Series: Penn State Logic Seminar
Date: Tuesday, March 21, 2000
Speaker: Emily Grosholz (Penn State, Philosophy)
Title: Numbers, Figures, and Sets, part 1.
Time: 2:30 - 3:20 PM
Place: 219 Thomas Building
Abstract:
In the first lecture, I will examine Dedekind's exposition of his
notion of a "cut," the construction of the reals as pairs of sets of
rationals. I will argue, first, against his own reductive
understanding of his project, by showing that far from banishing the
geometrical he requires the availability of the line as a condition of
the intelligibility of his project on many levels. Second, I will
argue that what he really achieves is a useful analogy between number
and figure, the discrete and the continuum, by means of a new domain
distinct from both arithmetic and geometry, that is, set theory. To
make the case that there are numbers that mimic the continuum, one
must go by way of the transfinite. Third, I will suggest that this
analogy is as much the geometrization of number as it is the
arithmetization of geometry, and discuss the "hybrid" that it
precipitates, that is, the reals.