Rudolf Carnap

The first part of this entry details what is known about the personal encounters between Rudolf Carnap and Edmund Husserl. The second part looks at all the places in Carnap’s works where Husserl is cited.

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (shrink)

Robert Sinclair’s *Quine, Conceptual Pragmatism, and the Analytic-Synthetic Distinction* persuasively argues that Quine’s epistemology was deeply influenced by C. I. Lewis’s pragmatism. Sinclair’s account raises the question why Quine himself frequently downplayed Lewis’s influence. Looking back, Quine has always said that Rudolf Carnap was his “greatest teacher” and that his 1933 meeting with the German philosopher was his “first experience of sustained intellectual engagement with anyone of an older generation” (1970, 41; 1985, 97-8, my emphasis). Quine’s autobiographies contain only a (...) handful of biographical references to Lewis and he regularly soft-pedaled the latter’s influence in private correspondence. In this note, I discuss some archival evidence that helps us better understand Quine’s reluctance to acknowledge Lewis’s influence. I contextualize the relation between Lewis and Quine and argue that the latter viewed his teacher as a retrograde force in modern epistemology, impeding the more rigorous approach that Carnap had been developing in Europe. Next, I briefly discuss Lewis’s contribution to the development of scientific philosophy in the United States and argue that Quine underestimated his teacher’s role in this process. In doing so, I hope to show that Quine’s zealous commitment to Carnap’s approach negatively affected his assessment of Lewis’s influence, thereby supplementing Sinclair’s praiseworthy reconstruction with an explanation of why Quine himself underestimated Lewis’s role. (shrink)

Carnap and Quine first met in the 1932-33 academic year, when the latter, fresh out of graduate school, visited the key centers of mathematical logic in Europe. In the months that Carnap was finishing his Logische Syntax der Sprache, Quine spent five weeks in Prague, where they discussed the manuscript “as it issued from Ina Carnap’s typewriter”. The philosophical friendship that emerged in these weeks would have a tremendous impact on the course of analytic philosophy. Not only did the meetings (...) effectively turn Quine into Carnap's disciple, they also paved the way for their seminal debates about meaning, language, and ontology---the very discussions that would change the course of analytic philosophy in the decades after the Second World War. -/- Yet surprisingly little is known about these first meetings. Although Quine has often acknowledged the impact of his Prague visit, there appears to be little information about these first encounters, except for the fact that the Quines “were overwhelmed by the kindness of the Carnaps” and that it was Quine’s “most notable experience of being intellectually fired by a living teacher”. Neither their correspondence nor their autobiographies offer a detailed account of these meetings. In this paper, I shed new light on Carnap’s and Quine’s first encounters by examining a set of previously unexplored material from their personal and academic archives. Why did Quine decide to visit Carnap? What did they discuss? And in what ways did the meetings affect Quine’s philosophical development? In what follows, I address these questions by means of a detailed reconstruction of Quine’s year in Europe based on a range of letters, notes, and reports from the early 1930s. (shrink)

Philosophers often write in a particular mood; their work is playful, strident, strenuous, or nostalgic. On the face of it, these moods contribute little to a philosophical argument and are merely incidental. However, I will argue that the cognitive science of moods and emotions offers us reasons to suspect that mood is relevant for philosophical texts. I use examples from Friedrich Nietzsche and Rudolph Carnap to illustrate the role moods play in their arguments. As readers and writers of philosophical texts, (...) we do well to attend to mood. (shrink)

In this paper, I look at Susan Stebbing’s articles and reviews that critically engage logical positivism. These appeared before the publication of A.J. Ayer’s Language, Truth and Logic and helped shape the early British reception of logical positivism. I highlight Stebbing’s adoption of G.E. Moore’s tripartite distinction between knowing a proposition, understanding it, and giving an analysis of it and, in light of this distinction, her focus on whether the principle of verifiability can ground a plausible account of communication. Stebbing (...) thinks not, and I reconstruct her reasons, as well as her own account of communication. In doing this, I relate her criticisms to her rejection of methodological solipsism and her dissatisfaction with the logical positivist treatment of statements about other minds and the past. I also argue that Stebbing’s work provides a bridge to later criticisms of logical positivism from ordinary language philosophers. Foregrounding Stebbing’s engagement with logical positivism, especially her focus on communication, paints a fuller picture of how the logical positivists came to be part of analytic philosophy despite having different concerns than many of the British philosophers engaging their work. (shrink)

Semantic analysis in early analytic philosophy belongs to a long tradition of adopting geometrical methodologies to the solution of philosophical problems. In particular, it adapts Descartes’ development of formalization as a mechanism of analytic representation, for its application in natural language semantics. This article aims to trace the mathematical roots of Frege, Russel and Carnap’s analytic method. Special attention is paid to the formal character of modern analysis introduced by Descartes. The goal is to identify the particular conception of “form” (...) developed by the analytic tradition, from Descartes to early analytic philosophy, and to determine its relation to similar notions, like ‘function’ and ‘syntax’. Finally, I focus on how Frege, Russell and Carnap’s methods of semantic analysis fit the general characterization of formal analysis previously developed. (shrink)

Carnaps Werk zwischen den späten 1920er- und frühen 1930er-Jahren nimmt verschiedentlich auf Begrifflichkeiten und Debatten der philosophischen und experimentellen Psychologie seiner Zeit Bezug. Diese Bezugnahmen sind jedoch nicht immer konsistent oder explizit. Beispielsweise bedient Carnap sich sowohl im Aufbau als auch in seinen Ausführungen zur Psychologie in einer physikalischen Sprache einiger Grundannahmen der experimentellen Psychologie, führt dies jedoch nicht konsequent zu Ende. Umgekehrt sieht er seine Auffassungen zur Physikalisierung der psychologischen Sprache nicht zuletzt auch als potenzielles Korrektiv für die existierende (...) Psychologie seiner Zeit, was bei dem Gestaltpsychologen Carl Duncker auf Unverständnis stößt. In dem vorliegenden Aufsatz belege ich meine These von Carnaps spannungsvolle Verhältnis zur Psychologie und versuche, dieses Verhältnis historisch und systematisch einzuordnen. (shrink)

The history of the relationship between science and metaphysics is riddled with controversy. Aristotle and his followers see metaphysics as providing the foundations on which science and other human intellectual endeavors build. In opposition to the thoughts of Aristotle, Plato and his followers separate metaphysics from science as independent and unrelated sciences. With the Logical positivists, the debate is a reject of metaphysics in favour of science. Metaphysics then is seen as a pseudo-science. Rudolf Carnap's the "Elimination of Metaphysics through (...) the Logical Analysis of Language" and Alfred Jules Ayer's elimination of metaphysics from the domain of knowledge are examined, while Heidegger is brought in to salvage the situation given that he holds on to the superiority of metaphysics over science. (shrink)

I offer an interpretation of Carnap and Quine’s views on cognitive significance and insignificance. The basic idea behind their views is as follows: to judge an expression is insignificant is to recommend it not be used in or explicated into languages used to express truth-valued judgments in inquiry; to judge an expression is significant is to recommend it be used in or explicated into such languages. These judgments are pragmatic judgments, made in light of purposes for language use in inquiry. (...) For Carnap at least, these pragmatic judgments are non-cognitive. This basic idea is only a roughly correct statement of their views. This is because the details of the scientific languages they recommend for inquiry are necessary to understand their views and the way they understand their own views. Even so, I offer two reasons to suggest that this basic idea is worthy of our consideration today. First, it provides a conception of significance that captures the natural thought that epistemological concerns can lead us to consider expressions to be insignificant without requiring an objectionable form of verificationism. Second, if we appeal also to Carnap and Quine’s pluralistic attitude toward explication, we can make a pragmatic judgment that an expression is insignificant while judging it to be significant on a distinct explication of significance fit for describing and explaining natural language. (shrink)

Bilimi ve bilimsel bilgiyi kültür, değer ve öznel yargılardan izole ederek nesnel bir şekilde ortaya koyabilmeye yönelik hararetli tartışmaların yaşandığı yirminci yüzyıl bilim anlayışının temel gayesi, deney ve gözleme tabi olabilecek fiziki dünyadaki olguları, mantıksal çözümlemeye tabi tutarak birleştirilmiş bilime ulaşmaktır. Bu amaca giden yolda olgulara dayanmayan ve sınanamayan her türlü metafizik öge yok sayılır. Bilimsel bilginin sadece deney ve gözleme tabi olana, diğer bir deyişle olgu verilerine dayandığı iddiasını taşıyan bu düşünce sistemi, özellikle Viyana Çevresi üyeleri tarafından benimsenmiştir. Bu (...) bakımdan Çevre üyelerinin bilimsellik anlayışındaki temel ölçüt olgulara dayanan önermelerin ya da yargıların doğrulanabilmesidir. Bilimsel bilginin sadece olgusal dünyanın gözlemlenmesi ve bu gözlem sonucunda ortaya konulan önermelerin ya da ifadelerin doğrulanmasıyla sağlandığını düşünen Çevre üyelerinin bu savlarındaki amacı bilimi ve onun bilgisini her türlü kültür ve değer alanından uzaklaştırarak metafiziksel unsurlardan arındırılmış nesnel bilgiye ulaşmaktır. Çevre üyelerinin birçoğu bilim alanı içerisinde tartışmaya yol açan meselelerin aslında metafiziksel içerikli ve dolayısıyla bunların görünüşte problemler olduğunu belirterek bu tartışmaların bilimsel bilginin gelişimi önünde bir engel oluşturacağı kanaatindedir (Hızır, 1965, s. 254). Söz gelimi, Carnap’a göre, metafizik ögeler olgusal içeriğe sahip olmadığı ve sınanabilir nitelikte olmadıkları için bilim alanı içerisinde değerlendirilemez. Bu nedenle, metafizik ögeler hem doğrulanması mümkün olmadığı hem de dilin mantıksal dizimine genellikle uymadığı gerekçesiyle anlamsızdır (Öztürk, 2011, s. 155). Bu bakımdan Çevre üyelerine göre, olgulara dayanmayan ve bilimde yanılsamalara yol açan metafizik söylemler bilimden ayıklanmalı ve bilimsel bilgi ancak olgu ve deneye dayanan önermeler üzerinden yürütülmelidir. Öte yandan Çevre düşünürleri mantıksal çözümleme yoluyla olgulara dayanan önermelerin metafiziksel unsurlar içeren önermelerden ayırt edilebileceğini ifade etmiştir. Bu bağlamda metafizik önermeleri, metafizik olmayan önermelerden ayırt edecek ölçütün doğrulanabilirlik olduğunu savunurlar. Çevre üyelerinin bu tutumları bir bakıma bilim ve sözde bilim arasında ayrım yapma ve metafiziği bilimin dışında tutma çabası olarak da değerlendirilebilir (Kabadayı, 2011, s. 39-40). Yirminci yüzyıl bilim anlayışında bilimsel etkinlikte gözlemin ve gözlemi yürüten bilim insanlarının dolaysız öznel duyu verileriyle ilişkili olduğu bu nedenle gözlem verilerinin psikolojizmin etkisinde olduğu fikri ortaya atılır. Başta Neurath olmak üzere dönemin bilim felsefecileri bilimsel bilginin kültür, değer ve psikoloji gibi öznel unsurlardan uzaklaştığı sürece değerli olduğu kanısında olduğu için bu fikre karşı çıkmaktadır (Gillies, 2018, s. 123). Görüldüğü üzere, Çevre üyelerinin temel amacı metafizik önermelerden arındırılmış, olgulara dayanan bir bilime ulaşmaktır. Bu amacın gerçekleşmesine olanak sağlayacak yöntem ise mantıksal çözümlemedir. Bu bağlamda Çevre üyeleri olgulara dayanan ve doğrulanabilen önermelerin, söz dizimi (sentaks) ve anlamsal (semantik) açıdan incelemeye tabi tutulması gerektiğini düşünmektedir (Yardımcı, 2018, s. 13-15). Özellikle Carnap (1935, s. 9-10) doğrulamanın ancak öne sürülen önermenin mantıksal analize tabi tutularak yapılması gerektiğini iddia etmiştir (Irzık, 1962, s. 65). Bununla birlikte, felsefenin işlevi, önermeleri mantıksal analize tabi tutarak yalın hale getirmektir. İşte felsefenin bu yönü Neurath’da bilimin birliği, Carnap’ta ise bilimin sentaksı, yani bilimin mantığı üzerine çalışma anlamına gelir (Hızır, 1965, s. 252). Bilimi, bilim olmayandan ayırma yöntemi olarak kullanılan doğrulama işlemi, teorik bir söylem ve gözlem önermesi arasında yapılan bir işlem olması bakımından mantıksal ve dilsel bir özellik taşır. Buradaki temel sorun ise teorik bir önermenin gözlem önermelerine indirgenebilir nitelikte olması ve gözlem önermelerinin, gözlem ile nasıl ilişki kurduğunu saptamaktır. İşte Viyana Çevresi üyeleri bu ilişkinin protokol önermeleri ile kurulduğu kanaatindedir (Ural, 2012, s. 105-107) çünkü onlara göre; öznelerarası bir bilimin sağlanması için yansız ve anlam karmaşasından arındırılmış bir dil gereklidir (Serin, 2015, s. 55). Bu dil de ancak protokol önermeler aracılığıyla kurulabilir. Bu bağlamda Çevre üyelerinin, metafiziksel ifadeler barındıran önermelerin anlamsızlığı ve bilimleri ortak bir paydada birleştiren fiziksel bir dil oluşturma olmak üzere iki temel hedefinin olduğu söylenebilir (Godfrey-Smith, 2003, s. 25; Salgar, 2012, s. 187). (shrink)

This Open Access volume is based on the 'Early Carnap in Context’ workshop that took place in Konstanz in 2017 and looks at Rudolf Carnap’s philosophy, documented in his recently released diaries, from a combination of historical, cultural and philosophical perspectives. It enables further evaluation of the diaries and traces newly found interrelationships and their systematic definition. From a cultural and historical point of view, Logical Empiricism and Carnap’s pivotal opus, The Logical Structure of the World, did not evolve in (...) a vacuum. This applies equally in a history of philosophy context as well as under consideration of contemporary historical and cultural influences such as the socio-cultural setting in Vienna and Prague, the correlation between Logical Empiricism and Bauhaus modernism, the connection to the Life Reform Movement or the Youth Movement with its own life philosophy. Pursuing Carnap’s progression on a micro level of history and referring the results back to Carnap’s philosophy is now facilitated by recent access to his Diaries from 1908–1935. These shorthand records, reading lists, travel reports and notes constitute a valuable source for the research of networks and social movements which left their mark on him. (shrink)

In the late 1930s, a few years before the start of the Second World War, a small number of European philosophers of science emigrated to the United States, escaping the increasingly perilous situation on the continent. Among the first expatriates were Rudolf Carnap and Hans Reichenbach, arguably the most influential logical empiricists of their time. In this two-part paper, I reconstruct Carnap’s and Reichenbach’s surprisingly numerous interactions with American academics in the decades before their move in order to explain the (...) impact of their arrival in the late 1930s. This second part traces Reichenbach’s development and focuses on his frequent interactions with American academics throughout the 1930s. I show that Reichenbach was quite ignorant about developments in Anglophone philosophy in the first stages of his career but became increasingly focused on the United States from the late 1920s onwards. I reconstruct Reichenbach’s efforts to find a job across the Atlantic and show that some of his English publications—most notably Experience and Prediction—were attempts to change the American narrative about logical empiricism. Whereas U. S. philosophers identified scientific philosophy with the views of the Vienna Circle, Reichenbach aimed to market his probabilistic philosophy of science as a subtler alternative. (shrink)

In the years before the Second World War, Rudolf Carnap and Hans Reichenbach emigrated to the United States, escaping the quickly deteriorating political situation on the continent. Once in the U. S., the two significantly changed the American philosophical climate. This two-part paper reconstructs Carnap’s and Reichenbach’s surprisingly numerous interactions with American academics in the decades before their move in order to explain the impact of their arrival in the late 1930s. Building on archival material of several key players and (...) institutions, I take some first steps toward answering the question why logical empiricism became so successful in the United States after the War. This first part reconstructs Carnap’s development between 1923, when he first visited New York, and 1936, when he was offered a position at the University of Chicago. I describe Carnap’s first substantive contacts with American philosophers as well as the events leading up to his decision to emigrate. In addition, I argue that some of Carnap’s work from the mid-1930s—in particular “Testability and Meaning”—can be better understood if we take into account his attempts to correct the American narrative about logical positivism and his increasingly desperate efforts to find a position in the United States. (shrink)

Friedrich Nietzsche was among the figures from the history of nineteenth century philosophy that, perhaps surprisingly, some of the Vienna Circle’s members had presented as one of their predecessors. While, primarily for political reasons, most Anglophone figures in the history of analytic philosophy had taken a dim view of Nietzsche, the Vienna Circle’s leader Moritz Schlick admired and praised Nietzsche, rejecting what he saw as a misinterpretation of Nietzsche as a militarist or proto-fascist. Schlick, Frank, Neurath, and Carnap were in (...) different ways committed to the view that Nietzsche made a significant contribution to the overcoming of metaphysics. Some of these philosophers praised the intimate connection Nietzsche drew between his philosophical outlook and empirical studies in psychology and physiology. In his 1912 lectures on Nietzsche, Schlick maintained that Nietzsche overcame an initial Schopenhauerian metaphysical-artistic phase in his thinking, and subsequently remained a positivist until his last writings. Frank and Neurath made the weaker claim that Nietzsche contributed to the development of a positivistic or scientific conception of the world. Schlick and Frank took a further step in seeing the mature Nietzsche as an Enlightenment thinker. (shrink)

W. V. Quine’s first philosophical monograph, Word and Object, is widely recognized as one of the most influential books of twentieth century philosophy. Notes, letters, and draft manuscripts at the Quine Archives, however, reveal that Quine was already working on a philosophical book in the early 1940s; a project entitled Sign and Object. In this paper, I examine these and other unpublished documents and show that Sign and Object sheds new light on the evolution of Quine’s ideas. Where “Two Dogmas (...) of Empiricism” is usually considered to be a turning point in Quine’s development, this paper redefines the place of ‘Two Dogmas’ in his oeuvre. Not only does Quine’s book project reveal that his views were already fairly naturalistic in the early 1940s ; Sign and Object also unearths the steps Quine had to take in maturing his perspective; steps that will be traced in the second half of this paper. (shrink)

This paper gives a historical overview of the rise and fall of the Vienna Circle. It also explains its philosophical roots, methodological principles, the scientific world-conception it promoted, and how it influenced later generations of philosophers.

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which LTL has (...) helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

Working from Within: The Nature and Development of Quine's Naturalism. By Verhaegh Sander.

Due to their acceptance of the verifiability principle, the only way left for logical positivists to argue for the meaningfulness of religious language was to accept some sort of emotivistic conception of it or to reduce it to the description of religious attitude. The verifiability principle, however, suffers from some severe limitations that make it inadequate as a criterion for cognitive meaning. To resolve these problems, logical positivists gave up the requirement of conclusive verifiability and defended a sort of ‘liberalization’ (...) of the verifiability principle. Carnap’s confirmability criterion for cognitive meaning, which is a liberalized form of the verifiability principle, is compatible with an orthodox conception of religious language since, from a theistic perspective, the existence of God can be confirmed through our observational statements. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

Contemporary analytic philosophy is dominated by metaphilosophical naturalism, the view that philosophy ought to be continuous with science. This naturalistic turn is for a significant part due to the work of W. V. Quine. Yet, the development and the reception of Quine’s naturalism have never been systematically studied. In this paper, I examine Quine’s evolving naturalism as well as the reception of his views. Scrutinizing a large set of unpublished notes, correspondence, drafts, papers, and lectures as well as published responses (...) to Quine’s work, I show how both internal tensions and external criticisms forced him to continuously develop, rebrand, and refine his metaphilosophy before he explicitly decided to label his view ‘naturalism’ in the late 1960s. (shrink)

The main task in this paper is to detail and investigate Carnap’s conception of a “linguistic framework”. On this basis, we will see whether Carnap’s dichotomies, such as the analytic-synthetic distinction, are to be construed as absolute/fundamental dichotomies or merely as relative dichotomies. I argue for a novel interpretation of Carnap’s conception of a LF and, on that basis, will show that, according to Carnap, all the dichotomies to be discussed are relative dichotomies; they depend on conventional decisions concerning the (...) logical syntax of LF. Thus, all of the dichotomies directly hinge on the conception of the LF. The LF’s logical structure, in turn, is an immediate consequence of adopting the linguistic doctrine of logical truths. As we will see, no appeal to any of these distinctions is necessary in establishing a LF and all of its components. I will also draw attention to the differences between what Carnap labels a “way of speaking”, “language”, and “artificial language”. Consequently, I will briefly conclude that none of Quine’s major objections address the main points of Carnap’s theory. (shrink)

Marc Champagne argues that the supposedly ’professional’ style of the analytic tradition does not ensure professionalism, nor indeed, clear-mindedness.

Author's replies to an APA book symposium on "Carnap, Tarski, and Quine at Harvard.".

This paper takes up the challenge which Carnap poses in his Aufbau: to make of it a basis for continued epistemological research. I try to close some gaps in Carnap’s original presentation and to make at least the first few steps of his constructional outline more accessible to the modern reader. Particularly emphasized is Carnap’s implicit recognition that, to be effective, “structural” models of epistemology (using logical symbols) must be complemented with “procedural” models (his “fictitious operations”). The paper shows how (...) a procedural model, a computer program,can “bypass” Nelson Goodman’s counter example to Carnap’s logical construction of “similarity circles”. (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)