65 episodes

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.

MCMP – Philosophy of Physics Ludwig-Maximilians-Universität München

    • Philosophy

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.

    • video
    Shape Dynamics

    Shape Dynamics

    Tim A. Koslowski (New Brunswick) gives a talk at the Mini-Workshop on the Foundations of Shape Dynamics (23 June, 2014) titled "Shape Dynamics". Abstract: Based on the introduction to shape dynamics by Sean Gryb, I will discuss the question: "Given that gravity (from the perspective of shape dynamics) is fundamentally the evolution of spatial conformal geometry and not spacetime: How is the arrow of time generated? How is the illusion of a spacetime generated? What are the limitations of the spacetime description? I will give explicit answers to several aspect of these questions and I will explain where the uncharted territory begins.

    • 32 min
    • video
    Bohmian Mechanics, speakable quantum physics

    Bohmian Mechanics, speakable quantum physics

    Detlef Dürr (LMU) gives a talk at the MCMP Colloquium (23 January, 2013) titled "Bohmian Mechanics, speakable quantum physics". Abstract: I introduce Bohmian Mechanics, which is a theory of particles in motion. The law of motion is not classical, i.e. the particles do not move on Newtonian trajectories. As this is often not appreciated I shall discuss some features which will help to sharpen one's intuition about this theory of nature.

    • 1 hr 17 min
    • video
    Quantisation as a guide to ontic structure

    Quantisation as a guide to ontic structure

    Karim Thébault (MCMP/LMU) gives a talk at the MCMP Colloquium (9 January, 2013) titled "Quantisation as a guide to ontic structure". Abstract: The ontic structural realist stance is motivated by a desire to do philosophical justice to the success of science, whilst withstanding the metaphysical undermining generated by the various species of ontological underdetermination. We are, however, as yet in want of general principles to provide a scaffold for the explicit construction of structural ontologies. Here we will attempt to bridge this gap by utilising the formal procedure of quantisation as a guide to ontic structure of modern physical theory. The example of non-relativistic particle mechanics will be considered and, for that case, it will be argued that, modulo certain mathematical ambiguities, a consistent candidate structural ontology can be established.

    • 45 min
    • video
    Gravity. An exercise in quantization

    Gravity. An exercise in quantization

    Igor Khavkine (Utrecht) gives a talk at the MCMP workshop "Quantum Gravity in Perspective" (31 May-1 June, 2013) titled "Gravity. An exercise in quantization". Abstract: The quantization of General Relativity (GR) is an old and chellenging prob- lem that is in many ways still awaiting a satisfactory solution. GR is a partic- ularly complicated field theory in several respects: non-linearity, gauge invari- ance, dynamibal causal structure, renormalization, singularities, infared effects. Fortunately, much progress has been made on each of these fronts. Our under- standing of these problems has evolved greatly over the past century, together with our understandig of quantum field theory (QFT) in general. Today, the state of the art in QFT knows how to address each of these challenges, as they occur in isolation in ohter field theories. There is still an active research program aiming to combine the relevant methods and apply them to GR. But, at the very least, the problem of the quantization of GR can be formulated as a well defined mathematical question. On the other hand, quantum GR also faces a different set of obstacles: timelessness, non-renormalizability, naturality, unification, which reflect, not its technical difficulty, but rather the aesthetic and philosophical preferences of practing theoretical physicists. I will briefly discuss how the technical state of the art and a scientifically conservative philosophical position make these obstacles irrelevant. Time per- mitting, I will also briefly touch on some aspects of the state of technical state of the art that have turned the quantization of GR into a (still challenging) exercise: covariant Poisson structure, BV-BRST treatment of gauge theories, deformation quantization, Epstein-Glaser renormalization.

    • 42 min
    • video
    Against Dogma: Locality, Conditionalisation, and Collapse in Relativistic Quantum Mechanics

    Against Dogma: Locality, Conditionalisation, and Collapse in Relativistic Quantum Mechanics

    Thomas Pashby (Pittsburgh) gives a talk at the MCMP Colloquium (28 May, 2014) titled "Against Dogma: Locality, Conditionalisation, and Collapse in Relativistic Quantum Mechanics". Abstract: I argue here against the widespread view (due to David Malament) that the non-commutativity of non-instantaneous localisation projections implies the existence of act-outcome correlations in relativistic QM. There are two facets to my argument: first, I claim that the interpretation of collapse as a process brought about by the experimenter is mistaken; second, I contend that a fully relativistic model should not condition on the occurrence of spacelike separated instantaneous events. This leaves the door open to define a relativistically invariant (but non-commuting) system of localization, which I interpret in terms of conditional probabilities for the occurrence of events. In accord with Tumulka (2009), I conclude that non-local correlations of events in a relativistic quantum theory need not imply the sort of action at a distance that worries Malament (1996).

    • 54 min
    • video
    An Introduction to Shape Dynamics: a New Perspective on Quantum Gravity

    An Introduction to Shape Dynamics: a New Perspective on Quantum Gravity

    Sean Gryb (Nijmegen) gives a talk at the Mini-Workshop on the Foundations of Shape Dynamics (23 June, 2014) titled "An Introduction to Shape Dynamics: a New Perspective on Quantum Gravity". Abstract: Shape Dynamics is a theory of gravity where the fundamental ontology is that of evolving conformally invariant spatial geometry. This implements a notion of local spatial scale invariance such that what is seen to be physically meaningful is the information about the local "shapes" (as opposed to size) of a system. Perhaps surprisingly, this theory can be proven to reproduce a vast number of the solutions to the Einstein equations. However, black hole solutions are known to differ from those of GR past the horizon and do not lead to singularities. Shape Dynamics, thus, provides an intriguing new starting point for a theory of quantum gravity. In this introductory chalkboard talk, I will try to give some motivations for Shape Dynamics and will describe the basic structure of the theory, outlining how one can prove equivalence with GR. This will lay the ground work for Tim Koslowski's talk, which will discuss some recent developments of the theory.

    • 37 min

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