Mic Detlefsen – Freedom in Mathematics
The Montreal Inter-University Workshop on the History and Philosophy of Mathematics presents:
Mic Detlefsen (Notre-Dame): Freedom in Mathematics
Friday, October 29th, 2010. 3:30-5:30pm
McGill University, Leacock Building, Room 927
Abstract: There are different types of freedom that figured in the discussions of foundational thinkers in the nineteenth and early twentieth centuries. Prominent among these was one which was commonly known as freedom of concept-formation (freie Begriffsbildung) or concept-introduction. Freedom of concept-introduction was essentially a negative freedom. Speciﬁcally, it was a freedom from the traditional empiricist-constructivist constraint on concept-introduction, a constraint I will generally refer to as the Instantiation Condition.
According to this condition, a concept can be legitimately introduced into mathematical practice only if its content is obtainable from that of an intuition or experience by application of an identiﬁed process of abstraction. The concern was not ultimately with how, as a matter of human psychology, we manage to form concepts (and/or such linguistic expressions as are generally used to represent them). Rather, it was with what constitutes the admission of a concept into mathematical practice, and the conditions under which such admission is justiﬁed. These will therefore be my chief concerns here too.
For more information, please contact:
Gregory Lavers (Concordia), Mathieu Marion (UQÀM),
Jean-Pierre Marquis (UdM), Dirk Schlimm (McGill).