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The main thesis of this paper is that Pap’sThe Functional A PrioriinPhysical Theoryand Cassirer’sDeterminism and Indeterminism in Modern Physicsmay 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.

The aim of this paper is to present a topological method for constructing discretizations (tessellations) 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 Gardenfors 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 Gardenfors’s conceptual spaces, geometrically defined discretizations (so-called Voronoi tessellations) 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 Gardenfors’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 (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) 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.

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 Gardenfors’ 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.

ZusammenfassungDie Physikalisierung der Psychologie war für Carnap Teil eines Programms, das die Sonderstellung der Psychologie als Wissenschaft desmenschlichenDenkens 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 derGrafologieals zentraler Teildisziplin der Psychologie. Die Grafologie 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 Grafologie als physikalisierbar, stehe einer durchgehenden PhysikalisierungallerWissenschaften nichts mehr im Wege.Als Episode in Carnaps philosophischer Entwicklung ist dem Grafologieprojekt 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.

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein., 10 pages, published in Journal of Humanistic Mathematics http://scholarship.claremont.edu/jhm/vol8/iss1/7/

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 for runner 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.

We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of mathematical techniques in the sciences, and introduce a distinction between techniques that are applicable and those that are merely instrumental. Unfortunately the authors have not shown that their distinction is a clear and fruitful one, as the examples they provide are superficial and unconvincing. Moreover, their analysis is vitiated by a reliance on a naive version of object realism which has long been abandoned by most philosophical realists in favor of truth-value realism. ET's argument against the applicability of hyperreals based on automorphisms of hyperreal models involves massaging the evidence and is similarly unconvincing. The purpose of the ET text is to argue that Robinson's infinitesimal analysis is merely instrumental rather than applicable. Yet in spite of Robinson's techniques being applied in physics, probability, and economics, ET don't bother to provide a meaningful analysis of even a single case in which these techniques are used. Instead, ET produce page after page of speculations mainly imitating Connesian chimera-type arguments `from first principles' against Robinson. In an earlier paper Easwaran endorsed real applicability of the sigma-additivity of measures, whereas the ET text rejects real applicability of the axiom of choice, voicing a preference for ZF. Since it is consistent with ZF that the Lebesgue measure is not sigma-additive, Easwaran is thereby walking back his earlier endorsement. We note a related inaccuracy in the textbook Measure Theory by Paul Halmos., 41 pages, published in Mat. Stud

Die Philosophen Nietzsche, Schopenhauer und Schlick in einem Atemzug zu nennen, mag auf den ersten Blick seltsam erscheinen. Zwar ist die Beziehung zwischen Schopenhauer und Nietzsche ein gangiges Thema der Philosophiegeschichtsschreibung was aber hat Schlick damit zu tun? Die Vermutung liegt nahe, es gabe keine relevanten Bezuge zwischen Schlick auf der einen und Nietzsche und Schopenhauer auf der anderen Seite. Der von Mathias Iven im Rahmen der Moritz Schlick Gesamtausgabe (MSGA) herausgegebene und eingeleitete Band Nietzsche und Schopenhauer (Vorlesungen) (im Folgenden (V)) belegt, dass diese Vermutung unzutreffend ist: Schlick hat Nietzsche und Schopenhauer nicht nur gelesen, diese Lekture hatte auch einen nicht unerheblichen Einfluss auf seine Philosophie. Wie Schlicks Tochter Barbara in ihren Erinnerungen berichtet, zahlte Nietzsche fur Schlick zur Gruppe der ‘‘great men’’ wie Planck, Einstein oder Wittgenstein, denen er grosse Bewunderung, wenn nicht gar emphatische Verehrung entgegenbrachte. Bevor ich auf den Inhalt von (V) im Einzelnen eingehe, sei vorausgeschickt, dass Mathias Iven als Herausgeber eine in jeder Hinsicht exzellente Arbeit geleistet hat. Sowohl seine ausfuhrliche und kenntnisreiche Einleitung wie auch die sorgfaltige Edition des Manuskriptes selbst, die zahlreiche Varianten akribisch berucksichtigt, setzt Masstabe fur jede kritische Edition philosophischer Klassiker des 20. Jahrhunderts. (V) zeigt Schlick als Mitglied einer langen Reihe namhafter Philosophen, Soziologen, Intellektueller und Literaten des fruhen 20. Jahrhunderts, die Nietzsches Werk entscheidende Impulse verdanken—man denke etwa an Thomas und Heinrich Mann, Rilke, Benn, oder an Soziologen wie Simmel, Tonnies und Max Weber. Was die Philosophen betrifft, sei nur daran erinnert, dass Nietzsches zentraler Begriff des ‘‘Willens zur Macht’’

Die Wissenschaftsphilosophie als eigenstandige philosophische Disziplin ist relativ jung. Ohne Anspruch auf Genauigkeit lassen sich ihre Anfange auf das letzte Drittel des 19. Jahrhunderts datieren. Einen in der zeitgenossischen Diskussion lange vergessenen Ansatz der fruhen Wissenschaftsphilosophie bilden die verschiedenen Stromungen des Neukantianismus, der bis in die ersten Jahrzehnte des 20. Jahrhunderts in Deutschland eine dominierende Rolle spielte.

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 toward 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 ...

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. Keywords: First order logic; infinitesimal calculus; ontology; procedures; Leibniz; Weierstrass; Abraham Robinson, 22 pages, to appear in Foundations of Science

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 the 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 proceeds 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 shortcoming, I propose to reconsider C.I. Lewis’s account of a pragmatic priori, recently modernized and elaborated by Hasok Chang. This may be considered as a first step to a dynamics of an embodied reason, less theoretical and more concrete than Friedman’s Neokantian proposal.

In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator.

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological composition. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail.

Álvaro Peláez Cedrés, Breve introducción al pensamiento de Carnap, Universidad Autónoma Metropolitana, México, 2008, 235 pp.

In this paper some classical representational ideas of Hertz and Duhem are used to show how the di- chotomy 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 re- lation between empirical facts and theoretical laws in a new way.

Quine’s classic interpretation succinctly characterized 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.

Zusammenfassung Einer der institutionellen Hohepunkte in der Begegnung von osterreichischer „wissenschaftlicher Philosophie“ und franzosischer „Philosophie scientifique“ in der ersten Halfte des 20. Jahrhunderts war der „Erste Internationale Kongress fur Einheit der Wissenschaft“, der im September 1935 in Paris stattfand. In meinem Beitrag geht es um eine Episode dieses philosophischen Grosereignisses, deren Protagonist der amerikanische Philosoph und Semiotiker Charles William Morris war. Auf dem Kongress prasentierte er sein Programm einer umfassenden praxisorientierten wissenschaftlichen Philosophie, das er 1937 in Logical Positivism, Pragmatism and Scientific Empiricism (Charles W. Morris, „Logical Positivism, Pragmatism and Scientific Empiricism“, in: Exposes de Philosophie Scientifique 449, Paris: Hermann 1937) ausarbeitete. Morris zielte auf eine Synthese von Formalismus, Pragmatismus und traditionellem Empirismus, welche die Vorteile dieser Ansatze bundeln und ihre Einseitigkeiten und Unzulanglichkeiten vermeiden sollte. Der Kern seines Ansatzes war eine umfassende Theorie des Bedeutungsbegriffes. Vom Begriff der Bedeutung aus wollte er die vorhandenen Differenzen und die Moglichkeiten eines zukunftigen Zusammengehens von logischem Empirismus und Pragmatismus analysieren. Gegen das zu enge logisch-empiristische Verstandnis von Philosophie als Syntax der Wissenschaftssprache pladierte Morris fur einen „wissenschaftlichen Pragmatismus“, der vier Ebenen umfasste, namlich (1) Philosophie als Wissenschaftslogik (Carnap), (2) Philosophie als Bedeutungsklarung (Peirce), (3) Philosophie als empirische Wertlehre (Dewey), und (4)Philosophie als empirische Kosmologie (Whitehead).

The notion of idealization has received considerable attention in contemporary philosophy of science but less in philosophy of mathematics. An exception was the ‘critical idealism’ of the neo-Kantian philosopher Ernst Cassirer. According to Cassirer the methodology of idealization plays a central role for mathematics and empirical science. In this paper it is argued that Cassirer's contributions in this area still deserve to be taken into account in the current debates in philosophy of mathematics.

Value judgments are meaningless. This thesis was one of the notorious tenets of Carnap’s mature logical empiricism. Less well known is the fact that in the Aufbau values were considered as philosophically respectable entities that could be constituted from value experiences. About 1930, however, values and value judgments were banished to the realm of meaningless metaphysics, and Carnap came to endorse a strict emotivism. The aim of this paper is to shed light on the question why Carnap abandoned his originally positive attitude concerning values. It is argued that his non-cognitivist attitude was the symptom of a deep-rooted and never properly dissolved tension between conflicting inclinations towards Neokantianism and Lebensphilosophie. In America Carnap’s non-cognitivism became a major obstacle for a closer collaboration between logical empiricists and American pragmatists. Carnap’s persisting adherence to the dualism of practical life and theoretical science was the ultimate reason why he could not accept Morris’s and Kaplan’s pragmatist theses that cognitivism might well be compatible with a logical and empiricist scientific philosophy.

Wahrend der Weimarer Republik war Cassirer einer der fuhrenden Philosophen und offentlichen Intellektuellen Deutschlands. Zu dem weitgespannten Netz von Kontakten, das er seit den ersten Jahrzehnten des 20. Jahrhunderts mit Literaten, Kunstlern, Wissenschaftlern und Philosophen geknupft hatte, gehorten auch Mitglieder des Wiener Kreises und der Gruppe um Hans Reichenbach in Berlin. Aus diesen Verbindungen resultierten eine Reihe von Diskussionen und intellektuellen Auseinandersetzungen, von denen in der Wissenschaftsphilosophie am wohl Cassirers Debatten mit Schlick und Reichenbach uber Einsteins Relativitatstheorien und das Verhaltnis von empiristischer und neukantianischer Wissenschaftsphilosophie in den fruhen zwanziger Jahren am bekanntesten geworden sind (Friedman 1999; Ryckman 2005). Tatsachlich umfaste Cassirers kritische Rezeption der Philosophie des Wiener Kreises ein viel weiteres Spektrum.

Es gilt als ausgemacht, dag3 die Logischen Empiristen des Wiener Kreises mit Ethik wenig im Sinn hatten. Aussagen iiber ethische Sachverhalte hielten sie fur kognitiv bedeutungslos, und Werte waren Artefakte einer abstrusen Metaphysik. Eine wissenschaftlich akzeptable Beschaftigung mit ethischen Problemen kam fur sie hochstens als Metaethik in Frage. Schaut man genauer hin, liegen die Dinge vielleicht nicht ganz so klar, aber zumindest fur einen exemplarischen Logischen Empiristen wie Rudolf Carnap scheint zu gelten, seine Beschiftigung mit Problemen der Ethik habe sich auf eher beilaufige Bemerkungen zur Metaethik beschrinkt. Bei naherem Besehen erweist sich jedoch der Stellenwert des Themas ,,Werte" in Carnaps Philosophie als nicht so unbedeutend wie es zunachst den An schein hat

Carnap’s Metrical Conventionalism versus Differential Topology Abstract . Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincare 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 clas--sical 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.

Resume Depuis l'ekpoque du Cercle de Vienne on consiere l'explication en tant que tâche centrale de la philosophie analytique. Cependant il n'y a pas unanimite autour de la comprehension du concept d'explication. Dans cet article nous suggerons, tout en suivant Bachelard, de considerer une explication d'un concept en tant que sa generalisation propre dans le cadre d'une theorie explicative. Nous examinons notre approche en envisageant l'explication des concepts logiques («mplication»), mathematiques («ombre» et «ligne droite») et de la philosophie des sciences («reduction»).

Science and Technology Studies (STS) generally assume that the traditional philosophy of science has nothing valuable to contribute to the question of what science might mean for humankind in the 21st century. In particular, logical empiricism is considered obsolete. But this assessment is mistaken. In contrast to received views, the logical empiricism of the Vienna Circle showed a vigorous interest in political and social issues such as education, technology, and art. The Vienna Circle considered itself part and parcel of a general modernist movement promoting a thorough-going modernization of philosophy, science, and society. In the case of the philosopher and scientist Otto Neurath (1882–1945), there are important points of contact between Vienna Circle logical empiricism and STS. Many of the difficulties with which STS is confronted today correspond to those faced by the logical empiricists, including questions of interdisciplinarity, tensions between ‘academic’ and ‘activist’ factions, and the difficulties of finding a way between the diverging requirements of ‘objective’ science and ‘engaged’ politics.