Göran Sundholm – Three kinds of function
The Montreal Inter-University Workshop on the History and Philosophy of Mathematics
Göran Sundholm (Leiden): Three kinds of function
Thursday, October 6, 2011
McGill University, Leacock Building, Room 927. 5:30-7:00pm
Abstract: The development of the notion of function in commonly held to have gone from the idea that functions are (anchored in) expressions with free variables to the idea that they are mappings not tied to expressions and that the "sets of ordered pairs unique in the last component" conception is the precise version of this. I shall, to the contrary, distinguish three notions and discuss examples : 1. Euler-Frege functions — dependent objects of lowest level, with substitution taking the role of application; 2. Riemann-Dedekind mappings — independent objects of higher level, with a primitive notion of application; 3. Courses of value ("graphs"), used by Frege, Von Neumann, and set theory (Russell, Hausdorff, …) —independent objects of lowest level, where one needs a special application function of kind 1. (Frege’s curved arch, Von Neumann’s [x,y], Russell’s elevated inverted comma for descriptive functions.
For more information, please contact:
Gregory Lavers (Concordia), Mathieu Marion (UQÀM),
Jean-Pierre Marquis (UdM), Dirk Schlimm (McGill).