Against Thomas Mormann's argument that differential topology does not support Carnap's conventionalism in geometry we show their compatibility. However, Mormann's emphasis on the entanglement that characterizes topology and its associated metrics is not misplaced. It poses questions about limits of empirical inquiry. For Carnap, to pose a question is to give a statement with the task of deciding its truth. Mormann's point forces us to introduce more clarity to what it means to specify the task that decides between competing (...) hypotheses and in what way such a task may be both in practice and/or in principle impossible to carry out. (shrink)

Rudolf Carnap's 'Principle of Tolerance' was undoubtedly one of the most infl uential precepts in 20th Century philosophy. Introduced in The Logical Syntax of Language, Carnap's Principle suffered from ambiguities which aroused important philosophical questions from Moritz Schlick and Alberto Coffa. Specifi cally, their questions arise from the application of the Principle to the matter of including extra-logical transformation rules in the defi nition of a language, which Carnap regarded as an important difference between his own conventionalist philosophy of logic (...) and the 'absolutist' conception of Wittgenstein's Tractatus. Yet both Schlick and Coffa suggested that applying the Tolerance precept to this matter exceeds the limits of its legitimate deployment. Upon considering their objections, as well as the criticism of Wittgenstein which evoked them, it is argued that the philosophical signifi cance of the Principle of Tolerance requires its strict limitation to matters pertaining to the determination of meaning. (shrink)

In broadest terms, this thesis is concerned to answer the question of whether the view that arithmetic is analytic can be maintained consistently. Lest there be much suspense, I will conclude that it can. Those who disagree claim that accounts which defend the analyticity of arithmetic are either unable to give a satisfactory account of the foundations of mathematics due to the incompleteness theorems, or, if steps are taken to mitigate incompleteness, then the view loses the ability to account for (...) the applicability of mathematics in the sciences. I will show that this criticism is not successful against every view whereby arithmetic is analytic by showing that the brand of "conventionalism" about mathematics that Rudolf Carnap advocated in the 1930s, especially in Logical Syntax of Language, does not suffer from these difficulties. There, Carnap develops an account of logic and mathematics that ensures the analyticity of both. It is based on his famous "Principle of Tolerance", and so the major focus of this thesis will to defend this principle from certain criticisms that have arisen in the 80 years since the book was published. I claim that these criticisms all share certain misunderstandings of the principle, and, because my diagnosis of the critiques is that they misunderstand Carnap, the defense I will give is of a primarily historical and exegetical nature. Again speaking broadly, the defense will be split into two parts: one primarily historical and the other argumentative. The historical section concerns the development of Carnap's views on logic and mathematics, from their beginnings in Frege's lectures up through the publication of Logical Syntax. Though this material is well-trod ground, it is necessary background for the second part. In part two we shift gears, and leave aside the historical development of Carnap's views to examine a certain family of critiques of it. We focus on the version due to Kurt Gödel, but also explore four others found in the literature. In the final chapter, I develop a reading of Carnap's Principle - the `wide' reading. It is one whereby there are no antecedent constraints on the construction of linguistic frameworks. I argue that this reading of the principle resolves the purported problems. Though this thesis is not a vindication of Carnap's view of logic and mathematics tout court, it does show that the view has more plausibility than is commonly thought. (shrink)

As is well known, Carnap's conventionalism was a rejection to Kant's view ofmathematics and was fully developed in his Logische Syntax der Sprache.The purpose of this article is to step back to Der Logische Aufbau der Weltto show that the Logical Syntax of Language is an attempt to solve difficultiesfound in the earlier construction. I first clarify the notion of conventionalism, whichplays a central role in the application of mathematics to the reconstruction of empiricalknowledge. By not strictly distinguishing (...) between the intuitive notion and thetopological concept of dimension, Carnap is led to a construction which is highlyquestionable. To illustrate the constructive method developed in the Aufbauand some of its inherent difficulties, I consider the computational aspects of theconstruction of phenomenological space via the mathematical concept of dimension.Contrary to Carnap's conventionalism, a dual nature of mathematical statements isbrought into existence by his logical reconstruction. So, if Carnap wants to retainhis mathematics as devoid of content, he must make a clear-cut distinction betweenanalytic and synthetic statements. Thus the natural follow-up to the Aufbau isthe Logical Syntax of Language. (shrink)

Geometry was a main source of inspiration for Carnap's conventionalism. Taking Poincaré as his witness, Carnap asserted in his dissertation Der Raum that the metrical structure of space is conventional while the underlying topological structure describes ‘objective’ facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. It is shown that his metrical conventionalism is indefensible for mathematical (...) reasons. This implies that the relation between topology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as the logical empiricists used to say. (shrink)

Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincaré as his witness Carnap asserted in his dissertation Der Raum (Carnap 1922) that the metrical structure of space is conventional while the underlying topological structure describes "objective" facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. By this means his metrical conventionalism turns out to (...) be indefensible for mathematical reasons. This implies that the relation between to-pology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as logical empiricists used to say. (shrink)

Revision of the author's thesis--Oxford University, 1977. Bibliography: p.[142]-144.

We discuss in this paper the question of the scope of the principle of tolerance about languages promoted in Carnap's The Logical Syntax of Language and the nature of the analogy between it and the rudimentary conventionalism purportedly exhibited in the work of Poincaré and Hilbert. We take it more or less for granted that Poincaré and Hilbert do argue for conventionalism. We begin by sketching Coffa's historical account, which suggests that tolerance be interpreted as a conventionalism (...) that allows us complete freedom to select whatever language we wish—an interpretation that generalizes the conventionalism promoted by Poincaré and Hilbert which allows us complete freedom to select whatever axiom system we wish for geometry. We argue that such an interpretation saddles Carnap with a theory of meaning that has unhappy consequences, a theory we believe he did not hold. We suggest that the principle of linguistic tolerance in fact has a more limited scope; but within that scope the analogy between tolerance and geometric conventionalism is quite tight. (shrink)

For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly (...) should we characterise Carnap's actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these issues by looking at Carnap's response to the incompleteness theorems. Drawing on arguments put forward by Gödel and Beth, I show that some crucial aspects of Carnap's positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap's position requires are made. (shrink)

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...) the concepts of science through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap's understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap's logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap's program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts. The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language, and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap's entire program. My third chapter argues that this reading makes Carnap's program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap's program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful. (shrink)

Recent scholarship (by mainly Michael Friedman, but also by Thomas Uebel) on the philosophy of Rudolf Carnap covering the period from the publication of Carnap’s’ 1928 book Der Logische Aufbau der Welt through to the mid to late 1930’s has tended to view Carnap as espousing a form of conventionalism (epitomized by his adoption of the principle of tolerance) and not a form of empirical foundationalism. On this view, it follows that Carnap’s 1934 The Logical Syntax of Language is (...) the pinnacle of his work during this era, this book having developed in its most complete form the conventionalist approach to dissolving the pseudoproblems that often attend philosophical investigation. My task in this paper, in opposition to this trend, is to resuscitate the empiricist interpretation of Carnap’s work during this time period. The crux of my argument is that Carnap’s 1934 book, by eschewing for the most part the empiricism he espouses in the Aufbau and in his 1932 The Unity of Science, is led to a form of conventionalism that faces the serious hazard of collapsing into epistemological relativism. My speculation is that Carnap came to recognize this deficiency in his 1934 book, and in subsequent work (“Testability and Meaning”, published in 1936/37) felt the need to re-instate his empiricist agenda. This subsequent work provides a much improved empiricist epistemology from Carnap’s previous efforts and, ashistory informs us, sets the standard for future research in the theory of confirmation. (shrink)

Providing a principled characterization of the distinction between logical and non-logical expressions is a longstanding issue in the philosophy of logic. In the Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by "syntactic" means which sentences are valid and which are (...) not. Despite a renewed interest in the philosophical benefits of analyticity, both inside and outside of Carnap scholarship, Carnap's definition of logical expressions seems to have drawn too little attention. I shall argue that it is worth a second look. More precisely, my aim will be to defend this idea against some technical problems faced by Carnap's way of implementing it and against Quinean attacks on syntax-based conventionalism. Section 1 presents Carnap's definition in the context of Logical Syntax of Language, that is, how exactly the definition works, and why Carnap needs it. In section 2, I review three challenges that have been raised in the literature, and I propose to revise the definition accordingly. I argue that its modified version is immune to the previous challenges, and, to some extent, immune to new challenges as well. In the last section, I suggest that the definition has a philosophical interest of its own, because standard Quinean objections are not as conclusive as one might think when attention is paid to the fact that Carnap requires complete syntactic specification of validities. (shrink)

In sections 18 and 73 of Carnap’s Logical Syntax of Language , Carnap famously presents what he understands to be decisive objections to Wittgenstein’s Tractarian distinction between saying and showing. However, Carnap has been criticized in recent literature for severely misinterpreting that distinction. Against this criticism it is argued that Carnap reads that distinction as applying to two distinct classes of expressions ( Unsinn and sinnlos ) that he holds to emerge from his reading of Tractatus 4.1212 and related Tractarian (...) theses. It is then argued that Carnap’s counterexamples to Wittgenstein’s theses are successful given his reading, and that our analysis of his counterexamples puts us in a unique position to reevaluate his conventionalism. (shrink)

Alan Richardson’s Carnap’s Construction of the World is a well-researched, richly-detailed, and highly instructive study of a crucial moment in the history of the analytic tradition: the transitional stage between the classical or early period dominated by Frege, Moore, and Russell, and the neo-classical or middle period dominated by Wittgenstein and the Vienna Circle. This stage marks a shift from ontic analysis to linguistic analysis; from platonism to conventionalism; from realistic metaphysics to anti-metaphysics; from rationalism to empiricism; and from (...) logicism to logical positivism. Only the firm commitments to antipsychologism, to “logic as the essence of philosophy,” and to semantics remain the same. But above all it is the moment at which the positive influence of Kant upon analytic philosophy—in the form of a vestigial neo-Kantianism—is finally extinguished. All this and more is packed into Rudolf Carnap’s 1928 treatise Der logische Aufbau der Welt ; hence Richardson aptly concentrates his account by unpacking the philosophical content, context, and consequences of the Aufbau. (shrink)

In this paper, the connection between logicism and the principle of tolerance in Carnap’s philosophy of logic and mathematics is to be presented in terms of the history of its development. Such development is conditioned by two lines of criticism to Carnap’s attempt to combine Logicism and Conventionalism, the first of which comes from Gödel, the second from Alfred Tarski. The presentation will take place in three steps. First, the Logicism of Carnap before the publication of The Logical Syntax (...) of Language will be analyzed in its main features. Second, the relationship between Logicism and the Principle of Tolerance at the time of the publication of Logical Syntax, and thirdly, in the so-called semantical phase of Carnap’s thought will be examined. On the basis of the two preceding points, we will then critically analyze two interpretations of the possibility to maintain a philosophical position like that of Carnap nowadays. (shrink)

This article examines how Quine and Sellars develop informatively contrasting responses to a fundamental tension in Carnap’s semantics ca. 1950. Quine’s philosophy could well be styled ‘Essays in Radical Empiricism’; his assay of radical empiricism is invaluable for what it reveals about the inherent limits of empiricism. Careful examination shows that Quine’s criticism of Carnap’s semantics in ‘Two Dogmas of Empiricism’ fails, that at its core Quine’s semantics is for two key reasons incoherent and that his hallmark Thesis of Extensionalism (...) is untenable. The tension in Carnap’s semantics together with Quine’s exposure of the severe limits of radical empiricism illuminate central features of Sellars’s philosophy: the fully general form of the myth of givenness, together with Sellars’s alternative Kantian characterisation of understanding; the full significance of Carnap’s distinction between conceptual analysis and conceptual explication, and its important methodological implications; the specifically pragmatic character of Sellars’s realism; and Sellars’s methodological reasons for holding that philosophy must be systematic and that systematic philosophy must be deeply historically and textually informed. This paper thus re-examines this recent episode of philosophical history for its philosophical benefits and systematic insights. (shrink)

One of the reasons for Carnap’s (1922) analysis of space was the confounding status of many arguments around the state of the art on that topic at that time. The unsatisfactory views supplied by mathematicians, physicists and philosophers led Carnap to propose a new conception of space. His proposal, which employs the notion of intuition as a fundamental tool, fared better, but clashed with his conventionalists intentions derived from an allegedly tolerant attitude. The notion of intuition here examined allows us (...) to claim that Carnap’s target was also an objectivist epistemological program dependent on certain realistic reminiscences embodied in the notion of evidence or matter of fact (Tatbestand). (shrink)

Kurt Gödel criticizes Rudolf Carnap's conventionalism on the grounds that it relies on an empiricist admissibility condition, which, if applied, runs afoul of his second incompleteness theorem. Thomas Ricketts and Michael Friedman respond to Gödel's critique by denying that Carnap is committed to Gödel's admissibility criterion; in effect, they are denying that Carnap is committed to any empirical constraint in the application of his principle of tolerance. I argue in response that Carnap is indeed committed to an empirical requirement (...) vis‐à‐vis tolerance, a fact that becomes clear upon closer scrutiny of Carnap's relevant writings. *Received July 2009; revised January 2010. †To contact the author, please write to: Department of Philosophy, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK S7N 5A5, Canada; e‐mail: [email protected]. (shrink)

In November of 1934, over successive Thursdays, the 26-year-old Willard van Orman Quine gave three “Lectures on Carnap” at Harvard University, the ostensive aim of which was a presentation of the “central doctrine” of Carnap’s Logische Syntax der Sprache, “that philosophy is syntax.” These were among Quine’s very first public lectures, and they constituted the American premier of Carnap’s logische Syntax program. As such, these lectures are of considerable significance to the history of analytic philosophy. They show, for example, one (...) way Carnap’s syntactical program was presented and understood in the 1930s, and indeed they show how Quine, emerging even in 1934 as one of America’s brightest logicians, understood that particular project. Moreover, they promise to tell something about how Quine himself was thinking about central philosophical issues—the a priori, analyticity, and philosophy itself—early in his career, before he wrote the papers and books on those topics that established his reputation. This paper takes up this last topic. My aim is to reconstruct and understand how Quine was thinking about the a priori, analyticity, and philosophy itself in 1934, what he aimed to accomplish in the “Lectures on Carnap,” and the considerable extent to which he accomplished that aim. What Quine accomplished, in short, was the outline of a fascinating and original anti-metaphysics, with conventionalism at its heart. This was an anti-metaphysics that invited adoption of a particular conception of philosophy. (shrink)

This article focuses on the conventions that sustain social interaction and argues that they are central to Simon's decision-making theory. Simon clearly identifies two kinds of coordination by convention: behavioral mores that shape human actions, and shared mental models that govern human perceptions. This article argues that Poincaré–Carnap's conventionalism provides powerful support for Simon's theory; it contends that this theory offers a more convincing account of decision and coordination than Lewis' concept of convention. Simon's approach to applying conventionalist logic (...) to social interaction emphasizes the normative role played by mental models in solving coordination problems and considers rationality in terms of both cognitive and moral considerations. By connecting conventional phenomena to social identifications, Simon stresses the resulting complexity of coordination problems. (shrink)

We compare Carnap's and Kuhn's views on science. Although there are important differences between them, the similarities are striking. The basis for the latter is a pragmatically oriented semantic conventionalist picture of science, which suggests that the view that post-positivist philosophy of science constitutes a radical revolution which has no interesting affinities with logical positivism must be seriously mistaken.

Rudolf Carnap’s principle of tolerance states that there is no need to justify the adoption of a logic by philosophical means. Carnap uses the freedom provided by this principle in his philosophy of mathematics: he wants to capture the idea that mathematical truth is a matter of linguistic rules by relying on a strong metalanguage with infinitary inference rules. In this paper, I give a new interpretation of an argument by E. W. Beth, which shows that the principle of tolerance (...) does not suffice to remove all obstacles to the employment of infinitary rules. (shrink)

We compare Carnap's and Kuhn's views on science. Although there are important differences between them, the similarities are striking. The basis for the latter is a pragmatically oriented semantic conventionalist picture of science, which suggests that the view that post-positivist philosophy of science constitutes a radical revolution which has no interesting affinities with logical positivism must be seriously mistaken.

I want to analyse the Quine-Carnap discussion on analyticity with regard to logical, mathematical and set-theoretical statements. In recent years, the renewed interest in Carnap’s work has shed a new light on the analytic-synthetic debate. If one fully appreciates Carnap’s conventionalism, one sees that there was not a metaphysical debate on whether there is an analytic-synthetic distinction, but rather a controversy on the expedience of drawing such a distinction. However, on this view, there can be no longer a single (...) analytic-synthetic distinction, because several kinds of statements could be regarded as analytic (L-determinate). L-equivalence between extra-logical linguistic predicates has already been heavily debated. The recent consensus states that Quine’s rejection of this analytic-synthetic is pragmatically grounded in his linguistic behaviorism. However, Carnap’s logical frameworks also contain other kinds of statements, and it is worthwhile to compare both Quine and Carnap’s grounds for considering these statements as analytic or not analytic. First, I will discuss logical statements. I will argue that Quine draws a very sharp distinction between first order logic and set theory, which should be regarded as a (pragmatic) analytic-synthetic distinction (as Quine admits in an interview, see Theoria, 40, 1994, p. 199). In fact, Quine’s major worry is whether identity statements are analytic. Second, I will discuss mathematical statements. In Carnap’s Foundations of Logic and Mathematics, it is clear that mathematical statements are analytic. For Quine, all mathematical statements are reducible to set-theoretical statements. Third, I discuss the analyticity of set-theoretical statements. For Quine, the membership predicate should be regarded as an interpreted extra-logical predicate. Quine’s work in set theory and his later philosophy of set theory naturally lead to the view that set-theoretical statements cannot be analytic. A major complication for the Quine-Carnap comparison is that Carnap has no elaborate reflections on set theory, while the influence of set theory on Quine’s views can hardly be underestimated. I conclude with some lessons for the contemporary debate on analyticity. (shrink)

Carnap’s work was instrumental to the liberalization of empiricism in the 1930s that transformed the logical positivism of the Vienna Circle to what came to be known as logical empiricism. A central feature of this liberalization was the deployment of the Principle of Tolerance, originally introduced in logic, but now invoked in an epistemological context in “Testability and Meaning”. Immediately afterwards, starting with Foundations of Logic and Mathematics, Carnap embraced semantics and turned to interpretation to guide the choice of a (...) theoretical language for science. The first thesis of this paper is that recourse to an intended interpretation led to a partial retrenchment of the conventionalism implied by the Principle of Tolerance. It required that the choice of a language be based on abstraction from a context; this procedure later became a component of the process of explication that was distinctive to Carnap’s mature views. The interpretive origin of formal systems also ensured their likely syntactic consistency, an issue on which Carnap was strongly criticized by figures such as Beth and Gödel. The second thesis of this paper is that this reliance on an intended interpretation enabled constructed formal systems to be relevant to the development of empirical science. (shrink)

David Lewis presented Convention as an alternative to the conventionalism characteristic of early-twentieth-century analytic philosophy. Rudolf Carnap is well known for suggesting the arbitrariness of any particular linguistic convention for engaging in scientific inquiry. Analytic truths are self-consistent, and are not checked against empirical facts to ascertain their veracity. In keeping with the logical positivists before him, Lewis concludes that linguistic communication is conventional. However, despite his firm allegiance to conventions underlying not just languages but also social customs, he (...) pioneered the view that convening need not require any active agreement to participate. Lewis proposed that conventions arise from “an exchange of manifestations of a propensity to conform to a regularity” (87–8). In reasserting the conventional quality of languages and other practices resting on mutual expectations, Lewis comfortably works within the analytic tradition. Yet he also deviates from his predecessors because his conventionalist approach is comprehensively grounded in instrumentalism. Lewis adopts an extension of David Hume's desire-belief psychology articulated in rational choice theory. He develops his philosophy of convention relying on the highly formal mid-twentieth-century expected utility and game theories. This attempt to account for language and social customs wholly in terms of instrumental rationality has the implication of reducing normativity to preference satisfaction. Lewis’ approach continues in the trend of undermining normative political philosophy because institutions and practices arise spontaneously, without the deliberate involvement of agents. Perhaps Lewis’ Convention is best seen as a resurgent form of analytic philosophy, characterized by “a style of argument, hostility to [ambitious] metaphysics, focus on language, and the dominance of logic and formalization” that solves the dilemma of “combining the analytic inheritance…with normative concerns” by reducing normativity to individuals’ preference fulfillment consistent with the axioms of rational choice. (shrink)

Thorough a detailed analysis of version III of Gödel's Is mathematics syntax of language?, we propose a new interpretation of Gödel's criticism against the conventionalist point of view in mathematics. When one reads carefully Gödel's text, it brings out that, contrary to the opinion of some commentators, Gödel did not overlook the novelty of Carnap's solution, and did not criticise him from an old-fashioned conception of science. The general aim of our analysis is to restate the Carnap/Gödel debate in the (...) Fregean heritage. We stress the way both of them try to answer, from different Fregean perspectives, to the question of the nature of logic and mathematics in knowledge. (shrink)

The daring idea that convention - human decision - lies at the root both of necessary truths and much of empirical science reverberates through twentieth-century philosophy, constituting a revolution comparable to Kant's Copernican revolution. This book provides a comprehensive study of Conventionalism. Drawing a distinction between two conventionalist theses, the under-determination of science by empirical fact, and the linguistic account of necessity, Yemima Ben-Menahem traces the evolution of both ideas to their origins in Poincaré's geometric conventionalism. She argues (...) that the radical extrapolations of Poincaré's ideas by later thinkers, including Wittgenstein, Quine, and Carnap, eventually led to the decline of conventionalism. This book provides a fresh perspective on twentieth-century philosophy. Many of the major themes of contemporary philosophy emerge in this book as arising from engagement with the challenge of conventionalism. (shrink)

The daring idea that convention - human decision - lies at the root both of necessary truths and much of empirical science reverberates through twentieth-century philosophy, constituting a revolution comparable to Kant's Copernican revolution. This book provides a comprehensive study of Conventionalism. Drawing a distinction between two conventionalist theses, the under-determination of science by empirical fact, and the linguistic account of necessity, Yemima Ben-Menahem traces the evolution of both ideas to their origins in Poincaré's geometric conventionalism. She argues (...) that the radical extrapolations of Poincaré's ideas by later thinkers, including Wittgenstein, Quine, and Carnap, eventually led to the decline of conventionalism. This book provides a fresh perspective on twentieth-century philosophy. Many of the major themes of contemporary philosophy emerge in this book as arising from engagement with the challenge of conventionalism. (shrink)

We argue that (1) a purported example of an infinite inference we humans can actually perform admits a faithful, finitary description, and (2) infinite inference contravenes any view which does not grant our minds uncomputable powers. These arguments block the strategy, dating back to Carnap's Logical Syntax of Language, of using infinitary inference rules to secure the determinacy of arithmetical truth on conventionalist grounds.

The Analysis of Matter is perhaps best known for marking Russell's rejection of phenomenalism and his development of a variety of Lockean representationalism–-Russell's causal theory of perception. This occupies Part 2 of the work. Part 1, which is certainly less well known, contains many observations on twentieth-century physics. Unfortunately, Russell's discussion of relativity and the foundations of physical geometry is carried out in apparent ignorance of Reichenbach's and Carnap's investigations in the same period. The issue of conventionalism in its (...) then contemporary form is simply not discussed. The only writers of the period who appear to have had any influence on Russell's conception of the philosophical issues raised by relativity were Whitehead and Eddington. Even the work of A. A. Robb fails to receive any extended discussion;1 although Robb's causal theory is certainly relevant to many of Russell's concerns, especially those voiced in Part 3, regarding the construction of points and the topology of space-time. In the case of quantum mechanics, the idiosyncrasy of Russell's selection of topics is more understandable, since the Heisenberg and Schrödinger theories were only just discovered. Nevertheless, it seems bizarre to a contemporary reader that Russell should have given such emphasis2 to G. N. Lewis's suggestion that an atom emits light only when there is another atom to receive it–-a suggestion reminiscent of Leibniz, and one to which Russell frequently returns. In short, the philosophical problems of modern physics with which Russell deals seem remote from the perspective of post-positivist philosophy of physics. (shrink)

The early sections describe the pre‐theoretic realism of the mathematician, survey the basic forms of realism in philosophy, and attempt to disentangle the issues of realism from debates over the nature of truth. The final section begins by laying out traditional Platonism, intuitionism, and formalism. Quine's famous critique of Carnap's conventionalism then leads to Quine's realism, and Putnam's developments thereof, while a different sort of mathematical realism is found in Gödel's writings. Set theoretic realism emerges as an effort to (...) build on the strengths of Quine's and Gödel's realisms, while avoiding their weaknesses and filling in their lacunae. (shrink)

W. V. Quine famously argues that though all knowledge is empirical, mathematics is entrenched relative to physics and the special sciences. Further, entrenchment accounts for the necessity of mathematics relative to these other disciplines. Michael Friedman challenges Quine’s view by appealing to historicism, the thesis that the nature of science is illuminated by taking into account its historical development. Friedman argues on historicist grounds that mathematical claims serve as principles constitutive of languages within which empirical claims in physics and the (...) special sciences can be formulated and tested, where these mathematical claims are themselves not empirical but conventional. For Friedman, their conventional, constitutive status accounts for the necessity of mathematics relative to these other disciplines. Here I evaluate Friedman’s challenge to Quine and Quine’s likely response. I then show that though we have reason to find Friedman’s challenge successful, his positive project requires further development before we can endorse it. (shrink)