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Thomas Mormann
Ludwig Maximilians Universität, München (PhD)
  1. Topological Epistemology as Epistemology First.Thomas Mormann - manuscript
    Abstract. The aim of this paper is to sketch a topological epistemology that can be characterized as a knowledge first epistemology. For this purpose, the standard topological semantics for knowledge in terms of the interior kernel operator K of a topological space is extended to a topological semantics of belief operators B in a new way. It is shown that a topological structure has a kind of “derivation” (its “assembly” or “lattice of nuclei”) that defines a profusion of belief operators (...)
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  2. 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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  3. 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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  4. 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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  5. Structure-Preserving Representations, Constitution and the Relative A Priori.Thomas Mormann - 2021 - Synthese 198 (Supplement 21):1-24.
    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 (...)
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  6. Prototypes, Poles, and Topological Tessellations of Conceptual Spaces.Thomas Mormann - 2021 - Synthese 199:3675 - 3710.
    Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...)
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  7. Topological Models of Columnar Vagueness.Thomas Mormann - 2022 - Erkenntnis 87 (2):693 - 716.
    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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  8. 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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  9. Structural Universals as Structural Parts: Toward a General Theory of Parthood and Composition.Thomas Mormann - 2010 - Axiomathes 20 (2-3):229 - 253.
    David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. 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 (...)
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  10. 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.
  11. 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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  12. Topological Aspects of Epistemology and Metaphysics.Thomas Mormann - 2020 - In Silvano Zipoli Caiani & Alberto Peruzzi (eds.), Structures Meres, Semantics, Mathematics, and Cognitive Science. New York: Springer. pp. 135 - 152.
    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 (...)
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  13. 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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  14.  99
    Idealization in Cassirer's Philosophy of Mathematics.Thomas Mormann - 2008 - Philosophia Mathematica 16 (2):151 - 181.
    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. For extremely useful criticisms on earlier versions (...)
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    Prototypes, Poles, and Tessellations: Towards a Topological Theory of Conceptual Spaces.Thomas Mormann - 2021 - Synthese 199 (1-2):3675-3710.
    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, (...)
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  16. 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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  17. 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.
  18. Rudolf Carnap.Thomas Mormann - 2000 - C.H. Beck.
  19. New Work for Carnap’s Quasi-Analysis.Thomas Mormann - 2009 - Journal of Philosophical Logic 38 (3):249-282.
    Carnap's quasi-analysis is usually considered as an ingenious but definitively flawed approach in epistemology and philosophy of science. In this paper it is argued that this assessment is mistaken. Quasi-analysis can be reconstructed as a representational theory of constitution of structures that has applications in many realms of epistemology and philosophy of science. First, existence and uniqueness theorems for quasi-analytical representations are proved. These theorems defuse the classical objections against the quasi-analytical approach launched forward by Goodman and others. Secondly, the (...)
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  20. Geometrical Leitmotifs in Carnap’s Early Philosophy.Thomas Mormann - 2007 - In Richard Creath & Michael Friedman (eds.), Cambridge Companion to Rudolf Carnap. Cambridge University Press.
  21. Carnap’s Logical Empiricism, Values, and American Pragmatism.Thomas Mormann - 2007 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (1):127-146.
    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 (...)
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  22. Husserl's Philosophy of Science and the Semantic Approach.Thomas Mormann - 1991 - Philosophy of Science 58 (1):61-83.
    Husserl's mathematical philosophy of science can be considered an anticipation of the contemporary postpositivistic semantic approach, which regards mathematics and not logic as the appropriate tool for the exact philosophical reconstruction of scientific theories. According to Husserl, an essential part of a theory's reconstruction is the mathematical description of its domain, that is, the world (or the part of the world) the theory intends to talk about. Contrary to the traditional micrological approach favored by the members of the Vienna Circle, (...)
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  23. 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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  24.  33
    The Significance of Quasizerlegung for Carnap's Aufbau and Scientific Philosophy in General.Caterina del Sordo & Thomas Mormann - 2022 - PHILINQ 10 (1):234 - 253.
  25. 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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  26. Carnap’s Logical Empiricism, Values, and American Pragmatism.Thomas Mormann - 2006 - Journal of General Philosophy of Science 38 (1):127 - 146.
    Abstract. 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 con-sidered as philosophically respectable entities that could be constituted from value experiences. About 1930, however, values were banished to the realm of meaning-less me-taphysics, and Carnap came to endorse a strict emotivism. The aim of this paper is to shed new light on the question why Carnap abandoned his originally positive (...)
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  27. 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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  28. 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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  29.  69
    Topological Epistemology and the Gettier Problem.Thomas Mormann - manuscript
    The aim of this paper is to elaborate a topological semantics of knowledge and belief operators that can be used for an epistemological characterisation of Gettier cases. Relying on this semantics it will be shown that in Stalnaker’s logic KB every topological knowledge operator K is accompanied with a partially ordered family of belief operators B compatible with K in the sense that the pairs (K, B) of modal operators K and B satisfy all axioms of KB (except the contentious (...)
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  30.  27
    Completeness and Doxastic Pluralitiy for Topological Operators of Knowledge and Belief.Thomas Mormann - manuscript
    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) (...)
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  31. On the Mereological Structure of Complex States of Affairs.Thomas Mormann - 2012 - Synthese 187 (2):403-418.
    The aim of this paper is to elucidate the mereological structure of complex states of affairs without relying on the problematic notion of structural universals. For this task tools from graph theory, lattice theory, and the theory of relational systems are employed. Our starting point is the mereology of similarity structures. Since similarity structures are structured sets, their mereology can be considered as a generalization of the mereology of sets..
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  32. 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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  33. Are All False Theories Equally False?Thomas Mormann - 1988 - British Journal for the Philosophy of Science 39 (4):505-519.
  34. Natural Predicates and Topological Structures of Conceptual Spaces.Thomas Mormann - 1993 - Synthese 95 (2):219 - 240.
    In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing between (...)
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  35. Carnap’s Aufbau in the Weimar Context.Thomas Mormann - 2016 - In Christian Damböck (ed.), Influences on the Aufbau. Springer Verlag.
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  36. 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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  37. 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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  38. 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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  39. Zwischen Weisheit und Wissenschaft - Schlicks weites philosophisches Spektrum.Thomas Mormann - 2010 - Grazer Philosophische Studien 80 (1):263 - 285.
  40. 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.
  41. 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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  42.  29
    A Topological Completeness Theorem for a Weak Version of Stalnaker's Logic of Knowledge and Belief.Thomas Mormann - manuscript
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  43. 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.
  44. Synthetic Geometry and Aufbau.Thomas Mormann - 2003 - In Thomas Bonk (ed.), Language, Truth and Knowledge. Kluwer Academic Publishers. pp. 45--64.
  45.  7
    Trope Sheaves. A Topological Ontology of Tropes.Thomas Mormann - 1995 - Logic and Logical Philosophy 3:129.
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  46. Topological Representations of Mereological Systems.Thomas Mormann - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 76:463 -486.
  47. 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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  48. 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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  49. Two Kindred Neo-Kantian Philosophies of Science: Pap's "The A Priori in Physical Theory" and Cassirer's "Determinism and Indeterminism in Modern Physics".Thomas Mormann - 2021 - Journal of Transcendental Philosophy 1.
    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 (...)
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  50. 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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