Dedekind and the Structuralist Transformation of Mathematics

The Philadelphia Area Seminar on History of Mathematics will meet on Thursday, March 16, 2017, from 6:00 p. m. to 8:00 p.m., in Saint Augustine Center Room 300.

In recent history and philosophy of mathematics, “structuralism" has become an important theme.  There are two different ways in which this theme is typically approached: (a) by focusing on a structuralist methodology for mathematics (concerning the tools used, the ways in which various parts of mathematics are organized, etc.); (b) in terms of a structuralist semantics for mathematics (a conception, or several related conceptions, of what we talk about when we study “the natural numbers”, “the real numbers”, “the cyclic group with five elements", etc.).  In this talk, I will show that Richard Dedekind’s writings from the nineteenth century should be seen as one of the main historical sources for both strands.  Moreover, the two strands are intimately connected for him, as I will also try to establish.  This will involve comparing his foundational work (on the natural and real numbers) with his contributions to algebra and number theory (his investigation of the notions of algebraic number, group, field, ring, lattice, etc., including his famous theory of ideals).  Dedekind built on the work of his teachers and mentors, to be sure, especially Gauss, Dirichlet, and Riemann.  But he went significantly beyond them precisely by initiating a structuralist transformation of modern mathematics, one that was later continued by Hilbert, Noether, Bourbaki, and in category theory. 

Some of the contents of this talk appeared in Professor Reck’s article “Dedekind’s Contributions to the Foundations of Mathematics” in the Stanford Encyclopedia of Philosophy.

Directions: Villanova University is located on route 30, Lancaster Avenue, just east of I-476. If you drive to the meeting, enter Villanova by the main gate on Ithan Avenue. By order of the Parking Office, all parking is now in the Saint Augustine Center lot, newly refurbished to a multistory structure.  You will need to display a parking pass, which will follow in a later email.  You can get in touch with me (Alan Gluchoff) at 610-905-1376 if you need help.  

Directions: Villanova University is located on route 30, Lancaster Avenue, just east of I-476. If you drive to the meeting, enter Villanova by the main gate on Ithan Avenue. By order of the Parking Office, all parking is now in the Saint Augustine Center lot, newly refurbished to a multistory structure.  You will need to display a parking pass, which will follow in a later email.  You can get in touch with me (Alan Gluchoff) at 610-905-1376 if you need help.