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 (...) consist? We seek to answer this question by placing Carnap’s shorthand manuscript in the context of his previous efforts to accommodate scientific theories and metalinguistic claims within Wittgenstein’s Tractatus theory of meaning. The breakthrough of January 1931 consists, from this viewpoint, in the rejection of the Tractatus theory in favor of the meta-mathematical perspective of Hilbert, Gödel, and Tarski. This was not yet the standpoint of the published Logical Syntax, as we show, but led naturally to the “principle of tolerance” and thus to Carnap’s mature philosophy, in which the inconsistencies between this first view and the principle of tolerance, which survived into the published Syntax, were overcome. (shrink)

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 (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

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.

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.

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 (...) are no implicit definers for the logical constants. Moreover, even if they existed, their epistemic analyticity would, on Boghossian's own account, be doubtful. (shrink)

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 (...) that it provides important insights intoCarnap''s development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnap''s logicism. Moreover, we show how theAxiomatics influenced Carnap''s student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnap''s project. (shrink)

This volume draws connections between Wittgenstein's philosophy and the work of Saul Kripke, especially his Naming and Necessity. Saul Kripke is regarded as one of the foremost representatives of contemporary analytic philosophy. His most important contributions include the strict distinction between metaphysical and epistemological questions, the introduction of the notions of contingent a priori truth and necessary a posteriori truth and original accounts of names, descriptions, identity, necessity and realism. The chapters in this book elucidate the relevant connections between Kripke's (...) work and Wittgenstein, specifically concerning the standard meter, contingent apriori and rule-following. The contributions shed light on how Kripke's philosophical outlook was influenced by Wittgenstein, and how mainstream analytic philosophy and Wittgensteinian philosophy can fruitfully engage with one another. Kripke and Wittgenstein will be of interest to philosophers working on Wittgenstein, Kripke, and the history of analytic philosophy. (shrink)

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. (...) I further maintain that Lewis was right to read Carnap this way and that the notion of a founded relation has a legitimate claim to be both logical and metaphysical. I also argue that Carnap’s initial response to Goodman’s puzzle about ‘grue’ relies upon a metaphysics of simple properties which also prefigures Lewis’s own response to Goodman invoking natural properties. (shrink)

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 (...) Freiburg abgeschlossen und kurze Zeit überlegt hatte, als Lehrer in der Schulreform-Bewegung zu arbeiten. Es folgte die philosophische Promotion im Jahr 1921, bei Bruno Bauch in Jena, mit einer Doktorarbeit zum Raumproblem. 1923 organisierte Carnap, gemeinsam mit Hans Reichenbach und anderen, eine für die Entstehung des Logischen Empirismus bedeutsame kleine Tagung in Erlangen. Auf Einladung von Moritz Schlick habilitierte er sich 1926 an der Universität Wien und verbrachte die Zeit bis 1931 zumindest teilweise in Wien, als eines der Kernmitglieder des Wiener Kreises um Moritz Schlick. Seine Habilitationsschrift erschien 1928 unter dem Titel Der logische Aufbau der Welt (hier immer Aufbau). 1931 folgte Carnap einem Ruf an die Deutsche Universität Prag. In den darauffolgenden Jahren blieb aber der enge Kontakt mit Wien und dem Wiener Kreis erhalten. Carnaps hauptsächliche Arbeit in dieser Zeit war seinem zweiten großen Buchprojekt gewidmet, der 1934 publizierten Logischen Syntax der Sprache. Daneben verfasste Carnap in seiner Zeit in Wien und Prag auch zahlreiche Aufsätze, zu unterschiedlichen Aspekten der Logik, der Metaphysikkritik und der Wissenschaftstheorie. Er war Mitautor des Manifests Wissenschaftliche Weltauffassung: Der Wiener Kreis und nahm regen Anteil an den zahlreichen wissenschaftlichen Aktivitäten des Logischen Empirismus, von der Gründung der Zeitschrift Erkenntnis bis hin zum Projekt einer Enzyklopädie der Einheitswissenschaft. Spätestens ab 1933 musste Carnap jedoch feststellen, dass an eine weitere wissenschaftliche Karriere in dem von Faschismus und Nationalsozialismus geprägten politischen Klima in Kontinentaleuropa nicht zu denken war. Er strebte deshalb die Emigration ins englischsprachige Ausland an, die schließlich Ende 1935 gelang, als Carnap ein Angebot von der Universität Chicago erhielt. Obwohl Carnap nur den kleineren Teil der in diesem Band abgedeckten eineinhalb Jahrzehnte in Wien verbracht hat, widmet sich der Großteil der hier versammelten Beiträge schwerpunktmäßig der für Carnaps philosophische Karriere zentralen Wiener Zeit. (shrink)

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 (...) whose presuppositions are critically investigated right away. At least one result remains: Claims of pseudoproblemship and their refutations must not be voiced casually - they are to be relativized and need substantial interpretive effort. (shrink)

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 (...) método do filosofar. (shrink)

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 (...) generation of analytic philosophers were born in the 1940s and 1950s. They began to teach in the 1970s and 1980s, and went on to publish papers and books in analytic philosophy. For many years, analytic philosophy had been known as kagaku tetsugaku, which may mean either philosophy of science or scientific philosophy. It had been frequently criticized as “non-philosophy.” Analytic philosophy, however, has changed the style of philosophical discussion and made it possible to form a language that is sufficient to express philosophical ideas and arguments in an intelligible way. (shrink)

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 (...) in order to produce the -politically correct- pons scholasticorum, a terministic version of the pons asinorum that relates the inventio medii with the dictum de omni et nullo. (shrink)

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 (...) about the compatibility of their philosophical projects. (shrink)

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 (...) affirmative answer. (shrink)

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 (...) in foundations, which we consider to have been greater than previously assumed. This conjecture is based on a hitherto neglected revision of Hilbert's talk "Über den Zahlbegriff". (shrink)

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 (...) themselves with Adorno's metaphysical reflections in a narrow sense, but also extend to other themes Adorno relates to metaphysics: critique of concepts, history, truth, and materialism. Thereby, they render a hardly investigated topic of the *Negative Dialectics* accessible. -/- Contributors: Emil Angehrn, Dirk Braunstein, Peggy H. Breitenstein, Gunnar Hindrichs, Axel Hutter, Philip Hogh, Christian Iber, Julia Jopp, Guido Kreis, Ansgar Martins, Brian O'Connor, Mario Schärli, Marc Nicolas Sommer, Tilo Wesche. (shrink)

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.

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.

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 (...) Carnap’s mature philosophy of mathematics. (shrink)

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.

We prove two theorems concerning expressive power of relational and functional languages. The theorems have interesting consequences for the history of philosophy and logic.

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.

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.

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 (...) chatbot like Tay does not sidestep meaning but rather carries and alters it, with unforeseen social and political consequences. A return to the work of Max Horkheimer and Theodor W. Adorno thus locates ideology in the digital world at the nexus of language’s ability to mean, language and meaning’s susceptibility to computation, and the design of a machine to compute both. Coming to critical terms with the antisemitism produced in Tay’s human-computer synthesis requires, as this article contends, addressing the uncanny embodiment and reflection of thought that is digital computation. (shrink)

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 (...) manera que la categoría horkheimeriana de “positivismo” se convierte en una entidad interpretativa respecto de la cual la Escuela de Fráncfort se considera antagónica. A partir de lo anterior se realiza una crítica a las interpretaciones del autor.This paper reconstructs the characterization of “positivism” in Horkheimer’s works. We argue that in the use of this term, Horkheimer makes a misinterpretation, then he uses it in order to refer to both nineteenth century positivism and the positivism of the twentieth century; at the same time, he does not recognize the significant contrasts between the positions of the twentieth century positivists. We also show that many of the features Horkheimer sets out for twentieth century positivists find no correlation in texts belonging to this tradition, which makes Horkheimer’s concept of “positivism” an interpretative entity in opposition to Frankfurt School. From the foregoing, we carry out a critique of the interpretations made by the author. (shrink)

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 (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

Steve Awodey and Erich H. Reck. Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.

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...

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 (...) other — despite their undeniable overlap. (shrink)

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 (...) the core axiomatic method is constructive in its character I briefly observe known constructive approaches in the foundations of mathematics and describe the place of my proposal in this context. The main difference of my and earlier constructive proposals for foundations of mathematics appears to be the following: while earlier proposals deal with the issue of admissibility of some particular mathematical principles and like choice and some putative mathematical objects like infinite sets my proposal concerns the very method of theory-building. As a consequence, my proposal unlike earlier constructive proposals puts no restriction on the existing mathematical practice but rather suggests an alternative method of organizing this practice into a systematic theoretical form. In the concluding section of the paper I argue that the constructive mathematics better serves needs of mathematically-laden empirical sciences than the formalized mathematics. (shrink)

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 (...) Functor Logic in order to avoid irrelevance and we offer some sort of intuitive semantics in terms of traditional inferential situations (e.g. propter quid, quia, non causa ut causa, and non sequitur). (shrink)