Series: Penn State Logic Seminar
Date: Tuesday, March 28, 2000
Speaker: Emily Grosholz (Penn State, Philosophy)
Title: Numbers, Figures, and Sets, part 2.
Time: 2:30 - 3:20 PM
Place: 219 Thomas Building
Abstract:
In the second lecture, I will examine the correspondence between
Cantor and Dedekind, and the emerging notion of set as a collection of
"distinct and separate" elements that have no intrinsic order
relations. I will note the conceptual innovation this leads to in
Cantor's proofs concerning the cardinality of the natural numbers,
rational numbers, algebraic numbers and reals, as well as of continua
of different dimensions. But I will also point out the problematic
nature of forming a set of natural numbers, as well as a set of
points, based on my arguments given earlier and the notion of
"condition of intelligibility" they rest on. These problems explain
both why geometry eludes set theory and why set theory does not
"reduce" either number theory or geometry; and why we should expect
that the debate over the Continuum Hypothesis will go unresolved.