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In an unpublished speech from 1991, David Lewis told his audience that he counted ‘the metaphysician Carnap ’ amongst his historical ancestors. Here I provide a novel interpretation of the Aufbau that allows us to make sense of Lewis’s claim. Drawing upon Lewis’s correspondence, I argue it was the Carnap of the Aufbau whom Lewis read as a metaphysician, because Carnap’s appeal to the notion of founded relations in the Aufbau echoes Lewis’s own appeal to the metaphysics of natural properties. (...) |
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This paper investigates how the doctrine of the epistemological given—long associated with empiricism and positivism and also informing Carnap’s first major work in 1928—was challenged and overcome by Neurath and Carnap in subsequent years. Particular attention is paid to the controversial issue of how precisely the dialectic between Neurath and Carnap played out: whether Neurath’s argumentation correctly engaged with Carnap’s actual positions, whether Carnap’s change of positions in turn fully engaged with Neurath’s challenge, and what all this may tell us (...) |
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Resumen Este trabajo reconstruye la caracterización de “positivismo” en tres obras centrales de Horkheimer. Se afirma que, en el uso del término, Horkheimer incurre en una doble equivocidad, pues lo utiliza indistintamente para referirse al positivismo decimonónico y al del siglo XX; además, no reconoce las diferencias internas entre las posiciones de los positivistas contemporáneos. Asimismo, se muestra que muchos rasgos que se consignan como propios del positivismo del siglo XX no tienen justificación en los textos de esa tradición, de (...) |
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Metaphysics is, as Adorno once notes, the nuisance of philosophy. On the one hand, metaphysics is the reasons of philosophy's existence; on the other hand, it is nearly impossible to characterise metaphysics precisely. This tension is reflected with reference to the contemporary political and cultural situation in Adorno's "Meditations on Metaphysics", the last part of his opus magnum *Negative Dialectics*. The essays in this volume are devoted to different facets of Adorno's examination of metaphysics. They do, however, not only concern (...) |
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Carnap’s lectures at the 1935 Paris Congress for the Unity of Science marked the beginning of his mature metaphilosophy. This paper considers what role remained for epistemology once it was “purified” of all psychological elements as Carnap there demanded. It is argued that while this did mean the end of traditional epistemology, room was found for nontraditional versions in the course of the further development of Carnap’s logic of science. |
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La philosophie analytique est ici considérée à son point de départ. Les conditions de l’expression sont vues comme synonymes de celles de la pensée. Une entreprise d’explicitation est à cette suite appliquée en retour à la méthode scientifique qui était auparavant le modèle. La distinction de la syntaxe et de la sémantique, commandée par l’analyse logique, est alors appliquée à l’ensemble des systèmes de représentation: oeuvre d’art, action humaine, esprit. Cette évolution montre un souci essentiel: l’instrument technique de la connaissance. |
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Im Zentrum dieses Bandes stehen die Beiträge einer Tagung, die im Oktober 2017 an der Universität Konstanz stattgefunden hat. Thema der Tagung war ein den historischen Kontext einbeziehender Blick auf den frühen Rudolf Carnap, vom Ende des Ersten Weltkriegs bis zur Emigration Ende 1935. Der 1891 in Ronsdorf bei Wuppertal geborene Rudolf Carnap entschloss sich erst relativ spät zu einer Karriere als akademischer Philosoph, nämlich 1920, nachdem er sein durch den Krieg unterbrochenes Studium der Physik und Philosophie in Jena und (...) |
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The traditional use of the expression 'pseudoproblem' is analysed in order to clarify the talk of pseudoproblems and related phenomena. The goal is to produce a philosophically serviceable terminology that stays true to its historical roots. This explicative study is inspired by and makes use of the method of logical reconstruction. Since pseudoproblems are usually expressed by pseudoquestions a formal language of questions is presented as a possible reconstruction language for alleged pseudoproblems. The study yields an informal theory of pseudoproblems (...) |
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I examine the thesis that Otto Neurath anticipated the programme of naturalised epistemology already at the time of the Vienna Circle and consider the relation between Neurath's proposals and those of two contemporary theorists whose research programmes he would thus have broadly anticipated. The thesis is confirmed by reference to Neurath's own writings. The connection between Neurath's programme and the programmes of his two successors considered here, however, is found to be highly indirect in one case and nonexistent in the (...) |
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In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 (...) |
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Hans Hahn's long-neglected philosophy of mathematics is reconstructed here with an eye to his anticipation of the doctrine of logical pluralism. After establishing that Hahn pioneered a post-Tractarian conception of tautologies and attempted to overcome the traditional foundational dispute in mathematics, Hahn's and Carnap's work is briefly compared with Karl Menger's, and several significant agreements or differences between Hahn's and Carnap's work are specified and discussed. |
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This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) |
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According to Carnap an account of the nature of mathematics, both pure and applied, must include the thesis that mathematical truths are devoid of factual content. He first formulated this thesis around 1930 and in its defence attempted to combine the reduction of mathematics to logic undertaken in the Principia with Wittgenstein’s insights into the nature of logic. In this paper I will show that this synthesis faces serious difficulties. Thus, it plays, with good reason, no longer a role in (...) |
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In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...) |
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Although logical positivism had been known before World War II, it was introduced into academic philosophy in Japan only after it. In this process, the US philosophers who came to Japan in order to participate in American Studies Seminar played an important role. The first generation of Japanese analytic philosophers, who were born in the 1920s and 1930s, began to have some influence in the 1960s, and some of them published original works of high quality in the 1970s. The second (...) |
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¿Cómo pensar hoy la naturaleza y el valor de la reflexión filosófica? La influencia omnipresente del modelo del conocimiento experto parece exigir una autocomprensión de la filosofía como una disciplina entre las disciplinas. Este artículo propone que la filosofía debe resistirse a esta tentación. Defenderé, por tanto, una especie de "excepcionalismo" para la filosofía basado en la idea de que no puede pretender ser una disciplina. Sea o no cierto que hoy en día las actividades filosóficas estén legitimadas institucionalmente por (...) |
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Trata-se da tradução de um ensaio clássico publicado por Rudolf Carnap na revista Erkenntnis. A tradução é precedida por um texto de apresentação, que situa o ensaio e sua importância no contexto da filosofia contemporânea e na obra de Carnap. No ensaio, Carnap indica as principais características que distinguem o que ele chama de nova lógica (a lógica simbólica matemática derivada das obras de Frege, Peano e Hilbert, entre outros) da lógica filosófica tradicional e explica a sua importância como novo (...) |
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This article is a critical genealogy of Tay, an artificial-intelligence chatbot that Microsoft released on Twitter in 2016, which was quickly hijacked by internet trolls to reproduce racist, misogynist, and antisemitic language. Tay’s repetition and production of hate speech calls for an approach that draws on both media and cultural theory—the Frankfurt School’s dialectical analyses of language and ideology, in particular. Revisiting the Frankfurt School in the age of algorithmic reason shows that, contrary to views foundational to computing, a neural-network (...) |
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Discussions of the relation between pragmatism and logical empiricism tend to focus on the period when the logical empiricists found themselves in exile, mostly in the United States, and then attempt to gauge the actual extent of their convergence. My concern lies with the period before that and the question whether pragmatism had an earlier influence on the development of logical empiricism, especially on the thought of the former members of the “first” Vienna Circle. I argue for a substantially qualified (...) |
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This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) |
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Resumen En esta contribución ofrecemos una interpretación del pons asinorum que se basa en una lógica de términos contemporánea. Esto nos permite revitalizar la idea del pons asinorum para generar el -políticamente correcto- pons scholasticorum, una versión terminística del pons asinorum que conecta la inventio medii con el dictum de omni et nullo.In this contribution we offer an interpretation of the pons asinorum by using a contemporary term logic. This interpretation allows us to revitalize the concept of the pons asinorum (...) |
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In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work (...) |
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The distinction between data and phenomena introduced by Bogen and Woodward (Philosophical Review 97(3):303–352, 1988) was meant to help accounting for scientific practice, especially in relation with scientific theory testing. Their article and the subsequent discussion is primarily viewed as internal to philosophy of science. We shall argue that the data/phenomena distinction can be used much more broadly in modelling processes in philosophy. |
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Term Functor Logic is a term logic that recovers some important features of the traditional, Aristotelian logic; however, it turns out that it does not preserve all of the Aristotelian properties a valid inference should have insofar as the class of theorems of Term Functor Logic includes some inferences that may be considered irrelevant (e.g. ex falso, verum ad, and petitio principii). By following an Aristotelian or syllogistic notion of relevance, in this contribution we adapt a tableaux method for Term (...) |
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Paul Boghossian advocates a version of the analytic theory of a priori knowledge. His defense of an "epistemic" notion of analyticity is based on an implicit definition account ofthe meaning of the logical constants. Boghossian underestimates the power of the classical Quinean criticisms, however; the challenge to substantiate the distinction between empirical and non-empirical sentences, as forcefully presented in Two Dogmas, still stands, and the regress from Truth by Convention still needs to be avoided. Here, Quine also showed that there (...) |
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I elaborate in some detail on the First Book of Euclid's ``Elements'' and show that Euclid's theory of geometry is \underline{not} axiomatic in the modern sense but is construed differently. Then I show that the usual commonly accepted notion of axiomatic theory equally fails to account for today's mathematical theories. I provide some polemical arguments against the popular view according to which a good mathematical theory must be axiomatic and point to an alternative method of theory-building. Since my critique of (...) |
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We prove two theorems concerning expressive power of relational and functional languages. The theorems have interesting consequences for the history of philosophy and logic. |
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En esta contribución proponemos una representación de un fragmento de la silogística estadística de Thompson usando la lógica de términos de Sommers. El resultado es una interpretación terminista de la silogística estadística. |
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The use of the three labels to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor the... |
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Steve Awodey and Erich H. Reck. Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics. |
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In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming. |
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Given some links between Lyndon’s Interpolation Theorem, term distribution, and Sommers and Englebretsen’s logic, in this contribution we attempt to capture a sense of interpolation for Sommers and Englebretsen’s Term Functor Logic. In order to reach this goal we first expound the basics of Term Functor Logic, together with a sense of term distribution, and then we offer a proof of our main contribution. |
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