The aim of this paper is to present a topological method for constructing discretizations of topological conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. The aim of this paper is to show that Alexandroff spaces, as they are called today, have many interesting properties that can be used to explicate and clarify a variety of problems in philosophy, cognitive science, and related disciplines. For instance, recently, (...) Ian Rumfitt used a special type of Alexandroff spaces to elucidate the logic of vague concepts in a new way. Moreover, Rumfitt’s class of Alexandroff spaces can be shown to provide a natural topological semantics for Susanne Bobzien’s “logic of clearness”. Mainly due to the work of Peter Gärdenfors and his collaborators, conceptual spaces have become an increasingly popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy. For Gärdenfors’s conceptual spaces, geometrically defined discretizations play an essential role. These tessellations can be shown to be extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces in general. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. The main aim of this paper is to show that this class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Weakly scattered Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox. Further, they provide a semantics for the logic of clearness that overcomes certain problems of the concept of higher-order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The specialization order of Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and non-prototypical stimuli in favor of a gradual distinction between more or less prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem”. Finally, it is shown that the Alexandroff spaces offer an appropriate framework to deal with digital conceptual spaces that are gaining more and more importance in the areas of artificial intelligence, computer science and related disciplines. (shrink)

The main thesis of this paper is that Pap’s The Functional A Priori of Physical Theory (Pap 1946, henceforth FAP) and Cassirer’s Determinism and Indeterminism in Modern Physics (Cassirer 1937, henceforth DI) may be conceived as two kindred accounts of a late Neo-Kantian philosophy of science. They elucidate and clarify each other mutually by elaborating conceptual possibilities and pointing out affinities of neo-Kantian ideas with other currents of 20th century’s philosophy of science, namely, pragmatism, conventionalism, and logical empiricism. Taking into (...) account these facts, it seems not too far fetched to conjecture that under more favorable circumstances Pap could have served as a mediator between the “analytic” and “continental” tradition thereby overcoming the dogmatic dualism of these two philosophical currents that has characterized philosophy in the second half the 20th century. (shrink)

Abstract. Gettier’s famous examples intended to show that knowledge cannot always be equated with justified true belief. The Gettier problem can also be considered as a problem for topological epistemic logic: If knowledge and justified belief are conceived as topological operators K and B on topological spaces (to be considered as universes of possible worlds), one may ask whether it happens that there is a proposition A such that KA ≠ A & BA or not. If this is the case, (...) the epistemological logic defined by the topological operators K and B may be said to be non-traditional since there is for them a “Gettier proposition” where knowledge does not coincide with justified true belief. As far as we know, for the first time, this topological Gettier problem is discussed in Steinvold’s PhD dissertation (Steinsvold 2012). In Baltag, Bezhanishvili, Özgün, and Smets (2013), Steinvold’s co-derived set account is criticized since it can be easily “Gettierized”. Baltag et alii claim (without proof) that their topological account of Stalnaker’s logic KB of knowledge and belief does not have this flaw. In the following we will give some topological conditions that determine whether a topological KB model does or does not cope with the Gettier challenge. First, it will be shown that every KB model defines a (topologically slightly simplified) model that is rather similar to it but a is a model of traditional JTB (knowledge = justified true belief) logic of knowledge and belief. The existence of such doppelgangers of all KB models may be read as a qualified and partial topological rehabilitation of traditional JTB epistemology. Second, we consider the Gettier problem for a special class of models of Stalnaker’s combined logic of knowledge and belief KB, namely, for T0 Alexandroff spaces. We prove that, that almost all Alexandroff spaces do not face Gettier counterexamples. Third, we prove that the Stone spaces of Boolean algebras of regular closed subsets of Hausdorff (or T2) spaces X do not face Gettier counterexamples if the X are not pseu–docompact, and these Stone spaces do face Gettier counterexamples for compact spaces X. Succinctly formulated, Stalnaker’s KB logic of knowledge and belief can avoid Gettier problems for some models, while it falls back to traditional pre-Gettier JTB epistemology for other models. In contrast, co-derived set semantics is doomed to fail always in the sense that its models always fall prey to Gettier counterexamples. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models of knowledge (...) and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological reconstruction (...) of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...) main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity, and to exploit it in making sense of infinitesimals and related concepts. (shrink)

Abstract. In Dynamics of Reason Michael Friedman proposes a kind of synthesis between the neokantianism of Ernst Cassirer, the logical empiricism of Rudolf Carnap, and the historicism of Thomas Kuhn. Cassirer and Carnap are to take care of the Kantian legacy of modern philosophy of science, encapsulated in the concept of a relativized a priori and the globally rational or continuous evolution of scientific knowledge,while Kuhn´s role is to ensure that the historicist character of scientific knowledge is taken seriously. (...) More precisely, Carnapian linguistic frameworks, guarantee that the evolution of science procedes in a rational manner locally,while Cassirer’s concept of an internally defined conceptual convergence of empirical theories provides the means to maintain the global continuity of scientific reason. In this paper it is argued that Friedman’s neokantian account of scientific reason based on the concept of the relativized a priori underestimates the pragmatic aspects of the dynamics of scientific reason. To overcome this short-coming, I propose to reconsider C.I. Lewis’s account of a pragmatic the priori, recently modernized and elaborated by Hasok Chang. This may be<br><br><br><br><br><br><br><br><br><br&g t;<br><br><br><br><br><br>Keywords: Dynamics of reason, Paradigms, Logical Empiricism,Neokantianism, Pragmatism, Mathematics, Communicative Rationality. (shrink)

Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this paper are (...) defined with the help of the (dense) nuclei of the Heyting algebra OX of open subsets on the topological space (X, OX). In this way, the natural context for the belief operators B related to topological knowledge operator K is shown to be the Heyting algebra NUC(OX) of the nuclei of the Heyting algebra OX.1 More precisely, the dense nuclei of NUC(OX) can be used to define a variety of bimodal logics of knowledge operators K and belief operators B. The operators K and B are compatible with each other in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB system with the exception of the axiom (NI). Therefore, for (X, OX), one obtains a bounded, partially ordered family of belief operators B defined by the elements of NUC(OX). (shrink)

Nach gängiger Auffassung nahm das Thema „Werte” in Carnaps Philosophie nur einen geringen Stellenwert ein. In dieser Arbeit soll gezeigt werden, daß diese Einschätzung der Korrektur bedarf: So wird der im „Aufbau“ vorgetragene Entwurf eines Konstitutionssystems mit Werten als der höchsten Schicht des Konstitutionssystems abgeschlossen. Auch die Quasianalyse als allgemeine Konstitutionsmethode steht in enger Beziehung zur Unterscheidung zwischen „Sein“ und „Gelten“, die für den werttheoretisch orientierten Neukantianismus der südwest-deutschen Schule charakteristisch war. Allgemein erlaubt die Wertthematik einen Blick auf Unterströmungen des (...) carnapschen Denkens, die in den offiziellen logisch-empiristischen Darstellungen seines Denkens meist vernachlässigt werden. Die Wertthematik, so die These dieser Arbeit, eröffnet überdies eine neue Perspektive auf die spezifisch Jenaer Konstellation von Neukantianismus und Lebensphilosophie, die Carnaps Philosophie wesentlich geprägt hat. (shrink)

Der Antirepräsentationalismus behauptet, es sei an der Zeit, das auf dem Begriff der Repräsentation basierende Paradigma der Philosophie zu verabschieden. Die von Rorty und anderen propagierte Unterscheidung von Repräsentationalismus und Antirepräsentationalismus beruht jedoch auf einem verkürzten Repräsentationsbegriff als Spiegelung. Der Begriff der Repräsentation, so wie er in der Philosophie und Wissenschaft gebraucht wird, hat nur wenig mit Spiegelung zu tun. Statt den Begriff der Repräsentation mit Hilfe der Spiegelungsmetapher zu explizieren, sollte man Repräsentation als strukturerhaltende Abbildung konzipieren. Dadurch lassen sich (...) die für den Repräsentationsbegriff wesentlichen pragmatischen Aspekte der Reduktion und Induktion von Komplexität explizieren. Der Zusammenhang der gegenläufigen Aspekte Reduktion und Induktion wird an Beispielen aus der Konstitution extensiver Größen sowie an Cassirers Theorie der Konstitution von Erkenntnis und Wirklichkeit erörtert. Man sollte daher den Begriff der Repräsentation nicht aus dem philosophischen Diskurs eliminieren, sondern versuchen, die Ansätze einer allgemeinen pragmatischen Repräsentationstheorie auszubauen. (shrink)

The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the 20th century. More precisely, it is argued that the accounts of Helmholtz and Hertz may be taken as prototypes of representational accounts in which structure preservation plays an essential role. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date version of (...) a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach’s early theory of a relativized constitutive but non-apodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept of representation that conceived of a particular representation as only one phase in a continuous process determined by pragmatic considerations. Pragmatic aspects of representations are further elaborated in the classical account of C.I. Lewis and the more modern of Hasok Chang. (shrink)

Einführung in die Philosophie Rudolf Carnaps.

Quine’s classical classic interpretation succinctly characterized characterizes Carnap’s Aufbau as an attempt “to account for the external world as a logical construct of sense-data....” Consequently, “Russell” was characterized as the most important influence on the Aufbau. Those times have passed. Formulating a comprehensive and balanced interpretation of the Aufbau has turned out to be a difficult task and one that must take into account several disjointed sources. My thesis is that the core of the Aufbau rested on a problem that (...) had haunted German philosophy since the end of the 19th century. In terms fashionable at the time, this problem may be expressed as the polarity between Leben and Geist that characterized German philosophy during the years of the Weimar Republic. At that time, many philosophers, including Cassirer, Rickert and Vaihinger, were engaged in overcoming this polarity. As I will show, Carnap’s Aufbau joined the ranks of these projects. This suggests that Lebensphilosophie and Rickert’s System der Philosophie exerted a strong influence on Carnap’s projects, an influence that is particularly conspicuous in his unpublished manuscript Vom Chaos zur Wirklichkeit. Carnap himself asserted that this manuscript could be considered “the germ of the constitution theory” of the Aufbau. Reading Chaos also reveals another strong but neglected influence on the Aufbau, namely a specific version of neutral monism put forward by the philosopher and psychologist Theodor Ziehen before World War I. Ziehen’s work contributed much to the invention of the constitutional method of quasi-analysis. -/-. (shrink)

The global relation between logical empiricism and American pragmatism is one of the more difficult problems in history of philosophy. In this paper I’d like to take a local perspective and concentrate on the details that concern the vicissitudes of a philosopher who played an important role in the encounter of logical empiricism and American pragmatism, namely, Ernest Nagel. In this paper, I want to explore some aspects of Nagel’s changing attitude towards the then „new“ logical-empiricist philosophy. In the beginning (...) Nagel welcomed logical empiricism whole-heartedly. This early enthusiasm did not last. At the end of his philosophical career Nagel’s early positive attitude towards logical empiricism shown in the 1930s had been replaced by a much more reserved one. Nagel’s growing dissatisfaction with the Carnapian version of logical empiricist philosophy was clearly expressed in Nagel’s criticism of Carnap’s inductive logic and more generally in his last book Teleology Revisited and Other Essays on History and Philosophy of Science. There he critized harshly Carnap’s philosophy of science in general as ahistoric and non-pragmatist. One of the distinctive features of Nagel’s philosophy of science is the emphasis that he put on the role of history of science for philosophy of science. A compelling evidence for this attitude are his works on the history and philosophy of geometry and algebra One may say that Carnap and Nagel represented opposed possibilities of how the profession of a philosopher of science could be understood: Carnap as a „conceptual engineer“ was engaged in the task of inventing the conceptual tools for a better theoretical understanding of science, while Nagel was to be considered more as a „public intellectual“ engaged in the project of realizing a more rational and enlightened society. (shrink)

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be useful (...) in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

In this paper some classical representational ideas of Hertz and Duhem are used to show how the dichotomy between representation and intervention can be overcome. More precisely, scientific theories are reconstructed as complex networks of intervening representations (or representational interventions). The formal apparatus developed is applied to elucidate various theoretical and practical aspects of the in vivo/in vitro problem of biochemistry. Moreover, adjoint situations (Galois connections) are used to explain the relation berween empirical facts and theoretical laws in a new (...) way. (shrink)

The aim of this paper is to discuss the “Austro-American” logical empiricism proposed by physicist and philosopher Philipp Frank, particularly his interpretation of Carnap’s Aufbau, which he considered the charter of logical empiricism as a scientific world conception. According to Frank, the Aufbau was to be read as an integration of the ideas of Mach and Poincaré, leading eventually to a pragmatism quite similar to that of the American pragmatist William James. Relying on this peculiar interpretation, Frank intended to bring (...) about a rapprochement between the logical empiricism of the Vienna Circle in exile and American pragmatism. In the course of this project, in the last years of his career, Frank outlined a comprehensive, socially engaged philosophy of science that could serve as a “link between science and philosophy”. (shrink)

A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between both. For the elucidation of this “knowledge relation ("Erkenntnisrelation") the Neokantians of the Marburg school used a variety of mathematical metaphors. In this con-tribution I reconsider some of these metaphors proposed by Paul Natorp, who was one of the leading members of the Marburg school. It is shown that Natorp's (...) metaphors are not unrelated to those used in some currents of contemporary epistemology and philosophy of science. (shrink)

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this endeavor (...) can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

Bis heute wird Russells Philosophie nicht selten der Vorwurf gemacht, es fehle ihr an Kohärenz und Zusammenhang. Russell wird als ein Autor charakterisiert, der alle paar Jahre eine neue alternative Philosophie vorgeschlagen habe. In der vorliegenden Arbeit soll dagegen argumentiert werden, daß diese These auf einer zu oberflächlichen Ein–schätzung von Russells Denken beruht. Seine Philosophie verfügte sehr wohl über eine Einheit, die durch ihre charakteristische einheitsstiftende Methode vermittelt wurde. Dies war die Methode der logischen Analyse, die sich als Invariante in (...) allen Phasen seines Denkens durchhielt. Die logische Analyse erlaubte es, die in gegebenen Sach–verhalten enthaltenen Möglichkeiten zu explizieren. Philosophie wurde damit für Russell zu einer “Möglichkeitswissenschaft”. (shrink)

Die Physikalisierung der Psychologie war für Carnap Teil eines Programms, das die Sonderstellung der Psychologie als Wissenschaft des menschlichen Denkens und Fühlens als Illusion entlarven und zeigen sollte, die Psychologie sei ein Teil der Physik wie alle anderen Wissenschaften auch. In etwas anderer Motivation zielte Carnaps Physikalismus ausserdem auf eine Überwindung der Trennung von Geistes–wissenschaften und Naturwissenschaften: Erwiese sich die Psychologie sich als physikalisierbar, wäre das ein wesentlicher Schritt für die Vereinheitlichung der Wissenschaften in Gestalt einer enzyklopädischen „Einheitswissenschaft“ überhaupt. Carnaps (...) Argument für die Physikalisierbarkeit der Psychologie als ganzer basierte auf der These der Physikalisierbarkeit der Graphologie als zentraler Teildisziplin der Psychologie. Die Graphologie sei der begrifflich am weitesten fortgeschrittene und deshalb am ehesten physikalisierbare Teil der Psychologie. Das verdanke sie in erster Linie den wegweisenden Arbeiten Ludwig Klages’. Erweise sich die Graphologie als physikalisierbar, stehe einer durchgehenden Physikalisierung aller Wissenschaften nichts mehr im Wege. Als Episode in Carnaps philosophischer Entwicklung ist dem Graphologieprojekt bis heute kaum Aufmerksamkeit geschenkt worden. Das ist ein Versäumnis, manifestiert sich in diesem Projekt doch der allgemeine Stil des Carnapschen Philosophierens besonders deutlich, nämlich von einer sehr abstrakten und idealisierten Vorstellung von Wissenschaft ausgehend weitreichende philosophische Folgerungen zu ziehen. (shrink)

Carnap and Twentieth-Century Thought: Explication as En lighten ment is the first book in the English language that seeks to place Carnap's philosophy in a broad cultural, political and intellectual context. According to the author, Carnap synthesized many different cur rents of thought and thereby arrived at a novel philosophical perspective that remains strik ing ly relevant today. Whether the reader agrees with Carus's bold theses on Carnap's place in the landscape of twentieth-century philosophy, and his even bolder claims concerning (...) the role that philosophy in Carnap's style should play in the thought of our century, does not matter so much as the excellent opportunity Carus's book offers to thoroughly rethink one's ideas about Carnap's philosophy. One reason why Carnap and Twentieth-Century Thought might change one's ideas is that Carus has unearthed much hitherto unknown material from the archives that sheds new light on Carnap's early life and thought. Indeed, the many archival findings presented in CTT for the first time suffice to make the book re warding reading for philosophers and historians of philosophy alike. CTT exhibits a high standard of historical scholarship, and the book itself is a beautiful example of high-quality academic publishing. Up to now, Carnap has remained a controversial figure on the philo sophical scene. On the one hand, he has a solid reputation as a leading figure of logical positivism . According to conventional wisdom, this was a school of thought characterized by its formal and technical philosophy, as well as being rather dismissive of other ways of doing philosophy, dogmatically sticking to its own theses. As a typical example of this arrogant logical empiricist attitude, one usually refers to Carnap's notorious Overcoming Metaphysics by Logical Analysis of Language , written when the Vienna Circle's Logical Empiricism had entered its most radical phase. Self-proclaimed postpositivist philosophers of science dismissed logical positivism, in particular Carnap's, as the dogmatic and orthodox “received view.” The tendency to portray logical empiricism as an obsolete doctrine centering around certain “dogmas” started with Quine's Two Dogmas of Empiricism and reached its somewhat ridiculous culmination in the early 1980s when allegedly “six or seven dogmas” were discovered . Thereby an allegedly un brid geable gap between classical “dogmatic” logical em pi ricism and its modern “enlightened” suc ces sors was construed. (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)

In Anglo-Saxon philosophy of science there is strong conviction that idealist philosophy of science on the the one hand and serious science and philosophy of science on the other do not go well together. In this paper I argue that this sweeping dismissal of the idealist tradition may have been too hasty. They may be some valuable insights for which it is striving. A promising case in question is provided by Ernst Cassirer’s Neo-Kantian „Critical Idealism“ that he put forward in (...) the first decades of the past century, or so I’d like to argue. (shrink)

The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many empirical (...) sciences can hardly be denied. The aim of this paper is to show that Quine’s and Goodman’s harsh verdicts about this notion are mistaken. The concept of similarity is susceptible to a precise logico-mathematical analysis through which its place in the conceptual landscape of modern mathematical theories such as order theory, topology, and graph theory becomes visible. Thereby it can be shown that a quasi-analysis of a similarity structure S can be conceived of as a sheaf (etale space) over S. (shrink)

In this paper I want to show that topology has a bearing on the theory of tropes. More precisely, I propose a topological ontology of tropes. This is to be understood as follows: trope ontology is a „one-category”-ontology countenancing only one kind of basic entities, to wit, tropes. 1 Hence, individuals, properties, relations, etc. are to be constructed from tropes.

Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from the central position it (...) used to have in philosophy of science and placed logic at center stage in the 20th century philosophy of science. Only in recent decades logic has begun to loose its monopoly and geometry and topology received a new chance to find a place in philosophy of science. (shrink)

According to general wisdom, Carnap's quasianalysis is an ingenious but definitively flawed approach to epistemology and philosophy of science. I argue that this assessment is mistaken. Rather, Carnapian quasianalysis can be reconstructed as a special case of a general theory of structural representation. This enables us to exploit some interesting analogies of quasianalysis with the representational theory of measurement. It is shown how Goodman's well-known objections against the quasianalytical approach may be defused in the new framework. As an application, I (...) sketch how the thesis of empirical underdetermination of theories may be elucidated in the framework of quasianalysis. (shrink)