Volker Halbach (Oxford) gives a talk at the Workshop on Mathematical Philosophy titled "Self-reference". Abstract: What does it mean for a sentence to say about itself that it is P? Here P can stand for any unary sentential function such as 'is provable', 'is not provable', 'is true', or 'is a sentence'. I will study this question in a metamathematical setting. After reviewing some early attempts to tackle the question and their impact on problems in metamathematics such as Henkin's problem, I will put forward a new proposal and test its adequacy with some examples.

Self-reference

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.

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.

Share Self-reference

Sign up to save your podcasts

Self-reference

Self-reference

More shows like MCMP – Mathematical Philosophy (Archive 2011/12)

Fakultät für Chemie und Pharmazie - Digitale Hochschulschriften der LMU - Teil 02/06

Hegel lectures by Robert Brandom, LMU Munich

LMU Statistik I für Studierende der Wirtschaftswissenschaften

Institut für Produktionswirtschaft und Controlling (LMU)

LMU Rechtsphilosophie

MCMP – Philosophy of Science

Epistemology and Philosophy of Science: Prof. Dr. Stephan Hartmann – HD

LMU Physik 2 für Chemiker (PN2) SS2016

Medizin - Open Access LMU - Teil 16/22