Synthese 193 (6):1875-1907 (2016)

Authors
Toby Meadows
University of California, Irvine
Abstract
It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched.
Keywords Philosophy of mathematics  Philosophy of set theory  Formal theories of truth  Absolute generality  Indefinite extensibility
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Reprint years 2017
DOI 10.1007/s11229-015-0818-x
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Spandrels of Truth.J. C. Beall - 2009 - Oxford University Press.
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.

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Citations of this work BETA

Fragmented Truth.Andy Demfree Yu - 2016 - Dissertation, University of Oxford

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