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TAMM: "CHAP05" --2005/11/23 --PAGE 179 --#3 Methodology and metaphysics in

Summary: TAMM: "CHAP05" -- 2005/11/23 -- PAGE 179 -- #3
Methodology and metaphysics in
the development of Dedekind's
theory of ideals
Jeremy Avigad
1 Introduction
Philosophical concerns rarely force their way into the average mathematician's
workday. But, in extreme circumstances, fundamental questions can arise as to
the legitimacy of a certain manner of proceeding, say, as to whether a particular
object should be granted ontological status, or whether a certain conclusion is
epistemologically warranted. There are then two distinct views as to the role that
philosophy should play in such a situation.
On the first view, the mathematician is called upon to turn to the counsel
of philosophers, in much the same way as a nation considering an action of
dubious international legality is called upon to turn to the United Nations for
guidance. After due consideration of appropriate regulations and guidelines
(and, possibly, debate between representatives of different philosophical fac-
tions), the philosophers render a decision, by which the dutiful mathematician
Quine was famously critical of such dreams of a `first philosophy.' At the oppos-


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


Collections: Multidisciplinary Databases and Resources; Mathematics