MCMP – Philosophy of Mathematics
by MCMP Team
Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical
Episodes
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Geometrical Roots of Model Theory: Duality and Relative Consistency
Georg Schiemer (Vienna/MCMP) gives a talk at the MCMP Colloquium (9 July, 2015) titled "Geometrical Roots of Model Theory: Duality and Relative Consistency". Abstract: Axiomatic geometry in Hilbert's Grundlagen der Geometrie (1899) is usually described as model-theoretic in character: theories…
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A Hypothetical Conception of Mathematics in Practice
José Ferreirós (Sevilla) gives a talk at the MCMP Colloquium (11 June, 2015) titled "A Hypothetical Conception of Mathematics in Practice". Abstract: The aim of the talk will be to present some of the basic aspects of my approach to mathematical epistemology, developed in the forthcoming book...
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On the Contingency of Predicativism
Sam Sanders (MCMP) gives a talk at the MCMP Colloquium (16 April, 2015) titled "On the Contingency of Predicativism". Abstract: Following his discovery of the paradoxes present in naive set theory, Russell proposed to ban the vicious circle principle, nowadays called impredicative definition, by...
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A Computational Perspective on Metamathematics
Vasco Brattka (UniBwM Munich) gives a talk at the MCMP Colloquium (29 January, 2015) titled "A Computational Perspective on Metamathematics". Abstract: By metamathematics we understand the study of mathematics itself using methods of mathematics in a broad sense (not necessarily based on any…
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Quantified Probability Logics: How Boolean Algebras Met Real-Closed Fields
Stanislav O. Speranski (Sobolev Institute of Mathematics) gives a talk at the MCMP Colloquium (4 December, 2014) titled "Quantified probability logics: how Boolean algebras met real-closed fields". Abstract: This talk is devoted to one interesting probability logic with quantifiers over events —...
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Symmetry and Mathematicians' Aesthetic Preferences: a Case Study
Irina Starikova (Sao Paulo) gives a talk at the MCMP Colloquium (8 January, 2015) titled "Symmetry and Mathematicians' Aesthetic Preferences: a Case Study". Abstract: Symmetry plays an important role in some areas of mathematics and has traditionally been regarded as a factor of visual beauty. In...
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An Aristotelian continuum
Stewart Shapiro (Ohio) gives a talk at the MCMP Colloquium (18 December, 2014) titled "An Aristotelian continuum". Abstract: Geoffrey Hellman and I are working on a point-free account of the continuum. The current version is “gunky” in that it does not recognize points, as part of regions, but it...
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Natural numbers in philosophy of mathematics and in cognitive science
Paula Quinon (Lund) gives a talk at the MCMP Colloquium (27 November, 2014) titled "Natural numbers in philosophy of mathematics and in cognitive science". Abstract: Natural numbers are the object of studies in various disciplines. Two such disciplines are the philosophy of mathematics and…
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On Mathematical Structuralism. A Theory of Unlabeled Graphs as Ante Rem Structures
Hannes Leitgeb (MCMP/LMU) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "On Mathematical Structuralism. A Theory of Unlabeled Graphs as Ante Rem Structures". Abstract: There are different versions of structuralism in present-day philosophy…
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Neuropsychology of numbers
Hourya Benis-Sinaceur (Paris I) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "Neuropsychology of numbers". Abstract: How do we extract numbers from our perceiving the surrounding world? Neurosciences and cognitive sciences provide us with a...
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IF epistemic logic and mathematical knowledge
Manuel Rebuschi (Poincaré Archives, University of Lorraine, Nancy) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "IF epistemic logic and mathematical knowledge". Abstract: Can epistemic logicstate anything interesting about the epistemology…
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What are the challenges of Benacerrafs Dilemma? A Reinterpretation
Marco Panza (Paris I) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "What are the challenges of Benacerrafs Dilemma? A Reinterpretation". Abstract: Despite its enormous influence, Benacerraf's dilemma admits no standard, unanimously…
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A useful method for obtaining alternative formulations of the analytical hierarchy
Stanislav O. Speranski (Sobolev Institute of Mathematics) gives a talk at the MCMP Colloquium (6 November, 2014) titled "A useful method for obtaining alternative formulations of the analytical hierarchy". Abstract: In mathematical philosophy one often employs various formal systems and…
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Discernibility from a countable perspective
Kate Hodesdon (Nancy) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "Discernibility from a countable perspective". Abstract: In this talk I discuss formal methods for discerning between uncountably many objects with a countable language,...
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Three ways in which logic might be normative
Florian Steinberger (MCMP/LMU) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "Three ways in which logic might be normative". Abstract: Logic, the tradition has it, is, in some sense, normative for reasoning. Famously, the tradition was...
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The Univalence Axiom
Steve Awodey (CMU) gives a talk at the MCMP Colloquium (16 July, 2014) titled "The Univalence Axiom". Abstract: In homotopy type theory, the Univalence Axiom is a new principle of reasoning which implies that isomorphic structures can be identified. I will explain this axiom and consider its...
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Anti-Mathematicism and Formal Philosophy
Eric Schliesser (Ghent) gives a talk at the MCMP Colloquium (25 June, 2014) titled "Anti-Mathematicism and Formal Philosophy". Abstract: Hannes Leitgeb rightly claims that "contemporary critics of mathematization of (parts of) philosophy do not so much put forward arguments as really express a...
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Haecceities and Mathematical Structuralism
Christopher Menzel (Texas A&M University) gives a talk at the MCMP Colloquium (18 June, 2014) titled "Haecceities and Mathematical Structuralism". Abstract: It is well-known that some earlier versions of mathematical structuralism (notably from Resnik and Shapiro) appeared to be committed to a...
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In Good Company? On Hume's Principle and the assignment of numbers to infinite concepts.
Paolo Mancosu (UC Berkeley) gives a talk at the MCMP Colloquium (8 May, 2014) titled "In Good Company? On Hume's Principle and the assignment of numbers to infinite concepts.". Abstract: In a recent article (Review of Symbolic Logic 2009), I have explored the historical, mathematical, and...
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Learning Experiences, Expected Inaccuracy, and the Value of Knowledge
Simon Huttegger (UC Irvine) gives a talk at the MCMP Colloquium (8 May, 2014) titled "Learning Experiences, Expected Inaccuracy, and the Value of Knowledge". Abstract: I argue that van Fraassen's reflection principle is a principle of rational learning. First, I show that it follows if one wants…
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Remarks on the foundations of mathematics
Helmut Schwichtenberg (LMU) gives a talk at the MCMP Colloquium (5 December, 2013) titled "Remarks on the foundations of mathematics". Abstract: We consider minimal logic with implication and universal quantification over (typed) object variables. Free type and predicate parameters may occur. For...
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Recent metamathematical wonders and the question of arithmetical realism
Andrey Bovykin (Bristol) gives a talk at the MCMP Colloquium (16 January, 2013) titled "Recent metamathematical wonders and the question of arithmetical realism". Abstract: Metamathematics is the study of what is possible or impossible in mathematics, the study of unprovability, limitations of...
About this show
Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical
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