What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, (...) logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...) J. Brouwer and D. Hilbert (1899). Part 2 is mainly devoted to Hilbert’s proof theory of the 1920s (1922–1931). I begin with an account of his early attempt to prove directly, and thus not by reduction or by constructing a model, the consistency of (a fragment of) arithmetic. In subsequent sections, I give a kind of overview of Hilbert’s metamathematics of the 1920s and try to shed light on a number of difficulties to which it gives rise. One serious difficulty that I discuss is the fact, widely ignored in the pertinent literature on Hilbert’s programme, that his language of finitist metamathematics fails to supply the conceptual resources for formulating a consistency statement qua unbounded quantification. Along the way, I shall comment on W. W. Tait’s objection to an interpretation of Hilbert’s finitism by Niebergall and Schirn, on G. Gentzen’s allegedly finitist consistency proof for Peano Arithmetic as well as his ideas on the provability and unprovability of initial cases of transfinite induction in pure number theory. Another topic I deal with is what has come to be known as partial realizations of Hilbert’s programme, chiefly advocated by S. G. Simpson. Towards the end of this essay, I take a critical look at Wittgenstein’s views about (in)consistency and consistency proofs in the period 1929–1933. I argue that both his insouciant attitude towards the emergence of a contradiction in a calculus and his outright repudiation of metamathematical consistency proofs are unwarranted. In particular, I argue that Wittgenstein falls short of making a convincing case against Hilbert’s programme. I conclude with some philosophical remarks on consistency proofs and soundness and raise a question concerning the consistency of analysis. (shrink)

For Kant, philosophical investigations are inherently analytic. The proper method of philosophy is analysis, and the object of analysis are concepts. Hence, Kant’s short description of philosophy as “rational cognition […] from concepts” (KrV, A 837/B 865) can be substituted by “philosophy is conceptual analysis”. The article shows that Kant follows a representationalism about concepts and a combination of intensional and extensional feature semantics. Against the claim that Kant is a proponent of the concept-judgement-inversion, it is argued that concepts are (...) being articulated in form of singular terms, propositions, and sets of propositions alike. Kant interlinks different kinds of concepts with different kinds of definitions, as the reconstruction of his theory of definitions reveals. Philosophy foremost deals with what Kant calls “given” empirical and pure concepts. Such concepts are object of analysis, i.e., explication and exposition. The article ends with answers to five possible objections. Is philosophy all about analysis? (shrink)

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings (...) — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts. (shrink)

Jarmo Pulkkinen, The threat of logical mathematism. A study on the critique of mathematical logic in Germany at the turn of the 20th century. Frankfurt a.M:Peter Lang, 1994. Scandinavian University Studies in the Humanities and Social Sciences; 7). 186 pp. 24 DM. ISBN 3-631-47409-1.

One of the characteristic features of contemporary logic is that it incorporates the Frege‐Russell thesis according to which verbs for being are multiply ambiguous. This thesis was not accepted before the nineteenth century. In Aristotle existence could not serve alone as a predicate term. However, it could be a part of the force of the predicate term, depending on the context. For Kant existence could not even be a part of the force of the predicate term. Hence, after Kant, existence (...) was left homeless. It found a home in the algebra of logic in which the operators corresponding to universal and particular judgments were treated as duals, and universal judgments were taken to be relative to some universe of discourse. Because of the duality, existential quantifier expressions came to express existence. The orphaned notion of existence thus found a new home in the existential quantifier. (shrink)

The project behind this and the following1 special issue of Angelaki first assumed concrete form in the shape of a three-day international conference, “Continental Philosophy and the Sciences,” hel...

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...) the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (shrink)

The impartial reader notices that Frege, in Die Verneinung, treats an opposing conception of negation, but without specifically naming its proponent. In this paper, it is proven for the first time that the view in question is that of his colleague in Jena, Bruno Bauch. Besides their different views, concerning above all the status of false thoughts, there are nonetheless broader points of agreement between the ideas of Bauch and Frege. These points of agreement cast light on both thinkers as (...) representatives of a current of Neo-Kantianism, having its source in Lotze, in which Kantian and Platonic elements are fused to form a ?transcendental Platonism? (shrink)

The form of the sentence, as it is understood in contemporary semantics and linguistics, is functional. This paper interprets the metaphors in which Frege shows what the functional sentence means, arguing that Frege's sentence is neither an adequate translation of natural language nor of use in feminist theorizing.

This paper outlines the intellectual biography of Walter Dubislav. Besides being a leading member of the Berlin Group headed by Hans Reichenbach, Dubislav played a defining role as well in the Society for Empirical/Scientific Philosophy in Berlin. A student of David Hilbert, Dubislav applied the method of axiomatic to produce original work in logic and formalist philosophy of mathematics. He also introduced the elements of a formalist philosophy of science and addressed more general problems concerning the substantiation of human knowledge. (...) What set Dubislav apart from the other logical empiricists was his expertise in the history of logic and exact philosophy which enabled him to elucidate and advance the thinking in both disciplines. In the realm of logic proper, Dubislav is best known for his pioneering work in theory of definitions. What is more, he did original work on the so called ‘quasi truth-tables’ which aided Reichenbach in developing his logic of probability. Dubislav also elaborated an influe.. (shrink)

The article presents Frege's distinction between Sense and Reference. After a short introduction, it explains the puzzle which gave rise to the distinction; Frege's earlier solution, and his reasons for its later repudiation. The distinction, which embodies Frege's second solution, is then discussed in two phases. The first, which is restricted to proper names, sets out its most basic features. The second discusses 'empty' names; indirect speech, and the distinction for predicates and for complete sentences. Finally, two criticisms, by Russell (...) and by Kripke, are briefly set out. (shrink)

Frege's extension of his distinction between Sinn and Bedeutung to predicate terms is widely considered to be problematic. Interpreters generally assume that the notion of Bedeutung comprises the name/bearer relation as a prototype and that the extension is justified only in so far as the relation of predicate terms to their alleged referents is analogous to the relation of names to their bearers. However, interpreters have generally paid insufficient attention to Frege's own dealing with the issue. By examining the relevant (...) passages in Frege's writings, I show that the standard ways of talking about Frege's ascription of Bedeutung to predicates as optional, less evident than the ascription of Sinn, and in need of justification are not in accord with Frege's own conception of predicate reference. There is no textual evidence that the extension takes place for analogical reasons and, in particular, no evidence for the claim that the name/bearer relation is used as a prototype. Frege is visibly not concerned with the relation between predicate terms and their referents, but applies the notion of Bedeutung for reasons of principle. There is indeed the invocation of an analogy, but if we consider the argument in which it occurs it appears that it does not play the justificatory role interpreters attribute to it. In sum, Frege's ascription of Bedeutung to predicates does not imply any mysterious or dubious referentiality of predicate terms. (shrink)

My concern in what follows is to give a comparative report on some important lectures held at the Hegel-Kongreß 1981 in Stuttgart. In discussing the views of Quine, Hacking, Davidson, Putnam and Habermas I want to confront them with some details of Rorty's recent critique of our philosophical tradition. At last I try to give a tentative answer whether there is an end or a turning-point for current analytical philosophy.

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

Quantifiers in Frege's Grundgesetze like are not well-defined because the part Fx & Gx stands for a concept but the yoking conjunction is horizontalised and must stand for a truth-value. This standard interpretation is rejected in favor of a substitutional reading that, it is argued, both conforms better to the text and is well-defined. The theory of the horizontal is investigated in detail and the composite reading of Frege's connectives as made up of horizontals is rejected. The sense in which (...) the Grundgesetze has a many-valued but classical logic is explained by proving that its propositional fragment (under the standard interpretation) and Bochvar's 3-valued logic are instances of the same metatheoretic methods. Historically, the paper argues for a more naive but well-defined reading of the text. Theoretically, it provides a formally adequate statement of that semantics, as well as developing the abstract metatheory which embraces Bochvar's language and the Fregean fragment. (shrink)

Michael Dummett has shown that the fragment ‘17 Kernsätze zur Logik’ is evidence that Frege knew Lotze's Logik Dummett’s dating of this fragment prior to 1879, however, must be rejected.The present paper shows that there are other articles of Frege’s which bear clear traces of Lotze's LogikFirst of all, the expressions Vorstellungsverlauf from ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, and veranlassenden Ursachen, from ‘Logik’, certainly are borrowed from Lotze.Second, there are links between ‘Booles rechnende Logik und die Begriffsschrift’ and Lotze's (...) Logik. Furthermore, it is shown that Frege’s ‘Kernsätze’, the ‘Dialog mit Pünjer über Existenz’, and his ‘Logik’ are intimately connected.All of this indicates that these texts were written in roughly the same period, namely the early 1880s.Conclusive evidence for this is that the terms Vorstellung and Vorstellungsverbindung are used indiscriminately in both a psychological and a logical sense in the ‘Begriffsschrift’, a fact which contradicts the ‘Kernsätze’. (shrink)

In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought (...) that Frege's priority principle is close to (or at least derivable from) Kant's. I argue that it is not. Nevertheless, there was a gradual historical development that began with Kant's priority thesis and culminated in Frege's new logic. (shrink)

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)

This paper addresses a number of closely related questions concerning Kant's model of intentionality, and his conceptions of unity and of magnitude [Gröβe]. These questions are important because they shed light on three issues which are central to the Critical system, and which connect directly to the recent analytic literature on perception: the issues are conceptualism, the status of the imagination, and perceptual atomism. In Section 1, I provide a sketch of the exegetical and philosophical problems raised by Kant's views (...) on these issues. I then develop, in Section 2, a detailed analysis of Kant's theory of perception as elaborated in both the Critique of Pure Reason and the Critique of Judgment; I show how this analysis provides a preliminary framework for resolving the difficulties raised in Section 1. In Section 3, I extend my analysis of Kant's position by considering a specific test case: the Axioms of Intuition. I contend that one way to make sense of Kant's argument is by juxtaposing it with Russell's response to Bradley's regress; I focus in particular on the concept of ‘unity’. Finally, I offer, in Section 4, a philosophical assessment of the position attributed to Kant in Sections 2 and 3. I argue that, while Kant's account has significant strengths, a number of key areas remain underdeveloped; I suggest that the phenomenological tradition may be read as attempting to fill precisely those gaps. (shrink)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

Two claims the present author has made about Frege's philosophy are defended against Michael Dummett's criticisms (The Interpretation of Frege's Philosophy and ?Objectivity and Reality in Lotze and Frege?, this journal, 1982). The claim that Frege was concerned primarily with epistemological problems rather than with the theory of meaning, and the claim (this journal, 1978) that the ascription of Wirklichkeit to Thoughts is evidence of Frege's realism, are clarified and defended. Dummett's own characterization of Frege's realism is considered and rejected.

The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.

Given the large literature on Frege, one might believe that it would be impossible to say anything essentially new on the subject. This book contradicts this belief, calling attention to Frege's in...

L'A. étudie la théorie classique du jugement telle qu'elle apparait dans «La logique» de A. Arnauld et P. Nicole et oppose la sémantique des termes généraux de Port-Royal à celles de Kant et Frege.

Ray Monk and Anthony Palmer, (eds) Bertrand Russell and the Origins of Analytical Philosophy, Thoemmes Press, Bristol, 1996; pp. xvi + 383; Hans-Johann Glock, (ed.) The Rise of Analytic Philosophy, Blackwell, 1997; pp. xiv + 95; Matthias Schirn, (ed.) Frege: Importance and Legacy, Walter de Gruyter, Berlin, 1996; pp. x + 466; Stuart G. Shanker, (ed.) Philosophy of Science, Logic and Mathematics in the Twentieth Century, Routledge History of Philosophy Volume IX, Routledge, 1996; pp. xxxviii + 461; John Blackmore, (ed.) (...) Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906, Kluwer, Dordrecht, 1995; pp. xvi + 266. (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)

The paper interprets Wittgenstein’s famous call to silence at the end of his Tractatus – that “whereof one cannot speak, thereof one must be silent” – as a critique of philosophy itself. Wittgenstein was concerned throughout his philosophical life with finding a way to delineate the limits of language. These limits, once we have them clearly in view, rob our attempts to put forth philosophical theories of their legitimacy. In order to give a critical assessment of this Wittgensteinian critique of (...) philosophy, the paper primarily focuses on the roots of that critique in Wittgenstein’s earliest writings – his notebooks, his 1913 “Notes on Logic,” the 1914 set of notes dictated to G. E. Moore, and the Tractatus itself. Wittgenstein’s influence by Fritz Mauthner and, mediated through Mauthner, by Kant receive special attention. The conclusion is that, far from Mauthner’s radical anti-philosophical bias, we can come to see a deep appreciation of the power, the draw, and the significance of philosophical problems in Wittgenstein’s writings. The text closes with a short look at how Wittgenstein’s thinking about the limits of language evolved later in his life. (shrink)

In British and American anthropological literature, the ethnology of Central and Eastern European countries has shared in the plight of descriptions of this part of the world: it was seen as exotic, foreign, remote, a backwater, focused on sideline problems and situated on the periphery of this field of science. This state of affairs has been the case since at least the beginning of the Cold War as the descriptions of the national characters of Eastern Bloc communities, drafted by American (...) scholars. The ethnography of these countries was automatically aligned with the same categories of description which were applied to the characteristics of these communities. This was, in part, an effect of entirely different research traditions in the subject matter, objectives and methods of these remote parts of the science. The differences of ’cultural wholes’ did have a decisive impact on the image of ethnology. Like all these communities, Polish ethnology was perceived as a homogeneous whole, which it never was. (shrink)

A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.