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Thomas Mormann
University of the Basque Country
  1. Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  2. Infinitesimals as an Issue of Neo-Kantian Philosophy of Science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.
    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 (...)
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  3. A Place for Pragmatism in the Dynamics of Reason?Thomas Mormann - 2012 - Studies in History and Philosophy of Science Part A 43 (1):27-37.
    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 (...)
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  4. Topological Models of Columnar Vagueness.Thomas Mormann - 2020 - Erkenntnis:1-24.
    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 (...)
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  5. Zur Mathematischen Wissenschaftsphilosophie des Marburger Neukantianismus.Thomas Mormann - 2018 - In Christian Damböck (ed.), Philosophie und Wissenschaft bei Hermann Cohen, Veröffentlichungen des Instituts Wiener Kreis, Bd. 28. Wien: Springer. pp. 101 - 133.
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  6. Werte bei Carnap.Thomas Mormann - 2006 - Zeitschrift für Philosophische Forschung 62 (2):169 - 189.
    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 (...)
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  7. What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel.Vladimir Kanovei, K. Katz, M. Katz & Thomas Mormann - 2018 - Journal of Humanistic Mathematics 8 (1):108 - 119.
    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.
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  8. Trope Sheaves. A Topological Ontology of Tropes.Thomas Mormann - 1995 - Logic and Logical Philosophy of Science 3:129-150.
    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.
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  9. The Structure of Scientific Theories in Logical Empiricism.Thomas Mormann - 2007 - In A. Richardson & T. Uebel (eds.), The Cambridge Companion to Logical Empiricism. Cambridge University Press.
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  10. Philipp Frank’s Austro-American Logical Empiricism.Thomas Mormann - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1): 56 - 86.
    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 (...)
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  11. Morris’ Pariser Programm einer wissenschaftlichen Philosophie.Thomas Mormann - 2016 - In Christian Bonnet & Elisabeth Nemeth (eds.), Wissenschaft und Praxis. Zur Wissenschaftsphilosophie in Österreich und Frankreich in der ersten Hälfte des 20. Jahrhunderts. Springer. pp. 73 - 88.
    Abstract: One of the institutional highlights of the encounter between Austrian “wissen¬schaftliche Philosophie” and French “philosophie scientifique” in the first half of the 20th century was the “First International Congress for Unity of Science” that took place 1935 in Paris. In my contribution I deal with an episode of the philosophical mega-event whose protagonist was the American philosopher and semiotician Charles William Morris. At the Paris congress he presented his programme of a comprehensive, practice-oriented scientific philosophy and, in a more (...)
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  12. Topology as an Issue for History of Philosophy of Science.Thomas Mormann - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer. pp. 423--434.
    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 (...)
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  13. Geometrical Leitmotifs in Carnap’s Early Philosophy.Thomas Mormann - 2007 - In Richard Creath & Michael Friedman (eds.), Cambridge Companion to Rudolf Carnap. Cambridge University Press.
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  14. Scientific Theories as Intervening Representations.Thomas Mormann & Andoni Ibarra - 2006 - Theoria 21 (1):21-38.
    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 (...)
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  15. Rudolf Carnap.Thomas Mormann - 2000 - C.H. Beck.
    Einführung in die Philosophie Rudolf Carnaps.
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  16. Set Theory, Topology, and the Possibility of Junky Worlds.Thomas Mormann - 2014 - Notre Dame Journal of Formal Logic 55 (1): 79 - 90.
    A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...)
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  17. Continuous Lattices and Whiteheadian Theory of Space.Thomas Mormann - 1998 - Logic and Logical Philosophy 6:35 - 54.
    In this paper a solution of Whitehead’s problem is presented: Starting with a purely mereological system of regions a topological space is constructed such that the class of regions is isomorphic to the Boolean lattice of regular open sets of that space. This construction may be considered as a generalized completion in analogy to the well-known Dedekind completion of the rational numbers yielding the real numbers . The argument of the paper relies on the theories of continuous lattices and “pointless” (...)
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  18. Carnap's Boundless Ocean of Unlimited Possibilities : Between Enlightenment and Romanticism.Thomas Mormann - 2012 - In Pierre Wagner (ed.), Carnap's Ideal of Explication and Naturalism. Palgrave-Macmillan.
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  19. History of Philosophy of Science as Philosophy of Science by Other Means.Thomas Mormann - 2010 - In F. Stadler, D. Dieks, W. Gonzales, S. Hartmann, T. Uebel & M. Weber (eds.), The Present Situation in the Philosophy of Science. Springer. pp. 29--39.
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  20. Is Leibnizian Calculus Embeddable in First Order Logic?Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry - 2017 - Foundations of Science 22 (4):73 - 88.
    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 pro- cedural 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 (...)
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  21. A Virtual Debate in Exile: Cassirer and the Vienna Circle After 1933.Thomas Mormann - 2012 - Vienna Circle Institute Yearbook 16:149 - 167.
    Ernst Cassirer, 2011, Symbolische Prägnanz, Ausdrucksphänomen und „Wiener Kreis“, Nachgelassene Manuskripte und Texte, vol. 4, ed. Christian Möckel, 478pp., Hamburg, Felix Meiner Verlag.
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  22. Toward a Theory of the Pragmatic A Priori. From Carnap to Lewis and Beyond.Thomas Mormann - 2012 - Rudolf Carnap and the Legacy of Logical Empiricism 16:113 - 132.
    The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. (...)
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  23. Carnap's Aufbau in the Weimar Context.Thomas Mormann - 2016 - Vienna Circle Institute Yearbook 18:115-136.
    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 (...)
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  24. A Representational Reconstruction of Carnap’s Quasianalysis.Thomas Mormann - 1994 - PSA 1994 1:96 - 103.
    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 (...)
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  25. Zwischen Weisheit und Wissenschaft - Schlicks weites philosophisches Spektrum.Thomas Mormann - 2010 - Grazer Philosophische Studien 80 (1):263 - 285.
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  26. Wien Und München: Zwei Stationen der Deutschsprachigen Wissenschaftsphilosophie Im 20. Jahrhundert.Thomas Mormann - 2010 - In Friedrich Stadler (ed.), Vertreibung, Transformation und Rückkehr der Wissenschaftstheorie. Am Beispiel von Rudolf Carnap und Wolfgang Stegmüller. Lit Verlag.
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  27. From Mathematics to Quantum Mechanics - On the Conceptual Unity of Cassirer’s Philosophy of Science.Thomas Mormann - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 31-64.
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  28. Wertphilosophische Abschweifungen Eines Logischen Empiristen: Der Fall Carnap.Thomas Mormann - 2010 - In Anne Siegetsleitner (ed.), Logischer Empirismus, Werte und Moral: eine Neubewertung. Springer.
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  29. Updating Classical Mereology.Thomas Mormann - 2009 - In C. Glymour, D. Westerstahl & W. Wang (eds.), Logic, Methodology and Philosophy of Science. Proceedings of the 13th International Congress. King’s College.
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  30. Synthetic Geometry and Aufbau.Thomas Mormann - 2003 - In Thomas Bonk (ed.), Language, Truth and Knowledge. Kluwer Academic Publishers. pp. 45--64.
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  31. Heyting Mereology as a Framework for Spatial Reasoning.Thomas Mormann - 2013 - Axiomathes 23 (1):137- 164.
    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 (...)
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  32. Topological Representations of Mereological Systems.Thomas Mormann - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 76:463 -486.
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  33. Mathematical Metaphors in Natorp’s Neo-Kantian Epistemology and Philosophy of Science.Thomas Mormann - 2005 - In Falk Seeger, Johannes Lenard & Michael H. G. Hoffmann (eds.), Activity and Sign. Grounding Mathematical Education. Springer.
    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 (...)
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  34. On the Vicissitudes of Idealism in Philosophy of Science: The Case of Cassirer's 'Critical Idealism'.Thomas Mormann - 2014 - Lectiones Et Acroases Philosophicae (1).
    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 (...)
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  35. Description, Construction and Representation. From Russell and Carnap to Stone.Thomas Mormann - 2006 - In Guido Imagire & Christine Schneider (eds.), Untersuchungen zur Ontologie.
    The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be <br>considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers of (...)
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  36. Truthlikeness for Theories on Countable Languages.Thomas Mormann - 2006 - In Ian Jarvie, Karl Milford & David Miller (eds.), Karl Popper: A Centenary Assessment vol. 3.
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  37. Similarity and Continuous Quality Distributions.Thomas Mormann - 1996 - The Monist 79 (1):76--88.
    In the philosophy of the analytical tradition, set theory and formal logic are familiar formal tools. I think there is no deep reason why the philosopher’s tool kit should be restricted to just these theories. It might well be the case—to generalize a dictum of Suppes concerning philosophy of science—that the appropriate formal device for doing philosophy is mathematics in general; it may be set theory, algebra, topology, or any other realm of mathematics. In this paper I want to employ (...)
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  38. Enlightenment and Formal Romanticism - Carnap’s Account of Philosophy as Explication.Thomas Mormann - 2010 - Vienna Circle Institute Yearbook 14:263 - 329.
    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 (...)
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  39. A Quasi-Analytical Constitution of Physical Space.Thomas Mormann - 2004 - In Carsten Klein & Steven Awodey (eds.), Carnap Brought Home - The View from Jena. Open Court.
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  40. Counterfactual Deformation and Idealization in a Structuralist Framework.Andoni Ibarra & Thomas Mormann - 1994 - Poznan Studies in the Philosophy of the Sciences and the Humanities 42:81 - 93.
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  41. Appropriating Kuhn’s Philosophical Legacy. Three Attempts: Logical Empiricism, Structuralism, and Neokantianism.Andoni Ibarra & Thomas Mormann - 2010 - Cadernos de Filosofia Das Ciencias 8:65 - 102.
    In this paper we discuss three examples of the appropriation of Kuhn’s ideas in philosophy of science. First we deal with classical logical empiricism. Perhaps somewhat surprisingly, the arch-logical empiricist Carnap considered Kuhn’s socio-historical account as a useful complementation, and not as a threat of the philosophy of science of logical empiricism. As a second example we consider the attempt of the so-called struc- turalist philosophy of science to provide a “rational reconstruction” of Kuhn’s approach. Finally, we will deal with (...)
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  42. Frank’s Austrian Reading of the Aufbau.Thomas Mormann - manuscript
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  43. Between Heidelberg and Marburg: On the Aufbau’s Neokantian Origins and the AP/CP-Divide.Thomas Mormann - 2006 - Sapere Aude! 1:22 - 50.
    In A Parting of the Ways Michael Friedman proposed to conceive the contemporary divide between analytic philosophy (AP) and continental philosophy (CP) as the outcome of the bifurcation between the Neokantians of Heidelbarg and Marburg. According to Friedman, Carnap can be characterized as the executor of the Marburg school, while Heidegger is to be considered as the heir of the Southwest Neokantianism. In this paper it is argued that Carnap was much closer to the Southwest Neokantianism than usually recognized. To (...)
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  44. Carnap's Metrical Conventionalism Versus Differential Topology.Thomas Mormann - 2004 - Proc. 2004 Biennial Meeting of the PSA, vol. I, Contributed Papers 72 (5):814 - 825.
    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 (...)
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  45. Theories as Representations.Andoni Ibarra & Thomas Mormann - 1997 - Poznan Studies in the Philosophy of the Sciences and the Humanities 61:39 - 87.
    In this paper we argue for the thesis that theories are to be considered as representations. The term "representation" is used in a sense inspired by its mathematical meaning. Our main thesis asserts that theories of empirical theories can be conceived as geometrical representations. This idea may be traced back to Galileo. The geometric format of empirical theories should not be simply considered as a clever device for displaying a theory. Rather, the geometrical character deeply influences the theory s ontology. (...)
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  46. Towards an Evolutionary Account of Conceptual Change in Mathematics: Proofs and Refutations and the Axiomatic Variation of Concepts.Thomas Mormann - 2002 - In G. Kampis, L.: Kvasz & M. Stöltzner (eds.), Appraising Lakatos: Mathematics, Methodology and the Man. Kluwer Academic Publishers. pp. 1--139.
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  47. Topological Aspects of Combinatorial Possibility.Thomas Mormann - 1997 - Logic and Logical Philosophy 5:75 - 92.
    The aim of this paper is to show that topology has a bearing on<br><br>combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on the mappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. Moreover, it is compatible with atomistic as well as with non-atomistic ontologies.It helps to elucidate the positions of logical atomism and monism (...)
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  48. Interactive Representations.Andoni Ibarra & Thomas Mormann - 2005 - Representaciones 1 (1):1 - 20.
    In this paper we argue that philosophy of science is in need of a comprehensive and deep theory of scientific representation. We contend that such a theory has to take into account the conceptual evolution of the notion of representation in the empirical science and mathematics.In particular, it is pointed out that the category-theoretical notion of an adjoint situation may be useful to shed new light on the intricate relation between the empirical and the theoretical by showing that scientific representations (...)
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  49. Not Much Higher-Order Vagueness in Williamson’s ’Logic of Clarity’.Nasim Mahoozi & Thomas Mormann - manuscript
    This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...)
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  50.  84
    From Cautious Enthusiasm to Profound Disenchantment - Ernest Nagel and Carnapian Logical Empiricism.Thomas Mormann - forthcoming - In Matthias Neuber & Adam Tamas Tuboly (eds.), Ernest Nagel: Philosophy of Science and the Fight for Clarity. Springer.
    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 (...)
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