Feferman on Set Theory: Infinity up on Trial

  • Peter Koellner
Part of the Outstanding Contributions to Logic book series (OCTR, volume 13)


In this paper I examine Feferman’s reasons for maintaining that while the statements of first-order number theory are “completely clear” and “completely definite,” many of the statements of analysis and set theory are “inherently vague” and “indefinite.” I critique his five main arguments and argue that in the end the entire case rests on the brute intuition that the concept of subsets of natural numbers—along with the richer concepts of set theory—is not “clear enough to secure definiteness.” My response to this final, remaining point will be that the concept of “being clear enough to secure definiteness” is about as clear a case of an inherently vague and indefinite concept as one might find, and as such it can bear little weight in making a case against the definiteness of analysis and set theory.


Predicativity Set theory The continuum hypothesis Definiteness Semi-constructive systems 

2010 Mathematics Subject Classification

00A30 03F35 03E60 03E50 


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Authors and Affiliations

  1. 1.Department of PhilosophyHarvard UniversityCambridgeUSA

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