Fortgeschrittenenseminar Axiomatic Metaphysics

The axiomatic theory of abstract objects will be developedand investigated, along with a precise theory of properties, relations, and propositions. Modal and higher-order versions of the theory will be applied so as to derive theorems about situations, possible worlds, impossible worlds, Platonic Forms, Leibnizian concepts, fictions, Fregean numbers, and Fregean senses. Topics and problems in modal metaphysics, philosophy of mathematics, intensional logic and philosophy of language will be discussed in an integrated philosophical environment. A comprehensive philosophy of mathematics will be developed and it will be shown how various elements of the traditional philosophies of mathematics (e.g., Platonism, structuralism, fictionalism, formalism/finitism, if-thenism, and inferentialism) are preserved. The theory will also be investigated computationally, by representing the axioms in an automated reasoning system capable of proof-discovery and not just proof-validation. Timetable: 10am-12noon, on the days: Lecture 1: Wed, Jun 1, Introduction Lecture 2: Fri, Jun 3, An Exact Science Lecture 3: Mon, Jun 6, Logical Objects Lecture 4: Wed, Jun 8, Forms and Fictions Lecture 5: Fri, Jun 10, Situations and Possible Worlds Lecture 6: Mon, Jun 13, Impossible Worlds and Leibnizian Concepts Lecture 7: Wed, Jun 15, Leibnizian Modal Metaphysics Lecture 8: Fri, Jun 17, Fregean Senses Lecture 9: Mon, Jun 20, Frege Numbers I Lecture 10: Wed, Jun 22, Frege Numbers II Lecture 11: Fri, Jun 24, Philosophy of Mathematics I Lecture 12: Mon, Jun 27, Philosophy of Mathematics II Make up day: Wed, Jun 29 W3-Professur für Logik und Sprachphilosophie (Univ. Prof. Dr. Dr. Hannes Leitgeb) seminar paper LMU München SoSe 2016 Prof. Zalta Ed