One difficulty with Lewis’s logics favourite systems, S1–S3, is that they have no intuitive semantics or proof theory. Another approach to constructing a logic of entailment is to begin with a semantic intuition and then adopt the logic characterized by the semantics. This is the approach of Carnap’s Meaning and Necessity. On Carnap’s view, entailment is just strict implication in the sense of the logic S5. The chapter examines Carnap’s semantics and its successor developed by Nino Cocchiarella, and finds that whereas they may give a good representation of the notion of logical truth, they do not provide an adequate analysis of entailment. Once again, the problem of implosion and nested entailments are problematic. This chapter also looks at attempts to solve these difficulties using worlds at which the logical truths differ, and raises philosophical worries about them.

This chapter will discuss Carnap’s engagement with various social issues through the lens of his scientific world view, and connect it to Thomas Uebel’s argument that Carnap’s philosophy was intended to be “political in its broadest sense.” I will build on Uebel’s characterization of Carnap as someone who believed in philosophy as fundamentally a collective effort and show how that played out in several of his organizational efforts. For example, Carnap notably protested the loyalty oaths required by the University of California, refusing both a lecture invitation and a visiting professorship on those grounds, citing concerns about academic freedom. Later in his life, Carnap, together with AJ Ayer, Max Black, Herbert Feigl, Carl Hempel, and Morris Lazerowitz, wrote a letter in the New York Times urging that Nicolas Molina Flores and Eli de Gortari be set free; Carnap also visited Molina and de Gortari in Mexico in 1970 and reported on it for the Journal of Philosophy. I will consider the extent to which social involvement like this, reflected in concern for the intellectual community as a whole, can be seen as continuous with his commitments to philosophy as a collective enterprise, and how those ideas might improve the practice of philosophy generally.

This chapter discusses how Carnap’s philosophy of language affects his position on language planning issues. Carnap was an Esperantist from an early age, and he kept his interest for international auxiliary languages active throughout his life. In his Intellectual Autobiography, he clearly mentions the relation between his activity of building symbol systems as a logician and his interest for language planning for international communication. His controversy with Wittgenstein regarding Esperanto illustrates two opposing views of language, one as a functional device for various purposes and one as a carrier of tradition and identity. Carnap’s dismissal of the latter is rooted both in his principle of tolerance (and its underlying instrumentalism) and in logical empiricism’s attack on metaphysical concepts such as Volksgeist, shared by other language planners who emphasized the instrumental purpose of language and supported locutors’ active intervention in it either by language reform or by language construction. We argue that the antimetaphysical rejection of the romanticist view of language, sustained by Vienna Circle, led to a more liberal and flexible attitude toward language planning issues. Finally, the internationalism of logical empiricists was effective in shaping their favourable disposition towards international auxiliary languages.

Carnap’s naturalism evidently differs from Quine’s, but the precise nature of this difference has proven elusive. This chapter focuses on what Quine defends as his “provincial” naturalism against a Carnapian “cosmopolitan” alternative. The problem with this contrast, however, is that Quine does not represent a pure form of what he calls a “provincial” view. This is illustrated by his tergiversations about analyticity; after initially denying that there was even an explicandum worth bothering about, he later offered his own ordinary-language-based account of analyticity, without feeling any need to supply a more exact explication; there would appear to be no way to resolve the resulting stand-off with the cosmopolitan standpoint. This paper suggests a more robust explicandum for analyticity (and cosmopolitanism more generally). We come back, in the end, to the confrontation between Carnap and Quine in Chicago in 1950, where Carnap convinced Quine that their differences did not concern any question about which there could be right or wrong, correct or incorrect; it is regretted that Quine soon lost this lesson from sight.

Carnap’s naturalism evidently differs from Quine’s, but the precise nature of this difference has proven elusive to generations of commentators. This chapter focuses on what Quine defends as his “provincial” naturalism against a Carnapian “cosmopolitan” alternative. The problem with this contrast, however, is that Quine does not represent a pure form of what he calls a “provincial” view – he vacillates between provincial and cosmopolitan temptations. To illustrate a purely provincial view the position of Peter Strawson is held up as an opposite, provincial extreme to Carnapian cosmopolitanism, and while Quine is clearly tempted by both these extremes, the attempt to locate him on a continuum between them is complicated by his evident indecisiveness. This is further illustrated by his tergiversations about analyticity; after initially denying that there was even an explicandum worth bothering about, he later offered his own ordinary-language-based account of analyticity, without feeling any need to supply a more exact explication; there would appear to be no way to resolve the resulting stand-off with the cosmopolitan standpoint. This chapter suggests a more robust explicandum for analyticity (and cosmopolitanism more generally). We come back, in the end, to the confrontation between Carnap and Quine in Chicago in 1950, where Carnap convinced Quine that their differences did not concern any question about which there could be right or wrong, correct or incorrect; it is regretted that Quine soon lost this lesson from sight.

A few years after his adoption of both a syntactical method and a principle of tolerance in the early thirties, Carnap turned to semantics when he learned about Tarski’s work on the definition of a truth predicate. How significant is this semantical turn? Carnap scholars have so much emphasized that The Logical Syntax anticipates Tarskian semantics that they tended to minimize the importance of Carnap’s adoption of a semantical approach. As a consequence, his semantical turn has not always been given the importance it deserves. Its meaning, scope and consequences have also often been misunderstood. This paper contributes to a re-evaluation of Tarski’s influence on Carnap in view of the fact that Carnap is far from having just followed Tarski’s way. We examine some specificities of Carnap’s approach of semantics. We also discuss what is left of the syntactic method after the adoption of semantics and what the relations between syntax and semantics become from the late thirties on. The following topics are given specific attention: languages, formal systems, and calculi; truth, L-truth, and L-validity; L-states, L-ranges, and state descriptions. We also analyze the impact of semantics on the principle of tolerance.

Carnap is commonly considered a great opponent of metaphysics. For good reason, as he made numerous derogatory remarks about metaphysics and metaphysicians. But what does Carnap reject when he rejects metaphysics? I distinguish between Early Carnap (before 1930) and Late Carnap (after 1930) and argue that Late Carnap does not reject a specific set of questions or views. Rather, he rejects a particular methodology that he regards as conflicting with empiricism. For example, in “Empiricism, Semantics and Ontology,” Carnap does not reject the thesis that numbers exist as meaningless. Instead, he defends the acceptance of numbers against empiricist concerns. But if merely the methodology and not the subject matter is the problem, then metaphysics can perhaps be saved by fixing the methodology. Indeed, I contend, much of contemporary metaphysics is, from Late Carnap’s perspective, in good standing.

Throughout his intellectual career, Carnap had developed original views on the nature of mathematical knowledge, its relation to logic, and the application of mathematics in the natural sciences. A general line of continuity in his philosophical work is the conviction that both mathematics and logic are formal or non-factual in nature. Carnap’s formality thesis can be identified in different periods, connecting his early contributions to the foundations of geometry and general axiomatics from the 1920s with his later work on the general syntax of mathematical languages in Logical Syntax. Given the centrality of this idea, how precisely did Carnap understand the formality thesis concerning mathematical knowledge? How was the thesis characterized at different stages in his philosophical work? The aim in the chapter will be to retrace the development of Carnap’s thinking about the formality of logic and mathematics from the 1920s until the late 1930s. As we will see, in spite of his general adherence to the thesis, there were several significant shifts in his understanding, corresponding to changes in his conceptual framework. Specifically, one can identify a transition from a semantic account of formality related to his study of axiomatic theories to a syntactic formalism developed in Logical Syntax.

It may seem odd that Rudolf Carnap chose to include in his philosophy of science textbook a whole chapter on the problem of free will and determinism. The problem, or better a tangle of related problems, had exercised metaphysicians and ethicists for thousands of years. And by his own account Carnap engaged in neither metaphysics nor ethics and wanted to leave traditional philosophy behind him. So, on the face of it, the chapter presents us with a puzzle about Carnap as well as about free will and determinism. Rather than a full treatment of the traditional issues, the chapter was a response to a then recent paper by Hans Reichenbach that argued that the deterministic laws of classical physics preclude genuine choice as well as any meaningful freedom. Reichenbach goes on to argue that if, however, the fundamental laws are statistical as in quantum mechanics, both choice and freedom are restored. Carnap rejects both of Reichenbach’s conclusions and in the process addresses questions about how we are to understand laws of nature and causation as well as freedom and choice. This chapter examines and assesses Carnap’s arguments and asks whether they amount to a deviation from his anti-metaphysical stance.

It is no secret that various versions of logical empiricism argued for the importance of unified science. Carnap was a proponent of unity of science views, although he expressed this in different idioms at different times. In the Aufbau (1928) he spoke of the unity of the object domain secured through definability in the constitutional system, in his physicalist period he argued that a physicalist language could serve as the universal language of science, and in his mature philosophical work he investigated a variety of meanings that might be attached to reductionist projects for unifying various scientific fields. Our essay focuses less on Carnap’s several proposals than on a prior interpretive question: what was philosophically at stake for Carnap in the question of the unity of science? We begin with some suggestions in Carnap’s 1963 Intellectual Autobiography, where he calls unity of science “one of the main tenets of our general philosophical conception” and one in which Neurath’s emphasis on the “interdependence of all decisions … made a strong impression” on him. We follow Carnap in the suggestion that an account of his approach to unity of science does not take us into questions of unity of nature but rather of the scientific attitude and the unity of reason.

The propositions of a scientific theory are connected with empirical states of affairs. Determining how theoretical propositions are connected with empirical facts, what Carnap called the “empirical significance” of a theory, is a complex affair. Carnap’s account of the relationship between theoretical frameworks and methods of observation has come in for plentiful criticism, alleging that Carnap’s theory of science does not allow for a sophisticated entwinement of theory and observation, instead favoring heavy formalism and a brittle reductionism. I present evidence that Carnap’s account of the distinction between theoretical and observation languages is more flexible than it is usually depicted to be and is motivated by his philosophy of science. In particular, in his mature work Carnap argues that the "specific calculus" of a scientific theory, including mathematical structure and physical laws, are included in the axiomatic foundations and linguistic framework of that theory. Carnap’s account of language thus turns out to be deeply entangled with his philosophy of science, and one cannot be understood independently of the other.

This chapter provides a critical survey of six of the most important interpretations of Carnap’s Logical Structure of the World or Aufbau. I argue that the variety of interpretations of the Aufbau reflect a reasonable pluralism of approaches. This pluralism can be traced to two factors. First, an interpretation of a philosophical text is sensitive to both normative and descriptive elements. Second, there is a reasonable pluralism with respect to the normative elements of an interpretation, especially the philosophical aim that an interpreter attributes to the author of the text. This analysis builds on recent discussions by Beaney of how the history of analytic philosophy should be done. The upshot of the chapter is that a more reflective approach to writing the history of philosophy should help us to acknowledge the plausibility of interpretations of a text that we refuse to endorse.

In current analytic philosophy, Carnapian explication has become a prominent method and theme again, also under the names of conceptual engineering and mathematical philosophy. But there are questions about the reach and limits of this method, and in particular, about the goals for which it is appropriate. In the present essay, this topic is approached by reconsidering the origins of Carnapian explication, in the sense of its original inspirations and guiding paradigms.This leads to the following questions: What were the underlying goals in those cases, thus the function or functions explication was supposed to serve, and how did it serve them? Also, were those functions sufficiently stable and uniform to provide helpful orientation for us, both with respect to Carnap and current appeals to explication? Insofar as answers to those questions are not as easy as one might think, already because the relevant aspects often remain implicit, an important dimension of explication should be subjected to further clarification and critique. What is at issue here, at bottom, is the dividing line, insofar as there is one, between philosophical and scientific goals, and with it, between the methodologies appropriate for each.

This chapter places Carnap in the history of twentieth-century philosophy by pointing out different tensions in canon formation of philosophy. It also introduces key concepts and notions of the volume, along with chapter summaries.

Rudolf Carnap’s began to write on probability and inductive logic in 1945, marking a surprising shift in his research interests midway through his post-PhD career (1921–1970). His 1950 Logical Foundations of Probability is unquestionably his best-known work in this area, and yet his views afterwards underwent a substantial change over the next two decades, the extent of which was (and remains) often unappreciated. Inevitably some of his views underwent critical examination, both during his lifetime and after, but he was fortunate in being able to benefit in meeting these from the contributions and support of a number of mathematically and philosophically gifted collaborators. This essay traces the origins of his interest, the nature of these shifts, and some of the contributions of the members of his invisible college. Although the special technical contributions of Carnap continue to engage the attention of a small but influential group of individuals, his more general impact was much broader, often shaping as it did the current widespread epistemic and Bayesian view of the field.

With a view to highlighting the importance of archival and less well-known primary sources for our understanding of Rudolf Carnap’s philosophy, this chapter investigates several examples of concrete influences on his thinking, from nineteenth-century Herbartianism and empiriocriticism, the German Youth Movement, Bauhaus modernism and the revolution from the right, toward the Vienna Circle and post-WWII analytic philosophy. These examples demonstrate that Carnap’s philosophy had always been shaped by practical motives; he developed a philosophical stance that is directed at the reality of life and integrates cognitive as well as non-cognitive elements. This meta-philosophical view that carefully investigates the borders between the scientifically comprehensible (viz., the cognitive) and those aspects of reasoning that merely comprise personal attitudes (viz. the noncognitive) developed through various stages, from the "scientific world-conception" and antimetaphysics of the Vienna Circle toward Carnap’s mature views on inductive logic and human decision-making. The upshot is that noncognitivism as being understood by Carnap and his philosophical allies rather than denouncing value statements as arbitrary and irrational embeds them into a rational scientific discourse, to maximize rationality in connection with moral and political decision making.

Toward the end of his life, Thomas Kuhn came to know the then new historical literature that substantially revised our understanding of Rudolf Carnap’s ideas. He was so taken with the emerging parallels between his own work and Carnap’s that he said “if I had known about it, if I had been into the literature at that level, I probably would never have written Structure.” Kuhn’s statement here is truly remarkable. There are, of course, both similarities and differences between Carnap and Kuhn. The similarities suggest that their two views are open to some of the same significant challenges and criticisms. But the differences suggest how each can help the other to meet the criticisms posed.

Many informed readers of Carnap (and Quine) have taken Quine’s objections to Carnap’s account of analyticity in terms of semantical rules to have failed. This paper counters this, arguing that Quine actually saw himself as applying Carnap’s own philosophical standards more strictly than Carnap himself did. Quine was, as he later reported, “just being more carnapian than Carnap.” This paper offers a careful analysis of Section 4 of “Two Dogmas of Empiricism,” which shows Carnap conflating two senses of “semantical rule.” Although the first is clear, Quine sees it as being of no use in defining analyticity. The second, though integral to Carnap’s method of defining analyticity, Quine shows to be left unexplained by Carnap’s definitions.

Recognition that people are divided by a common language is typically marked by a search for culprit ambiguities – but rarely so when name philosophers are involved, for whom continued talking past each other may seem the easier option.Whether the case of Carnap and Quine fits this profile is my quarry here. I begin with Quine’s conjecture that it was Neurath’s influence that made Carnap introduce the paragraphs into the Aufbau that promised, without elaboration, a conceptual genealogy on a physical basis. I argue that are good grounds to support Quine here. The analysis will be supplemented with remarks about later disagreements between Carnap and Neurath.

While a number of commentators have argued that Quine’s account of Carnap’s paper in terms of the category/subclass distinction is simply a misunderstanding of Carnap, this essay argues that it is not. Instead, Quine was correct to construe Carnap’s external questions of existence as all being category questions. Quine’s second claim – that answers to internal category questions of existence are trivial and analytic – was, however, incorrect. Here, this essay then dissents from a view of Ebbs, who has recently argued that Quine was right on both points. Instead, it is argued that epistemic considerations that support Quine’s first point undermine his second point.