Munich Center for Mathematical Philosophy (MCMP)

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Seminar: "Axiomatic Metaphysics" (Prof. Ed Zalta, Stanford)


The axiomatic theory of abstract objects will be developed and 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.


Lecture 1 Monday, May 27 10:00-12:00 Introduction
Lecture 2 Tuesday, May 28 10:00-12:00 An Exact Science
Lecture 3 Wednesday, May 29 10:00-12:00 Logical Objects
Lecture 4 Friday, May 31 10:00-12:00 Situations and Possible Worlds
Lecture 5 Monday, June 3 10:00-12:00 Routley Star and Possibilities
Lecture 6 Tuesday, June 4 10:00-12:00 Impossible Worlds and Leibnizian Concepts
Lecture 7 Wednesday, June 5 10:00-12:00 Leibnizian Modal Metaphysics
Lecture 8 Thursday, June 6 10:00-12:00 Fregean Senses
Lecture 9 Friday, June 7 10:00-12:00 Frege Numbers I
Lecture 10 Monday, June 10 10:00-12:00 Frege Numbers II
Lecture 11 Tuesday, June 11 10:00-12:00 Philosophy of Mathematics I
Lecture 12 Wednesday, June 12 10:00-12:00 Philosophy of Mathematics II


  • Statistic Library (Room 245, Ludwigstraße 33/II).

Course Assessment

  • Term paper OR (presentation(s)+essay/record), according to the lecturer's specification (= BA and general MA program in philosophy);
  • Alternative/equivalent forms of assessment by arrangement [9 ECTS-points]