Frege: Miscellaneous

Fregesche Variationen [Variations of Frege], a Festschrift edited by Matthias Wille, assembles twelve papers in honour of Christian Thiel on the occasion of his 80th birthday in 2017.

This paper presents a passage on truth from "Der Gedanke" and comments on its content and use in the classroom.

ABSTRACTThis article aims to analyse Wittgenstein’s 1929–1932 notes concerning Frege’s critique of what is referred to as old formalism in the philosophy of mathematics. Wittgenstein disagreed with Frege’s critique and, in his notes, outlined his own assessment of formalism. First of all, he approvingly foregrounded its mathematics-game comparison and insistence that rules precede the meanings of expressions. In this article, I recount Frege’s critique of formalism and address Wittgenstein’s assessment of it to show that his remarks are not so much (...) a critique of Frege as rather a defence of the formalist anti-metaphysical investment. (shrink)

Gottlob Frege’s conception of works of art has received scant notice in the literature. This is a pity since, as this paper undertakes to reveal, his innovative philosophy of language motivated a theoretically and historically consequential, yet unaccountably marginalized Wittgenstinian line of inquiry in the domain of aesthetics. The element of Frege’s approach that most clearly inspired this development is the idea that only complete sentences articulate thoughts and that what sentences in works of drama and literary art express are (...) ‘mock thoughts’. The early Wittgenstein closely followed Frege’s lead on this theme. One sees this, for example, in the Tractatus, where Wittgenstein announces that only sentential propositions model states of affairs whereas works of art are objects we perceive sub specie aeternitatis. By the early 1930s, however, Wittgenstein began to revise his view beyond his initial Frege-inspired standpoint. He came to insist that works of art can convey thoughts as well, but that thoughts do not model the world of facts and hence do not convey information about measurable objects and events. Rather, his contention was that aesthetically configured thoughts that artworks communicate impart information about our perspective on reality and reconfigure our view of life. To be more explicit, successful or ‘good’ works of art, in Wittgenstein’s view, can supply aesthetically instructive ‘gestures’ that open to living experience promising new ways of being. It is in this respect, he held, that artists ‘have something to teach’. (shrink)

Gottlob Frege’s conception of works of art has received scant notice in the literature. This is a pity since, as this paper undertakes to reveal, his innovative philosophy of language motivated a theoretically and historically consequential, yet unaccountably marginalized Wittgenstinian line of inquiry in the domain of aesthetics. The element of Frege’s approach that most clearly inspired this development is the idea that only complete sentences articulate thoughts and that what sentences in works of drama and literary art express are (...) ‘mock thoughts’. The early Wittgenstein closely followed Frege’s lead on this theme. One sees this, for example, in the Tractatus, where Wittgenstein announces that only sentential propositions model states of affairs whereas works of art are objects we perceive sub specie aeternitatis. By the early 1930s, however, Wittgenstein began to revise his view beyond his initial Frege-inspired standpoint. He came to insist that works of art can convey thoughts as well, but that thoughts do not model the world of facts and hence do not convey information about measurable objects and events. Rather, his contention was that aesthetically configured thoughts that artworks communicate impart information about our perspective on reality and reconfigure our view of life. To be more explicit, successful or ‘good’ works of art, in Wittgenstein’s view, can supply aesthetically instructive ‘gestures’ that open to living experience promising new ways of being. It is in this respect, he held, that artists ‘have something to teach’. (shrink)

In this paper I address G. C. Rota’s account of mathematical identity and I attempt to relate it with aspects of Frege as well as Husserl’s views on the issue. After a brief presentation of Rota’s distinction among mathematical facts and mathematical proofs, I highlight the phenomenological background of Rota’s claim that mathematical objects retain their identity through different kinds of axiomatization. In particular, I deal with Rota’s interpretation of the ontological status of mathematical objects in terms of ideality. Then (...) I detect certain similarities among Rota’s views and Frege’s account of the constitution of arithmetical identity on the grounds of 1–1 correspondence. I point out an epistemic as well as an ontological aspect of this issue. In the sequel, I attempt to deal with the problem of “mixed identities” in mathematics stated by Benacerraf by taking in account Rota’s use of the phenomenological notion “Fundierung”. (shrink)

Wittgenstein y Apel pretendieron definir el constitutivo formal del sujeto intérprete del lenguaje a partir de las propuestas de Frege o de Peirce, pero en ambos casos sus propuestas se acabaron volviendo paradójicas. Primero, Wittgenstein por no poder fundamentarlo ni de un modo crítico-transcendental a partir de una noción de “yo” metafísico ni de unos juegos del lenguaje en sí mismos conductistas que tampoco permiten remitirse a unos signos intérprete, al modo exigido por Frege. De todos modos, posteriormente, Apel habría (...) propuesto evitar estas paradojas mediante una interpretación pragmático-transcendental del sujeto intérprete a partir de Peirce, aunque finalmente comprobaría como también se acabarían fomentando el mismo tipo de paradojas. Wittgenstein and Apel sought to define the formal constitutive of the language interpreter subject based on the Frege or Peirce proposals, but in both cases their proposals ended up becoming paradoxical. First, Wittgenstein for not being able to ground it in a critical-transcendental way based on a notion of metaphysical "I" nor on behavioral language games in themselves that also do not allow to refer to some interpreter signs, in the way demanded by Frege. Anyway, later, Apel would have proposed to avoid these paradoxes by means of a pragmatic-transcendental interpretation of the interpreting subject starting from Peirce, although finally it would prove how the same type of paradoxes would also be fostered. (shrink)

Frege’s conception of science includes three features: a science is applicable to other sciences, or even to itself, a science consists of a more or less rigid system of judgements and a science presupposes elucidations, illustrative examples and a “catch on” among scientists. Together, I label these three features “The scientific Picture”. Both logic and mathematics are included among the sciences and are covered by the scientific picture. As I understand Frege, this picture guides his logical and philosophical reflections. Here (...) it is invoked in a treatment of two well-known and controversial Fregean topics: His claim, often repeated, that the axioms of Begriffsschrift and Grundgesetze are obvious and stand in no need of justification, and his use of a Kantian terminology in classifying judgements as analytic or synthetic, a priori or a posteriori. The most significant consequence of my reading is that it underscores the epistemological nature of Frege’s thinking and, at the same time, downplays a current, and in my mind unfortunate, trend of ascribing to Frege a rather “thick” metaphysics. Towards the end, I discuss different aspects of the notion of a judgment at play in Frege’s discussions: judgement as movement from thought to truth-value and judgement as represented by the judgement-stroke. These aspects point back to the distinction, so nicely illustrated by Frege’s own writings, between a scientist, engaged in scientific research, and a philosopher, explicating the scientific activity and its general presuppositions, respectively. (shrink)

This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place of (...) Frege’s work in the philosophical landscape more generally. The volume is therefore of direct relevance to several current debates in philosophy in general, in addition to Frege and Wittgenstein research in particular. Even though Frege’s great significance for contemporary philosophy is not disputed, the question of how we are to understand the character and aims of his project is debated. The debate has a starting point in Frege’s specific conception of logic. The volume elucidates this conception as well as the relation between natural language and the Begriffsschrift. It will help philosophers, researchers, and students better understand the nuances of this great thinker. By extension, it will also help readers seeking to understand Wittgenstein’s approach to philosophical difficulties and his struggle to find an apt form of presentation for his philosophical investigations. (shrink)

Derrida, for reasons which he never made clear publicly, published his mémoire for the diplôme d'études supérieures only in 1990, some thirty-five years after it had been written. Had it been published much earlier, some of the dispiritingly ill-informed remarks about his work might have been avoided. The mémoire, entitled The Problem of Genesis in Husserl's Philosophy, reveals that he is, when required, perfectly able to write a standard thesis in straightforward French. And that, in particular, he is aware of (...) the work of the great logician Gottlob Frege in its relation to Husserl. (shrink)

Paolo Bozzi developed his «experimental phenomenology» from the Gestalt psychology tradition, particularly from Gaetano Kanizsa’s method. The distinction between «phenomenal description» and «causal explanation» of the «perception» springs up from the analysis of Bozzi’s «S-D psychophysical scheme». What Frege, who was well-known by Bozzi, deals with in paragraph 71 of The Thought theoretically mirrors what is outlined in the Scheme and could also be intended as its source. The juxtaposition between a «science of observable things» or «experimental phenomenology» – conceived (...) as a science which is autonomous from what happens in the brain – and logics, which is set up autonomously from the thinking processes, is a programmatic element that is openly indicated by the author. Frege’s anti-psychologism and realism are both widely shared by Bozzi. The realism and the «naïve physics» Bozzi was a pioneer of lie at the basis of the so-called «New Realism». The following essay aims to localize and highlight some theoretical implications – up to their phenomenological origins – which can be detected particularly in paragraph 71 of The Thought. The present work tries to sketch out the boundaries and the autonomy of the «first person» perceptive experience and to define the scientific explanation that we can give of it. The distinction between science and experience, and the autonomy of experience from science and of the immediate experience of the content of consciousness from neuroscience, entail the impossibility of a naturalization of the phenomenological experience. In the examples taken from Frege can be found a theoretical bridge which connects the Gestalt perceptological tradition, Wittgenstein’s investigations of the philosophy of psychology, and the so called «New Realism». (shrink)

Although profoundly influential for essentially the whole of philosophy’s twenty-five hundred year history, the model of a science that is outlined in Aristotle’s Posterior Analytics has recently been abandoned on grounds that developments in mathematics and logic over the last century or so have rendered it obsolete. Nor has anything emerged to take its place. As things stand we have not even the outlines of an adequate understanding of the rationality of mathematics as a scientific practice. It seems reasonable, in (...) light of this lacuna, to return again to Frege—who was at once one of the last great defenders of the model and a key figure in the very developments that have been taken to spell its demise—in hopes of finding a way forward. What we find when we do is that although Frege remains true to the spirit of the model, he also modifies it in very fundamental ways. So modified, I will suggest, the model continues to provide a viable and compelling image of scientific rationality by showing, in broad outline, how we achieve, and maintain, cognitive control in our mathematical investigations. (shrink)

ABSTRACT Frege presents the eponymous distinction of "Über Sinn und Bedeutung" as a correction to the theory of identity he held in the Begriffsschrift.1 His retrospective assessment has prompted different reactions from commentators. Many have simply taken him at his word.2 Others, who have lingered over the relevant texts, have encountered a difficulty: in the Begriffsschrift Frege appears to raise the same problem with which he begins USB and to respond to it in words that are strikingly similar to those (...) found in the later work.3 Thus, a number of important scholars have been led to argue that Frege misrepresents his earlier view: contrary to what he says in USB, the Begriffsschrift already contains the distinction between Sinn and Bedeutung.4 Despite their obvious differences, the logic of both interpretations requires that the two works be responsive to the same problem. In this paper I challenge that fundamental premise.5 If I might be allowed to express my thesis tersely but suggestively: the problem of the Begriffsschrift is epistemological; that of USB, ontological.6 The two problems and Frege's solutions to them shall be explained in what follows. (shrink)

On which philosophical foundations is the attribution of numerical magnitudes to qualitative phenomena based? That is, what is the philosophical basis for attributing, through measurement operations, numbers to empirical qualities that our senses perceive in the outside world? This question, nowadays rarely addressed in such a way, actually refers to an old debate about the quantification of qualities. A historical analysis reveals that it was a major issue in the “context of discovery” of the first attempts to mathematize new fields (...) of knowledge, whereas the “context of justification” leading our contemporary perspective on such episodes often overlooks such problems. As a consequence, little attention has so far been given to tracing its emergence back to its original context, leaving in the shadows an important debate about measurement. In this respect, the work of William Stanley Jevons is worth analysis. As a preliminary step toward his ambitious project to mathematize economics, he first attempted to understand the mechanism underlying measurement in physics, through a very innovative approach. Its main merit consisted in trying to overcome the Aristotelian distinction between quantities and qualities. In this article, I will strive to highlight the significance of his work for the history of philosophy of science. (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)

É bem sabido que a discussão das relações entre conteúdo e objeto é um tema central na escola de Brentano após o decisivo ensaio de Twardowski de 1894. Todavia, pouco sabido é o fato de que esta discussão também tem lugar fora da escola mencionada e que a distinção entre conteúdo e objeto já está presente em outros autores antes de 1894.

Wer kennt GOTTLOB FREGE (1848-1925)? Nur wenige verbinden mit seinem Namen einen der größten Logiker aller Zeiten, ohne dessen "Logik von Funktion und Argument" die heutige Computertechnik kaum denkbar ist. Frege fühlte sich zeitlebens zu seiner Heimat im Norden Deutschlands hingezogen. In Wismar verbrachte er seine Kindheit und in Bad Kleinen, in unmittelbarer Nähe, seinen Lebensabend. Das im Jahre 2000 gegründete Gottlob-Frege-Zentrum der Hochschule Wismar organisierte ihm zu Ehren im Mai 2013 in seiner Geburtsstadt eine internationale Konferenz, an der Forscher (...) aus der mathematischen Grundlagenforschung und der Analytischen Philosophie teilnahmen. (shrink)

Pieranna Garavaso and Nicla Vassallo investigate Gottlob Frege's largely unexplored notion of thinking to provide insight into the roles of language in expressing thoughts and in fostering the development of human knowledge. The analysis will benefit studies of epistemology, logic, philosophy of mind, psychology, and philosophy of language.

Church has contributed a lot to the safeguard of G. Frege's theory of meaning after the discovery of antinomies in it. To achieve this he has adapted it by keeping parts, discarding others and adding new ones, most of which are clearly exposed in an informal way in the introduction to his Introduction to Mathematical Logic. As for any modification of a theory by another person, it is interesting to understand how the thoughts of the former survive in the new (...) theory even though radical changes have occurred, or on the contrary how it retains only the appearance of the initial theory. We shall therefore go through the basic concepts of logic he introduces in this introduction and assess their relation to Frege's original theory. (shrink)

Charles Travis’s new collection on perception brings together eleven of his previously published essays on this topic, some of which are substantially revised, plus one new essay. The intentionally ambiguous subtitle hints at the author’s endorsement of Fregean anti-psychologism, though influences from Wittgenstein and Austin are equally apparent. The work centres around two major questions in the philosophy of mind and perception. First, Travis argues against the view that perceptual experience, as distinct from perceptual judgement or belief, is representational, and (...) so belongs to what Travis calls ‘the conceptual’. This is contrasted with the ‘non-conceptual’, or ‘historical’; that is, environmental particulars which lack the generality of representational thought. The second is what Travis calls ‘the fundamental question of perception’; namely, how can perceptual experience make the world bear (rationally) upon what we are to think and do? The answer, he argues, cannot be found in terms of relations between thoughts—a purely conceptual affair—but in the way that thought is itself grounded in the particularity of experience. For perceptual experience to bear rationally upon thought at all—or, in more familiar Fregean terms, to bring ‘objects’ under ‘concepts’—perception must first make environmental particulars available to cognition. Thus, Travis argues, experience cannot itself be ‘conceptual’, or representational, on pain of undermining the very thing that grants us a recognisable, and so thinkable, world at all. (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.

Charles Travis presents a series of essays on philosophy of perception, inspired by the insights of Gottlob Frege. He engages with a range of contemporary thinkers, and explores key issues including how perception can make the world bear on what we do or think, and what sorts of capacities we draw on in representing something as (being) something.

As the history of analytic philosophy is written, Gottlob Frege sits among the pantheon, one of the core creators of a novel way of philosophical thinking. It is a way of thinking that is notably infused with logical and semantic insights that are original to Frege. The source of these insights is well known. They arise in the context of logicism, Frege’s mathematical project that unfolded in a body of thought punctuated by three seminal works, Begriffsschrift of 1879, Die Grundlagen (...) der Arithmetik of 1884, and the two volumes of Grundgesetze der Arithmetik, published in 1893 and 1903. In these works, Frege sets out to show that arithmetic can be reduced to logic; more technically, that (a version of) the Peano-Dedekind axioms are derivable as theorems in a definitional extension of impredicative second-order logic. To achieve this goal, Frege introduced both a new logic and a new semantics; the conceptual apparatus that Frege brought to bear in these works, and in an accompanying series of classic essays, including most famously “On Sense and Reference,” has animated philosophical thought ever since. (shrink)

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...) are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non-conceptual content. (shrink)

The aim of this paper will be to show how significant the logical theories of judgement which were worked out at the end of the nineteenth century have been for the ontological thought during the twentieth century. Against the classical - Aristotelian and Scholastic - analysis of predicative judgement, Franz Brentano on one hand and Gottlob Frege on the other hand have leveled two different criticisms, which then generated two radically divergent ontological paradigms. On one side, despite Brentano’s own nominalistic (...) stands, there was a tremendous extension of the general category of “object” as well as of the notion of “being” with, as a consequence, the exceptionnally luxuriant ontologies of Brentano’s heirs. On the other side, notwithstanding Frege’s own Platonistic affinities, there was a drastic deflation of the realm of objects to the benefit of the realm of concepts taken as classifying functions, and therefore a strong nominalistic trend among Frege’s heirs. The development of quantified modal logics at the middle of twentieth century however forced contemporary ontology to reconsider this simple alternative in order to give place to some hybrid entities such as individual concepts or other kinds of “intensional objects”. (shrink)

The article seeks to challenge the standard accounts of how to view the difference between Husserl and Frege on the nature of ideal objects and meanings. It does so partly by using Derrida’s deconstructive reading of Husserl to open up a critical space where the two approaches can be confronted in a new way. Frege’s criticism of Husserl’s philosophy of mathematics (that it was essentially psychologistic) was partly overcome by the program of transcendental phenomenology. But the original challenge to the (...) prospect of a fulfilled intuition of idealities remained and was in fact encountered again from within the transcendental analysis by Husserl himself in his last writings on geometry and language. According to the two standard and conflicting accounts, Husserl either changed his earlier psychologistic program as a result of Frege’s criticism, or he was in fact never challenged by it in the first place. The article shows instead how Husserl continued to struggle with the problem of the constitution of ideal objects, and how his quest led him to a point where his analyses anticipate a more dialectical and deconstructive conclusion, eventually made explicit by Derrida. It also shows not only how this development constitutes a philosophical continuity from the original dispute with Frege, but also how Frege’s critique in a certain respect could be read as an anticipation of Derrida’s deconstructive elaboration of Husserl’s phenomenology. (shrink)

The article is an overview of the main philosophical ideas of Gottlob Frege. The author stresses that Frege has built important tools for the analysis of language: the logic of sentences and the logic of predicates. He stresses also the importance of Frege’s work on the foundations of mathematics. He argues that his greatest achievement is the fact that thanks to Frege language has become main object of investigations in contemporary philosophy, and that theory of meaning has replaced the traditional (...) theory of knowledge. Frege’s ideas, taken together, constitute a well-defined method, a particular style of approach to philosophical problems and of their resolution. The effectiveness and enduring pertinence of Frege’s method is demonstrated by means of an analysis of several typical category mistakes, frequent in philosophical argumentation. Key words FREGE, LANGUAGE. (shrink)

In his work on the foundations of mathematics, Frege placed the problem in a wider context, namely that of science; the ontological status of thought as the carrier of truthfulness became for him the most important issue. The objectivity of truth and thought seems to require the existence of other people, which consequently requires the existence of the world. Thus, the polemics with epistemological idealism became a key issue for Frege; the topic appears in such works as The Basic Laws (...) of Arithmetic, The Logic, and The Thought. What seems to be most interesting in Frege’s work is his stress on weaknesses of both epistemological realism and immanent idealism. Reflecting upon the examples of the physiological psychology and physiology of the senses he demonstrated the process of entrapment in idealism. It is also interesting that he stressed the realistic character of language as well as the constant possibility of committing a mistake by assuming the existence of reference, and dangers of falling into traps of fiction resulting there from. Key words FREGE, SCIENCE, LANGUAGE. (shrink)

Michael Dummett has argued that the linguistic turn, initiated by Frege, is the decisive moment in the birth of the analytical tradition and what distinguishes that tradition from other movements. The thesis of the paper is that Dummett’s account of the origins of the analytical tradition understates the extent to which Frege’s work, and the linguistic turn more generally, are responses to antinomies in the modern philosophical project. An adequate characterisation of the origins of the analytic tradition presupposes an account (...) of the fundamental conceptual shift that occurred during the time of the scientific revolution and the epistemological problems that arose in conjunction with this shift. This is why it is misleading to assert, with Dummett, that the really interesting developments in terms of understanding the analytical tradition are subsequent to Frege. The most productive contrast in terms of understanding the origins of the analytical tradition is not between pre and post Fregean thought, the paper argues, but between modern and premodern conceptions of philosophy and its relation to the world of everyday experience.—Correspondence to [email protected] (shrink)

Este artículo se enmarca en el proyecto de investigación de la Maestría en Filosofía Latinoamericana, Bartolomé de Las Casas: Recepción de la filosofía analítica en Colombia y Latinoamérica de la Universidad Santo Tomás. Inicialmente fue redactado en inglés: The Quest for the Numbers: An Approach to Frege’s Philosophy, cuyo trabajo pretende acercarse al fundamento de la obra fregeana como hito fundamental del pensamiento filosófico; asimismo, desarrolla en detalle los temas y puntos más relevantes de su sistema de pensamiento. A partir (...) de un análisis del proyecto logicista, es decir, la búsqueda de una reducción de la matemática a la lógica, se demuestran las fuertes influencias del pensamiento de Frege en todas las ramas de la filosofía contemporánea. La comprensión de la filosofía de Frege entonces constituye un paso fundamental, para tener un horizonte acerca de las problemáticas de la filosofía en la actualidad y, asimismo, un fundamento o propedéutica para el desarrollo de un pensamiento latinoamericano maduro en diálogo con la tradición. (shrink)

In his book The Nature of Mathematical Knowledge and in a series of articles, Philip Kitcher attacks the traditional conception of a priori mathematical knowledge. The reliabilism he develops as an alternative situates all our knowledge within a psychological framework. However, in Frege‘s Epistemology he claims that Frege‘s conception of a priori knowledge is compatible with a psychological account. Kitcher attributes to Frege a traditional concept of proof, according to which mathematical and logical proofs are psychological activities. I shall argue (...) that Kitcher‘s interpretation conflicts with Frege‘s anti-psychologistic injunction against confusing reasons with causes. Moreover, the psychological explanation obscures one of the most interesting features of a priori knowledge. (shrink)

Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.