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Godel and the metamathematical tradition Jeremy Avigad

Summary: GĻodel and the metamathematical tradition
Jeremy Avigad
July 25, 2007
The metamathematical tradition that developed from Hilbert's pro-
gram is based on syntactic characterizations of mathematics and the
use of explicit, finitary methods in the metatheory. Although GĻodel's
work in logic fits squarely in that tradition, one often finds him cu-
riously at odds with the associated methodological orientation. This
essay explores that tension and what lies behind it.
1 Introduction
While I am honored to have been asked to deliver a lecture in honor of the
Kurt GĻodel centennial, I agreed to do so with some hesitations. For one
thing, I am not a historian, so if you are expecting late-breaking revelations
from the GĻodel Nachlass you will be disappointed. A more pressing concern
is that I am a poor representative of GĻodel's views. As a proof theorist by
training and disposition, I take myself to be working in the metamathemat-
ical tradition that emerged from Hilbert's program; while I will point out,
in this essay, that GĻodel's work in logic falls squarely in this tradition, one
often senses in GĻodel a dissatisfaction with that methodological orientation


Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University


Collections: Multidisciplinary Databases and Resources; Mathematics