Carnap Research Articles

Quine’s “predilection” for finitism

Rudolf Carnap’s notes of conversations he had in 1940–1941 with Alfred Tarski and W. V. Quine (a German transcription and English translation of which are now available in Frost-Arnold 2013) are packed with fascinating and sometimes puzzling clues about these logicians’ views. I shall focus here on just one of these clues: Quine’s commitment in the conversations to an austere sort of ontological finitism. Greg Frost-Arnold suggests that Quine’s interest in finitism in 1940–1941 was rooted in an epistemological foundationalism that he later recanted (FrostArnold 2013, 35–36). I shall try to show, on the contrary, that Quine’s interest in finitism in 1940–1941 was an early expression of an attitude toward ontological questions that was integral to his philosophy from the late 1930s on. Tarski is clearly the leader in the 1940–1941 conversations about finitism. He announces that he ‘‘truly understand[s] only a finite language S1; only individual variables, whose values are things; whose number is not claimed to be infinite (but perhaps also not the opposite).’’ On this view, a number is just one of a finite progression of concrete things. It follows that ‘‘many arithmetical sentences cannot be proved here, since we do not know how many numbers there are’’ (January 31, 1941; 156–157). Tarski rejects Carnap’s proposal that we view infinitary mathematics as analytic (March 6, 1940, 139–140) and says he ‘‘understands’’ the language of classical infinitary arithmetic—S2 for short—only insofar as he knows the formal rules (logical syntax) of S2; to ‘‘truly’’ understand S2, according to Tarski, a knowledge of its logical syntax is not enough (January 31, 1941; 157). Carnap’s notes record Quine as saying, in the weeks before Tarski introduces his finitism, that mathematics, like physics, involves ‘‘hypostases’’ that are underdetermined by experience. Quine also stresses that the paradoxes of set theory show that ‘‘familiar common sense results for finite classes’’ do not determine a general

The Epsilon-Reconstruction of Theories and Scientific Structuralism

Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of theoretical terms and a suitable choice semantics for it. Second, to analyze whether Carnap’s approach is compatible with a structuralist conception of mathematics.

Differentiation with Stratification: A Principle of Theoretical Physics in the Tradition of the Memory Art

The Art of Memory started with Aristotle's questions on memory. During its long evolution, it had important contributions from alchemist, was transformed by Ramon Llull and apparently ended with Giordano Bruno, who was considered the best known representative of this art. This tradition did not disappear, but lives in the formulations of our modern scientific theories. From its initial form as a method of keeping information via associations, it became a principle of classification and structuring of knowledge. This principle, which we here name {\it differentiation with stratification}, is a structural design behind classical mechanics. Integrating two different traditions of science in one structure, this physical theory became the modern paradigm of science. In this paper, we show that this principle can also be formulated as a set of questions. This is done via an analysis of theories, based on the epistemology of observational realism. A combination of Rudolph Carnap's concept of theory as a system of observational and theoretical languages, with a criterion for separating observational languages, based on analytical psychology, shapes this epistemology. The `nuclear' role of the observational laws and the differentiations from these nucleus, reproducing the general cases of phenomena, reveals the memory art's heritage in the theories. Here in this paper we argue that this design is also present in special relativity and in quantum mechanics.

Three challenges to the complementarity of the logic and the pragmatics of science

The bipartite metatheory thesis attributes to Rudolf Carnap, Philipp Frank and Otto Neurath a conception of the nature of post-metaphysical philosophy of science that sees the purely formal-logical analyses of the logic of science as complemented by empirical inquiries into the psychology, sociology and history of science. Three challenges to this thesis are considered in this paper: that Carnap did not share this conception of the nature of philosophy of science even on a programmatic level, that Carnap's detailed analysis of the language of science is incompatible with one developed by Neurath for the pursuit of empirical studies of science, and, finally, that Neurath himself was confused about the programme of which the bipartite metatheory thesis makes him a representative. I argue that all three challenges can be met and refuted.

Hilbert's axiomatic method and Carnap's general axiomatics

This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' ‘material’ talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics.

Two paradoxes of semantic information

Yehoshua Bar-Hillel and Rudolph Carnap’s classical theory of semantic information entails the counterintuitive feature that inconsistent statements convey maximal information. Theories preserving Bar-Hillel and Carnap’s modal intuitions while imposing a veridicality requirement on which statements convey information—such as the theories of Fred Dretske or Luciano Floridi—avoid this commitment, as inconsistent statements are deemed not information-conveying by fiat. This paper produces a pair of paradoxical statements that such “veridical-modal” theories must evaluate as both conveying and not conveying information, although Bar-Hillel and Carnap’s theory accommodates these statements without inconsistency. Moreover, the paradoxes are independently interesting as the mode in which they self-refer bears on their evaluation.

A forgotten strand of reception history: understanding pure semantics

I explore a strand of reception history that follows Rudolf Carnap’s shift from a purely syntactical analysis of constructed languages to his conception of pure semantics. My exploration focuses on Gustav Bergmann’s and Everett Hall’s interpretation of pure semantics (as centered around Carnap’s notion of ’rules of designation’), their understanding of what constitutes a ’formal’ investigation of language, and their arguments concerning the relationship between expressions and their extra-linguistic referents. I argue that Bergmann and Hall strongly misread Carnap’s semantic project and, subsequently, their misunderstanding is passed down through colleagues and students (found most notably in Wilfrid Sellars’ early philosophy).

Er „ist eine Künstlernatur von hinreissender Genialität“

AbstractThe correspondence between Ludwig Wittgenstein and Moritz Schlick presented in this publication is part of the complete correspondence of Schlick which is intended for publication in the context of the Moritz Schlick Gesamtausgabe (Collected Papers of Moritz Schlick). As explained and illustrated in the following essay, the present publication not only reproduced the complete known and comprehensively commented correspondence between Wittgenstein and Schlick, but complements it with letters from and to Friedrich Waismann and Rudolf Carnap. Only this context enables a broader understanding of the topics and facts addressed in the letters, some of which have be re-dated.

Carnapian rationality

Carnapian rationality

Carnap and Lewis on the External World

This paper compares the claims about our knowledge of the external world presented by Rudolf Carnap, in the book known as the Aufbau, to those of Clarence Irving Lewis, in Mind and the World-Order. This comparison is made in terms of the opposition to Kantian epistemology that both books establish; the Aufbau is regarded as the peak of the logicist tradition and Mind and the World-Order is taken in continuity with pragmatism. It is found that both books present knowledge of the external world as a consequence of a structural organization of human experience. However, there is an important point of divergence: the concept of verification each author adopts is different, such a concept was even a matter of discussion between Lewis and the Vienna Circle. This paper shows this disagreement but also shows how Carnap changed his point of view in the decade after the Aufbau was published, towards a standpoint which is much closer to Lewis’s ideas. In that process, nevertheless, Carnap changed his focus and did not deal with the problem of the external world anymore. This paper also seeks to draw attention to some features of the relation between Carnap and the pragmatist tradition which have only recently started to attract interest.

Outflanking the vicious circle

Sir Michael Dummett unfairly criticises Frank Ramsey for advocating full-fledged realism as a way to escape the problem of vicious circularity. Instead Ramsey uses a more moderate approach that only requires a thin commitment to theoretical terms. In ‘Theories’, Ramsey details a method to substitute observational terms for the theoretical terms appearing in a theory, but its early advocates, Rudolf Carnap and Carl Hempel, recognised that the resulting ‘ramsey-sentence’ does not intend to fully remove the theoretical content of the original theory. Through a model-theoretic approach, Jaakko Hintikka clarifies how the ramsey-sentence is embedded in the original theory, and, thereby, retains a commitment to the theoretical content that governs the substituted observable terms. By understanding how ramsey-sentences relate to the original theory, we will see that Ramsey need not assert a full-fledged realism to address vicious circularity. Instead of committing to the existence of all theoretical concepts involved in the original theory, ramsey-sentences assert the existence of an unspecified object that satisfies the substituted observable terms, and this commitment is sufficient to escape vicious circularity. Through this process of definition, Ramsey sidesteps Dummett's charge of full-fledged realism, and suggests a more moderate position that is consistent with Dummett's emphasis on domain specification.

X-Phi and Carnapian Explication.

The rise of experimental philosophy (x-phi) has placed metaphilosophical questions, particularly those concerning concepts, at the center of philosophical attention. X-phi offers empirically rigorous methods for identifying conceptual content, but what exactly it contributes towards evaluating conceptual content remains unclear. We show how x-phi complements Rudolf Carnap’s underappreciated methodology for concept determination, explication. This clarifies and extends x-phi’s positive philosophical import, and also exhibits explication’s broad appeal. But there is a potential problem: Carnap’s account of explication was limited to empirical and logical concepts, but many concepts of interest to philosophers (experimental and otherwise) are essentially normative. With formal epistemology as a case study, we show how x-phi assisted explication can apply to normative domains.

¿Con sentido o sin sentido? En torno a un argumento de Carnap

En el artículo “Empirismo, Semántica y Ontología” (1950), Rudolf Carnap propone un argumento a favor de la conclusión de que ciertos enunciados, algunos pertenecientes a la metafísica, carecen de significado lingüístico. El artículo se discute en general como parte de un debate más amplio entre Carnap y Quine en la década de 1950. En este trabajo me propongo hacer tres cosas: en primer lugar, presentar brevemente el debate, con el fin de aclarar los propósitos dialécticos de Carnap en el artículo mencionado; en segundo lugar, argumentar que la estrategia de Carnap de detectar el sinsentido, falla; y por último, analizar el argumento de Carnap desde una perspectiva metasemántica externista.

Husserl and Carnap: Structural Objectivity, Constitution, Grammar

Husserl and Carnap: Structural Objectivity, Constitution, Grammar

International Language and the Everyday: Contact and Collaboration Between C.K. Ogden, Rudolf Carnap and Otto Neurath

Although now largely forgotten, the international language movement was, from the 1880s to the end of the Second World War, a matter of widespread public interest, as well as a concern of numerous scientists and scholars. The primary goal was to establish a language for international communication, but in the early twentieth century an increasing accent was placed on philosophical considerations: wanted was a language better suited to the needs of modern science and rational thought. In this paper, we examine the example of the English scholar C.K. Ogden's international language Basic English and his efforts to win the Vienna Circle philosophers Otto Neurath and Rudolf Carnap over to the project. Basic is shown to be an implementation of key ideas in Ogden's philosophy of language, ideas shared to a large extent with Neurath and Carnap. This we see through an examination of their unpublished correspondence, as well as through the collaboration that emerged between Ogden and Neurath, in which Neurath's Isotype, a system for graphically representing statistical data, became closely aligned with Basic. Through the ideas and endeavours we investigate here, we gain a new perspective on this crucial period in the history of analytic philosophy.

ERNST CASSIRER'S MOMENT: PHILOSOPHY AND POLITICS

The emergence of the German Jewish philosopher Ernst Cassirer (1874–1945) as the object of scholarly attention has been both surprising and rapid. In the decades since his early death while in exile in the United States, Cassirer never fell into complete oblivion. His works remained known to specialists in German intellectual history; his participation in a famous 1929 debate with Martin Heidegger in Davos, Switzerland, one of the most iconic moments in modern Continental thought, made his name familiar to most students of modern philosophy. Yet Cassirer lacked the widespread recognition given to contemporaries such as Heidegger or Walter Benjamin, and his work never became the center of historical or philosophical study. This neglect stemmed, in part, from dismissal by his peers; as Edward Skidelsky explains in his new study, Rudolf Carnap found him “rather pastoral,” Isaiah Berlin dismissed him as “serenely innocent,” and Theodor Adorno thought he was “totally gaga” (125). The last few years, however, have seen the rise of a remarkable new interest in Cassirer in both Germany and the English-speaking world. Among this recent literature, Edward Skidelsky's and Peter Gordon's works lead the small “Cassirer renaissance” and offer the best English-language introduction to his thought. Both Gordon and Skidelsky ambitiously seek to relocate Cassirer at the forefront of modern German and European thought. Gordon goes as far as to call him “one of the greatest philosophers and intellectual historians to emerge from the cultural ferment of modern Germany” and one of the most important thinkers of the twentieth century (11). In making such bold statements, Gordon and Skidelsky clearly set their sights beyond the person himself; they aspire to highlight a central strand of thought that enjoyed a powerful presence in early twentieth-century Germany but fell into neglect in the postwar era. In doing so, they seek to reevaluate the nature and legacy of Weimar thought, its complex relationship with the period's unstable politics, and its relevance today.

New work in metaphysics of science

Metaphysics of science is currently a flourishing field of philosophical research touching issues both in metaphysics and in philosophy of science. From the perspective of early twentieth-century philosophy of science, this is a rather surprising development. For as is well known, logical empiricists tended to banish metaphysical questions. Thus, the issue of realism versus anti-realism (or idealism) was classified as a pseudo-problem by Rudolf Carnap in the late 1920s and Ernest Nagel some 30 years later called it a ‘‘conflict over preferred modes of speech.’’ A major step towards the rehabilitation of metaphysical questions within philosophy of science and analytical philosophy in general was the development that led to the debate about scientific realism in the 1970s. It seemed to Putnam and others that, without taking into account that scientific terms refer to real entities, philosophy of science is unable to explain how theories can be compared trans-theoretically. At the same time, metaphysical or ontological questions became respectable again in areas such as philosophy of language, which ultimately led to what is now called analytical metaphyics (see Loux and Zimmerman 2003). During this period, philosophical problems that were formerly treated as pertaining exclusively the language of science were transformed into problems about metaphysical issues. Thus, for instance, theories of laws of nature in the 1950s aimed to define the characteristics of laws of nature entirely in terms of the syntactic structure of law statements. From the late 1970s on the question was what it is in the world that

“Logical Positivism”—“Logical Empiricism”: What's in a Name?

Do the terms “logical positivism” and “logical empiricism” mark a philosophically real and signiacant distinction? There is, of course, no doubt that the arst term designates the group of philosophers known as the Vienna Circle, headed by Moritz Schlick and including Rudolf Carnap, Herbert Feigl, Philipp Frank, Hans Hahn, Otto Neurath, Friedrich Waismann and others. What is debatable, however, is whether the name “logical positivism” correctly distinguishes their doctrines from related ones called “logical empiricism” that emerged from the Berlin Society for Scientiac Philosophy around Hans Reichenbach which included Walter Dubislav, Kurt Grelling, Kurt Lewin and a young Carl Gustav Hempel. The person who called the co-referentiality of the two terms into question was Reichenbach himself. He did so in two publications of the second half of the 1930s—in an article in Journal of Philosophy (1936) and in his Experience and Prediction (1938)—in order to alert readers to important differences between his own philosophy and that of the Vienna Circle. Reichenbach’s distinction was taken up by his former student Wesley Salmon. Not only did Salmon restate it, but he also asserted, categorically and very much in Reichenbach’s spirit, that “our chief inheritance from logical positivism” is “logical empiricism” ([1985] 2005, p. 7). The story of this inheritance is the story of “twentieth-century scientiac philosophy”:

Non-zero probabilities for universal generalizations

This article discusses the classical problem of zero probability of universal generalizations in Rudolf Carnap’s inductive logic. A correction rule for updating the inductive method on the basis of evidence will be presented. It will be shown that this rule has the effect that infinite streams of uniform evidence assume a non-zero limit probability. Since Carnap’s inductive logic is based on finite domains of individuals, the probability of the corresponding universal quantification changes accordingly. This implies that universal generalizations can receive positive prior and posterior probabilities, even for (countably) infinite domains.

„Bilder zukünftiger Vollendung“ – Der freistudentische Serakreis 1913 in den Tagebüchern und Briefen von und an Wilhelm Flitner

Conceived as a collage, this essay presents annotated excerpts from diaries and correspondences from the year 1913. It recreates a plethora of voices, especially of young intellectuals, progressive students and artists, focusing on the Sera Circle around the publisher Eugen Diederichs in Jena. Among the voices included are Wilhelm Flitner, who became a professor of education at the University of Hamburg, Rudolf Carnap, who later joined the Vienna Circle, Helene Czapski-Holzman, an artist and student of Max Beckmann, as well as Franz Roh, an art critic, photographer and collage-artist.