REPLY TO FEFERMAN, KOELLNER, TAIT, AND SIEG

I comment on Feferman’s views on set theory, in particular criticizing a priori arguments claiming that the continuum hypothesis has no determinate truth value and commenting on his responses to my paper on his skepticism about set theory. I respond to criticisms of his of the structuralism that I h...

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Bibliographic Details
Published in:The Journal of philosophy 2016-05, Vol.113 (5/6), p.286-307
Main Author: PARSONS, CHARLES
Format: Article
Language:English
Subjects:
Analytic Philosophy
Contemporary Philosophy
Philosophy
Set theory
Online Access:Get full text
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Summary:I comment on Feferman’s views on set theory, in particular criticizing a priori arguments claiming that the continuum hypothesis has no determinate truth value and commenting on his responses to my paper on his skepticism about set theory. I respond to criticisms of his of the structuralism that I have advocated and comment on his view of proof theory. On Koellner’s paper, I register little disagreement but note a difference of sympathy about views such as constructivism. On Tait’s paper, I note that Kant gives more play to the notion of whole number than Tait seems to allow and that Kant’s conception of real numbers is unclear. Responding to Sieg’s paper, I note his emphasis on how much mathematics and its foundations changed from Kant’s time to that of Dedekind and Hilbert and mention my effort to find a limited role for an intuition distantly descended from Kant’s.
ISSN:0022-362X
1939-8549
DOI:10.5840/jphil20161135/619