Chapter

Proper Method

Penelope Maddy

in Defending the Axioms

Published in print January 2011 | ISBN: 9780199596188
Published online May 2011 | e-ISBN: 9780191725395 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199596188.003.0003
Proper Method

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This chapter lays out the meta-philosophical perspective from which the subsequent inquiry will take place, namely, that of the Second Philosopher. Beginning in her characteristic way, from within the practice, the Second Philosopher surveys a range of set-theoretic examples, historical and contemporary. Though the methods employed differ from her more familiar empirical approach, she judges that they are rational means toward the ends these various set-theoretic practices are out to achieve. Assuming for the moment that the historical and continuing inter-relations of pure mathematics with natural science are enough to warrant the Second Philosopher in regarding set theory as a body of truths, she concludes that its methods are reliable guides to those truths. The challenge, then, is to explain what sort of activity set theory is, what kind of things set are and how we know them, in such a way as to respect those methods. This means avoiding any variety of the familiar Robust Realism, which requires that apparently rational, reliable set-theoretic methods be supplemented or even rejected on the basis of an extra-mathematical metaphysics.

Keywords: meta-philosophy; metaphysics; set-theoretic method; Robust Realism; Second Philosophy; set theory; set theory

Chapter.  8108 words. 

Subjects: Philosophy of Mathematics and Logic ; Metaphysics

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