MCMP – Philosophy of Mathematics
By MCMP Team
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Description
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 Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.
| Name | Description | Released | Price | ||
|---|---|---|---|---|---|
| 1 | VideoGeometrical 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 | 7/13/2015 | Free | View in iTunes |
| 2 | VideoA 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 epist | 6/15/2015 | Free | View in iTunes |
| 3 | VideoOn 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, n | 5/4/2015 | Free | View in iTunes |
| 4 | VideoA 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 br | 2/3/2015 | Free | View in iTunes |
| 5 | VideoQuantified 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 proba | 1/15/2015 | Free | View in iTunes |
| 6 | VideoSymmetry 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 be | 1/12/2015 | Free | View in iTunes |
| 7 | VideoAn 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 | 12/22/2014 | Free | View in iTunes |
| 8 | VideoNatural 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 | 12/2/2014 | Free | View in iTunes |
| 9 | VideoOn 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 | 11/12/2014 | Free | View in iTunes |
| 10 | VideoNeuropsychology 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? Neuroscien | 11/12/2014 | Free | View in iTunes |
| 11 | VideoIF 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 | 11/12/2014 | Free | View in iTunes |
| 12 | VideoWhat 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 dile | 11/12/2014 | Free | View in iTunes |
| 13 | VideoA 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 | 11/12/2014 | Free | View in iTunes |
| 14 | VideoDiscernibility 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 | 11/12/2014 | Free | View in iTunes |
| 15 | VideoThree 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 | 11/12/2014 | Free | View in iTunes |
| 16 | VideoThe 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 | 8/6/2014 | Free | View in iTunes |
| 17 | VideoAnti-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 | 6/26/2014 | Free | View in iTunes |
| 18 | VideoHaecceities 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 a | 6/24/2014 | Free | View in iTunes |
| 19 | VideoIn 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 explor | 5/9/2014 | Free | View in iTunes |
| 20 | VideoLearning 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. | 5/9/2014 | Free | View in iTunes |
| 21 | VideoRemarks 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 | 12/27/2013 | Free | View in iTunes |
| 22 | VideoRecent 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, t | 1/17/2013 | Free | View in iTunes |
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