In this paper I examine the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. I argue that their positions are much closer than is standardly assumed. I attempt to establish this point on two fronts. First, I argue that Frege is not the metaphysical realist that he is standardly taken to be. Second, I argue that Carnap, where he does differ from Frege, can be seen to do so because of mathematical results proved (...) in the early twentieth century. The differences in their views are, then, not primarily philosophical differences. Also, it might be thought that Frege was interested in analyzing our ordinary mathematical notions, while Carnap was interested in the construction of arbitrary systems. I argue that this is not the case: our ordinary notions play, in a sense, an even more important role in Carnap’s philosophy of mathematics than they do in Frege’s. Finally, I address Tyler Burge’s interpretation of Frege which is in opposition to any Carnapian reading of Frege. (shrink)

In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well as mathematical. (...) In this paper, I will argue that Dedekind’s approach can be seen as a precursor to modern structuralism and as such, it enjoys many advantages over Frege’s logicism. I also show that from a modern perspective, Frege’s criticism of abstraction and psychologism is one-sided and fails against the psychological processes that modern research suggests to be at the heart of numerical cognition. The approach here is twofold. First, through historical analysis, I will try to build a clear image of what Frege’s and Dedekind’s views on arithmetic were. Then, I will consider those views from the perspective of modern philosophy of mathematics, and in particular, the empirical study of arithmetical cognition. I aim to show that there is nothing to suggest that the axiomatic Dedekind approach could not provide a perfectly adequate basis for philosophy of arithmetic. (shrink)

[ES] Gottlob Frege posiblemente era el primer filósofo analítico. La exégesis de su doctrina quedó durante varias décadas restringida casi naturalmente al ámbito de la filosofía analítica y angloparlante. El método que Frege heredó a la filosofía analítica se basa en el análisis abstracto y formal, y la aprehensión de su doctrina se desarrolló bajo el supuesto –tomado casi por autoevidente- que éste método es el único correcto para dar cuenta de los problemas filosóficos más fundamentales, muy particularmente el de (...) desarrollar una teoría de significado. Igualmente se asumía y asume todavía con cierto automatismo que las preocupaciones filosóficas de Frege son fundamentalmente las mismas de la filosofía analítica y las que no caben en este supuesto se desechan fácilmente como anacrónicas o absurdas. Este acercamiento al pensamiento de Frege exclusivamente bajo los supuestos de la filosofía analítica, sus méritos no obstante, no toma en cuenta el ambiente anti-naturalista y neo-kantiano en el cual Frege formó sus convicciones fundamentales. Algunos aspectos contenciosos como, por ejemplo, el principio de contexto, una posible jerarquía de sentidos indirectos o la suposición, casi tácita, de que la doctrina de Frege es una teoría sobre expresiones referenciales, aparecen en una luz diferente si nos damos cuenta de que su intento de construir un sistema es, en cuanto a filosofía, en el fondo una respuesta a problemas que Frege encontró en el sistema de Kant. [EN] Gottlob Frege was quite possibly the first analytical philosopher. For several decades the study of his teachings restricted itself almost naturally to the sphere of analytical and English speaking philosophy. The very method which Frege might have impressed upon analytical philosophy takes off with abstract and formal analysis and the apprehension of his doctrine developed under the assumption –taken to be almost self-evident- that this method is the only one capable of correctly accounting for the most fundamental philosophical problems, especially bringing forth a comprehensive theory of meaning. Hence it was taken for granted with certain automatism that the Frege´s philosophical worries were initially identical in its origins with those of contemporary analytical philosophy and those not amenable to easy adoptions are discharged as absurd anachronisms when viewed against current doctrines. Approaching Fregean thought exclusively under the assumptions of analytical philosophy, while having merit, does not take into account the anti-naturalist and neo-Kantian background which influenced the modelling of Frege’s fundamental convictions. Some contentious aspects like for example the context principle, a possible hierarchy of indirect senses or the almost tacit assumption that Frege’s doctrine is a theory about referential expressions appear in a different light, once we become aware that his attempt at system-construction, as far as it concerns philosophy, is fundamentally an answer to problems which Frege found in Kant’s system. (shrink)

Frege’s account, according to which the problem of how thoughts are apprehended should be a part of psychology, has led scholars to the idea that every consideration regarding subjectivity is absent in this author. From the latter follows a certain way of conceiving the relation between Frege and Husserl which establishes an absolute chasm between both authors regarding the topic mentioned. In the present contribution an extremely different view is defended, namely, that Frege plays an intermediate role between 19th century (...) Platonism and husserlian phenomenology. The main focus of the argument is the commitment between naturalism and idealism which characterizes Platonism before Frege and the beginning of its overcoming carried out by him. (shrink)

The central and probably most controversial point concerning the psychologism — anti-psychologism debate is the problem of Frege’s alleged influence on the change in Husserl’s views. Contemporary thinkers investigating the early period of Husserl’s philosophy have attempted to show that the opinion that Frege’s doctrine had a traumatic influence on Husserl’s views is not justified. This paper, which tries to maintain a balance between strictly philosophical argumentation and narrowly understood historical argumentation, suggests an alternative solution. By appealing to Frege’s works (...) published before 1894, the locus of psychologism will be determined. Afterwards, I will present Husserl’s and Frege’s views on the elucidation procedure and the distinction between calculus and ‘lingua characteristica’. By discussing Husserl’s works from 1894-1897, I will show that his standpoint changed dramatically as he entered into the anti-psychological program, involving a new theory of concepts, judgment, and the so-called ‘pure Fregean flavour’ — a new account of logical content. (shrink)

This paper explores the close connection in early phenomenology between the problem of objectless presentations and the concept of intentional objects. It clarifies how this basic concept of Husserl’s early phenomenology emerged within the horizons of Bolzano’s logical objectivism, Brentano’s descriptive psychology, Frege’s mathematical logicism, Twardowski’s psychological representationalism, and Meinong’s object theory. It shows how in collaboration with these thinkers Husserl argued that a theory of intentionality is incomplete without a concept of the intentional object. It provides a brief history (...) of the concept of intentional objects in the philosophical logic of the nineteenth century that demonstrates its relevance to the problem of objectless presentations in the early phenomenology of the twentieth century. It suggests that Husserl accepts Bolzano’s objectivism and Frege’s logicism, rejects Brentano’s conception of immanent objects and Twardowski’s notion of representational pictures, and ignores Meinong’s theory of objects. Thus the paper employs the formation of Husserl’s concept of the intentional object to enhance the understanding of the historical and philosophical relationships between early phenomenology and contemporaneous philosophical movements. (shrink)

The received view has it that analytic philosophy emerged as a rebellion against the German Idealists (above all Hegel) and their British epigones (the British neo-Hegelians). This at least was Russell’s story: the German Idealism failed to achieve solid results in philosophy. Of course, Frege too sought after solid results. He, however, had a different story to tell. Frege never spoke against Hegel, or Fichte. Similarly to the German Idealists, his sworn enemy was the empiricism (in his case, John Stuart (...) Mill). Genealogically, this stance is not difficult to explain. Frege grew up as a philosopher in the context of the German Idealists. He was a member of Karl Snell’s “Sunday Circle” of university teachers in Jena. The group was influenced with Schelling and the German romanticists. The first Anglophone scholar to point out what Frege's thought owes to nineteenth-century Germany philosophy, Hans Sluga, argued that Frege followed the philosophical-logical tradition originating with Leibniz and Kant which Trendelenburg and Lotze developed significantly. About the same time, a philosophical historian writing in German, Gottfried Gabriel, did much to bring this tradition to light, casting Frege as neo-Kantian. Advancing beyond Sluga and Gabriel, the present paper reveals that through the mediation of Trendelenburg and especially of Lotze many elements of German idealism found their way into Frege's logic and philosophy. (shrink)

[ES] El logicismo de Frege o, en términos más generales, su esfuerzo por construir un fundamento de razonamiento deductivo para las matemáticas fue motivado por el deseo de combatir el empirismo radical que empezaba a dominar la discusión científica en las tierras de habla alemana después de la muerte de Hegel. El objetivo similar de Russell unas décadas después, en cambio, se debe en su origen preponderantemente al deseo de superar el neohegelianismo de Bradley. El joven Wittgenstein formuló a partir (...) de lo que aprendió de ambos el sistema del Tractatus, rechazando algunos aspectos claves de uno y otro. Hay, por consiguiente, incompatibilidades importantes entre las tres propuestas de solución para los problemas relacionados con el concepto de la verdad y de la relación que debemos suponer que existe entre mundo, lenguaje y pensamiento. Si sus reflexiones se comparan con el manejo de preguntas aproximadamente equivalentes hoy en día, en particular a raíz del concepto semántico de la verdad que debemos a Tarski, nos podemos dar cuenta que hemos logrado una enorme flexibilidad en el manejo de los lenguajes simbólicos; a este dominio técnico de las herramientas que nos dio la formalización de la lógica simbólica debemos, entre otros avances, el Internet y los teléfonos inteligentes. En cambio, se perdió de vista la profundidad filosófica que estuvo en su origen, y, se podría decir, algo de lo filosófico de la filosofía. El brillo intenso de las tecnologías nuevas junto con la sensación de que tenemos a nuestra disposición una jerarquía infinita de lenguajes o metalenguajes, que nos permiten manejar cualquier problema heredado del nivel anterior, hacen que nos parezca superflua la ocupación con cuestiones más propiamente filosóficas como las entendían los primeros proponentes de la filosofía analítica. Es en parte a esta pérdida de sentido filosófico del quehacer del filósofo que se deben otros fenómenos que hablan de la trivialización de la filosofía: someter esta actividad en el marco académico a una medición cuantitativa que produce un diluvio de trabajos perfectamente inútiles, o la confusión de la filosofía con la elaboración de reglas operativas para hospitales. [EN] Frege’s logicism or, more generally, his efforts to construct a foundation for mathematics based on deductive reasoning was motivated by his wish to fight the radical empiricism that began to dominate scientific argument in German speaking countries after Hegel’s death. Russell’s similar purpose a few decades later, on the other hand, was originally due mainly to their wish to overcome Bradley’s neo-Hegelianism. Young Wittgenstein forged the system of the Tractatus drawing from his knowledge of both, refuting some key aspects of one or other. There are therefore important incompatibilities between the three proposed solutions for the problems related to the concept of truth and to the relation we must suppose exists between world, language and thought. When we compare their thoughts to today’s ways of handling questions which are approximately equivalent, particularly in the wake of the semantic concept of truth we owe to Tarksi, we may become aware that we have certainly gained enormous flexibility in the handling of symbolic languages; the Internet and intelligent telephones, among other signs of progress would have been impossible without this technical mastery of tools we obtained thanks to the formalization of symbolic logic. But, on the other hand, we also lost view of the philosophical depth that stood at its cradle and, it might be said, a bit of what makes philosophy philosophical. The intense sparkle of the new technologies together with the impression that we have an infinite hierarchy of languages or metalanguages at our disposal which allow us to handle any problem inherited from the previous level, may give us the impression that questions related to more deeply philosophical problems, such as the first proponents of analytical philosophy tried to deal with, are idle. Other phenomena which bear witness to the trivialization of philosophy are in part due to this loss of philosophical meaning of the business of philosophy: subduing this activity within the academic framework to methods of quantification which result in a deluge of perfectly useless publications, or the confusion of philosophy with the elaboration of operating rules for hospitals. (shrink)

On the background of explaining their different notions of analyticity, their different views on definitions, and some aspects of Frege’s notion of sense, three important Kantian strands that interweave into Frege’s view are exposed. First, Frege’s remarkable view that arithmetic, though analytic, contains truths that “extend our knowledge”, and by Kant’s use of the term, should be regarded synthetic. Secondly, that our arithmetical (and logical) knowledge depends on a sort of a capacity to recognize and identify objects, which are given (...) us in particular ways, constituting their senses (Sinne). Third, that there is a sense in which Frege’s view of definitions and explications gives new substance to Kant’s leading idea of analyticity, namely, the containment of a truth or a concept in another. In all these, Frege’s view does not endorse the Kantian strands as they are, but gives them special and sometimes quite sophisticated twists. (shrink)

Existe en Frege no solo una concepción intencional de la conciencia, sino también uma concepción motivacional de su causalidad, esto es, Frege concibe la idea de una causalidade específica, diferente de la científico-natural, y que tiene como presupuesto la existência de estados intencionales. En tal sentido, existe un interesante punto de contacto entre Frege y Husserl.

In the ‘analytic tradition’, Hans Sluga wrote thirty years ago in his book Gottlob Frege, there has been a ‘lack of interest in historical questions — even in the question of its own roots. Anti-historicism has been the baggage of the tradition since Frege’ (Sluga, 1980, p. 2). The state of the discussion of Frege among analytic philosophers, Sluga claimed, illustrated well this indifference. Despite the numbers of pages devoted to Frege, there was still, Sluga claimed, little understanding of the (...) sources of Frege’s ideas, his intellectual debts, and the historical circumstances of his thought. Sluga singled out Michael Dummett’s Frege: Philosophy of Language ‘as a paradigm for the failure of analytic philosophers to come to grips with the actual, historical Frege’. In that book, Dummett famously wrote that the logical system that Frege put forward in his 1879 Begriffsschrift ‘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) — and Dummett devoted almost none of its 700 pages to the relationship between Frege and his contemporaries. (shrink)

O presente texto tem como objetivo estabelecer algumas relações entre o poema de Parmênides e as Investigações Lógicas, de Frege. Mais especificamente, nosso objetivo é iluminar certos aspectos do poema de Parmênides por meio de uma comparação com certas noções utilizadas por Frege para caracterizar aspectos centrais de seu pensamento. The aim of this paper is to establish some relationships between Parmenides' Poem and Frege's Logical Investigations. More specifically, our objective is to illuminate some aspects of the Parmenides' Poem by (...) comparing it to certain notions used by Frege in his Logical Investigations. (shrink)

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (shrink)

The philosophy of mathematics has long been an important part of philosophy in the analytic tradition, ever since the pioneering works of Frege and Russell. Richard Dedekind was roughly Frege's contemporary, and his contributions to the foundations of mathematics are widely acknowledged as well. The philosophical aspects of those contributions have been received more critically, however. In the present essay, Dedekind's philosophical reception is reconsidered. At the essay’s core lies a comparison of Frege's and Dedekind's legacies, within and outside of (...) analytic philosophy. While the comparison proceeds historically, it is shaped by current philosophical concerns, especially by debates about neo-logicist and neo-structuralist views. In fact, philosophical and historical considerations are intertwined thoroughly, to the benefit of both. The underlying motivation is to rehabilitate Dedekind as a major philosopher of mathematics, in relation, but not necessarily in opposition, to Frege. (shrink)

(2012). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians – Two Recently Discovered Documents. British Journal for the History of Philosophy. ???aop.label???. doi: 10.1080/09608788.2012.692665.

Twentieth-century philosophy has often been pictured as divided into two camps, analytic and continental. This study challenges this depiction by examining encounters between some of the leading representatives of either side. Starting with Husserl and Frege's fin-de-siècle turn against psychologism, it turns to Carnap's 1931 attack on Heidegger's metaphysics (together with its background in the Cassirer-Heidegger dispute of 1929), moving on to Ayer's 1951 meeting with Bataille and Merleau-Ponty at a Parisian bar, followed by the 'dialogue of the deaf' between (...) Oxford linguistic philosophers and phenomenologists at the 1951 Royaumont colloquium, leading up to the Derrida-Searle controversy. Careful study shows that it is implausible to assume the existence of a century-old 'gulf' between two sides of philosophy. Vrahimis argues that miscommunication and ignorance over the exact content of the above encounters must to a large extent be held accountable for any perceived gap. (shrink)

English title: The Problem of the Synthetic a priori Judgements According to Hermann Lotze. The present article compares Kant’s and Lotze’s concepts of synthetic judgements. Lotze’s aim is a renewing of the Kant’s solutions, what he achieves thanks to introduction of the distinction between analytic (identical) content and synthetic form of these judgements which Kant recognised as synthetic. This distinction makes possible to lay down the concept of intentional sense which has influence over Frege and Husserl.

In 1913, in a draft for a new Preface for the second edition of the Logical Investigations, Edmund Husserl reveals to his readers that "The source of all my studies and the first source of my epistemological difficul­ties lies in my first works on the philosophy of arithmetic and mathematics in general", i.e. his Habilitationsschrift and the Philosophy of Arithmetic: "I carefully studied the consciousness constituting the amount, first the collec­tive consciousness (consciousness of quantity, of multiplicity) in its simplest and (...) higher levels (consciousness of sums, sums of sums etc.). I immediately separated proper (intuitive) and symbolic consciousness, in the characteriza­tion of the former I hit the radical difference of categorial consciousness [...] and sensuous consciousness of unity." Later on, in the Third Investigation, Husserl makes some very specific claims, that are of considerable importance to assess the development of his early works and their relation to his later phenomenology: "This first work of mine (an elaboration of my Habilitationsschrift, [...], 1887) should be compared with all assertions of the present work on compounds, moments of unity, complexes, wholes and objects of higher order. I am sorry that in many recent treatments of the doctrine of "Gestalt-qualities", this work has mostly been ignored, though quite a lot of the thought-content of later treatments by Cornelius, Meinong etc., of questions of analysis, apprehension of plurality and complexion is already to be found, differently expressed, in my Philosophy of Arithmetic. I think it would still be of use today to consult this work on the phenomenological and ontological issues in question, especially since it is the first work that attached importance to acts and objects of higher order and investigated them thoroughly." Hence, at the time of the Ideas, Husserl retrospectively considers his first works4 as being still relevant for phenomenological issues. Not only does Husserl advance a very interesting priority claim with respect to Von Ehrenfels’ development of the notion of Gestalt and Meinong’s development of Gegenstandstheorie, but also a strong affirmation of continuity and coherence of his position from 1887 all the way up to 1913, encompassing the alleged “revolution” in his position from psychologism to anti-psycho­logism in the 1890s. Indeed, according to much of the recent secondary literature, in 1894, right in the middle of the ten “incubation” years between the Philosophy of Arithmetic and the Logical Investigations, Frege’s destruc­tive review would have converted Husserl to antipsychologism practically overnight. This gives us two conflicting interpretations: on the one hand, Husserl himself in 1913 still seems to approve of the Philosophy of Arithmetic and even considers it to contain valuable phenomenological material, on the other, it is routinely dismissed by much of the secondary literature as hope­lessly psychologistic. So which one is it: do we have a phenomenological arithmetic or a psychologistic arithmetic in Husserl’s first book? On balance, I think that Husserl in his Philosophy of Arithmetic developed a position that does not fall prey to the exaggerated and poorly aimed critiques of Frege, while at the same time, as a descriptive psychology of the genesis and constitution of number, it can certainly be considered as providing phenome­nologically meaningful analyses, though of course not made from within an explicitly transcendental phenomenological framework. (shrink)

Eine vollständige Darstellung von Edmund Husserls Verhältnis zu Gottlob Frege steht noch aus, so dass es nicht verwundert, einige Missverständnisse, dieses Verhältnis betreffend, im Umlauf zu finden. Selbst scheinbar längst überwundene systematische Dogmen tauchen wieder auf, so z.B. die Auffassung, dass Husserl nicht nur entscheidend von Gottlob Frege beeinflusst wurde, sondern darüber hinaus auch seine schärfste Frege-Kritik 1891 zurückgenommen habe. Mein Beitrag enthält eine überwiegend historisch vorgehende Entgegnung auf solche fälschlich vertretenen Ansichten wie sie sich auch in dem neu erschienenen (...) und mit vielen dokumentarischen Belegen versehenen Frege-Kommentarbuch von W. Künne finden. Die wichtigsten Argumente, die in diesem Buch gegen Husserl gerichtet werden, stützen sich auf Stellen in Husserls Frühwerk, die zwar sehr aufschlussreich für die Beurteilung des philosophischen und menschlichen Habitus Husserls in den 1890er Jahre sind, nicht aber Künnes Thesen stützen oder gar beweisen können. Die als zurückgenommene Frege-Kritik verstandene Selbstkritik Husserls betrifft jedoch nach meinen Darlegungen gerade nicht die Kritik, die er an Freges Buch Grundlagen der Arithmetik geübt hatte, sondern seine eigene systematische Stellungnahme hinsichtlich der Begründung der Arithmetik. Ausgehend von dieser Einsicht werde ich auf ein wichtiges Spezifikum von Husserls Erstlingswerk (Philosophie der Arithmetik) aufmerksam machen, das voreiligen Interpretationen einen Riegel vorschiebt: Dieses Buch ist ein Mosaik aus Einsichten verschiedener Arbeits- und Denkperioden des Verfassers, die sich vor allem auch in dem zweifachen Begriff der Äquivalenz zeigen. Dies knüpft an einen langen geschichtlichen Entwicklungsprozess an, der in eine von Bolzano, Lotze, Brentano und Carl Stumpf geprägte Tradition zurückführt und das Problem der Unterscheidung zwischen Sinn und Gegenstand eines Aktes betrifft. (shrink)

A comprehensive and agreed-upon account of Husserl’s relation to Gottlob Frege does not yet exist. In this situation we encounter interpretations that allow systematic dogmas to reappear that should have long been vanquished—for instance, that the author of the Logical Investigations was not only decisively influenced by Frege, but also that he had already retracted his sharpest Frege-critique by 1891. The present essay contains a largely historical response to W. Künne’s new monograph on Frege that advocates such views. We will (...) concentrate on a small remark that turns out to reference a defining moment for any understanding of Husserl’s early philosophy. We shall argue that Husserl’s supposed self-criticism does not turn on the critique that he had earlier leveled at Frege’s Grundlagen der Arithmetik; rather, it has to do exclusively with his own earlier systematic positions on the grounding of arithmetic. In this context, an important particular of Husserl’s Philosophie der Arithmetik takes center stage: this book is a mosaic composed from old and new insights, a fact that becomes most evident in the two distinct concepts of “equivalence” that are founded there, which reflects Husserl’s transition from a theory of arithmetic based on the concept of number to one based on the parallelism between proper and symbolic (improper) presentations. This change involves a long historical development that goes back to a tradition marked by the work of Bolzano, Lotze, Brentano, and Stumpf, and it is closely tied to the problem of how to distinguish between the sense and the object of an act. Systematic neglect of the historical background of the Frege–Husserl relation has led to disputes over who owns the copyright to the sense/reference distinction, but it has obscured the very core of the original line of questioning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 161 7 In, respectively, PaciWsm in Britain and Semi-Detached Idealists: the British Peace Movement and International Relations (Oxford: Oxford U. P., 2000). 8 See Monk 2: Chap. 13. FUNCTIONS OR PROPOSITIONAL FUNCTIONS? Alexander Paul Bozzo Philosophy / Marquette U. Milwaukee, wi 53233, usa [email protected] Michael Potter and Tom Ricketts, eds. The Cambridge Companion to Frege. Cambridge, uk: Cambridge U. (...) P., 2010. Pp. vii, 630. isbn 978-0-521-62479-4 (pb). £57.00; £21.99 (pb). us$38.99 (pb). February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd 162 Reviews 1 Frege: Philosophy of Mathematics (Cambridge, ma: Harvard U. P., 1991), p. 111. The paragraph contains an expression of Frege’s Context Principle and the need for Hume’s Principle as a criterion of identity in the deWnition of number. 2 There are in fact Wve stated goals. The others are: (iii) to serve as a reference work for students and non-specialists, (iv) to provide a route into the study of Frege historically and to any relevant contemporary concerns in the philosophies of logic, language, mathematics, and mind, and (v) to provide, for new readers, the most convenient detailed guide to Frege currently available. Gottlob Frege is widely recognized as one of the chief progenitors of mathematical logic and philosophy of languagez—zindeed, the importance attributed to Frege’s innovations is such that Michael Dummett, when reXecting on§62 of Frege’s Die Grundlagen der Arithmetik, feels compelled to remark that the paragraph therein is “arguably the most pregnant philosophical paragraph ever written.”1 Whether or not one agrees with Dummett on this point, the magnitude of Frege’s inXuence on the current philosophical landscape is incontestable. Frege revolutionized the then dominant Aristotelian conception of logic, introducing a formal language now recognized as the predicate calculus. Central to this end were Frege’s insights on quantiWcation, the notation that expressed it, the logicist project, and the extension of mathematical notions like function and argument to natural language. The long-awaited Cambridge Companion to Frege is a compendium of Fregean scholarship that rigorously explores these and similar topics; editors Thomas Ricketts and Michael Potter have compiled a comprehensive collection of fourteen essays that individually provide focused appraisals of a number of Frege’s most substantial insights. On the advice of this journal’s editor, I have limited my review to the connections (or rather dissimilarities ) that exist between Frege and Russell, relying exclusively on Peter Hylton ’s contribution to the collection, “Frege and Russell”. Following a brief consideration of the volume as a whole, I move immediately into a detailed explication of Hylton’s analysis. The volume includes among its goals the following two aims: (i) to provide, for advanced students and specialists, a conspectus of recent interpretation of Frege, and (ii) to dispel the intimidation felt by readers who confront a diUcult thinker.2 I single out these ambitions because they most clearly represent the volume’s strengths and shortcomings. Enthusiasts of Frege will not be disappointed by the multitude of rigorously and technically written essays, essays that contribute substantially and originally to the collective understanding of Frege and his work. For instance, Thomas Ricketts provides a thoughtful and thorough analysis—an analysis that moves well beyond mere explication—of Frege’s concept/object distinction, in particular its relevance for Frege’s Context Principle and logicism more generally. Similarly, Richard Heck addresses a number of central yet largely unexplored issues pertaining to the overall signiWcance of February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 163 3 I strongly encourage that non-specialists augment The Cambridge Companion to Frege with Joan Weiner’s Frege Explained: from Arithmetic to Analytic Philosophy (Chicago : Open Court, 2004), one of the best available introductory texts on Frege. 4 The essay in fact was available as early as 2005 in Hylton’s Propositions, Functions, and Analysis: Selected Essays on Russell’s Philosophy (New York, ny: Oxford U. P., 2005). The editors of The Cambridge Companion to Frege partially... (shrink)