Set Theory, Type Theory, and Absolute Generality

Mind 123 (489):157-174 (2014)
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Abstract

In light of the close connection between the ontological hierarchy of set theory and the ideological hierarchy of type theory, Øystein Linnebo and Agustín Rayo have recently offered an argument in favour of the view that the set-theoretic universe is open-ended. In this paper, we argue that, since the connection between the two hierarchies is indeed tight, any philosophical conclusions cut both ways. One should either hold that both the ontological hierarchy and the ideological hierarchy are open-ended, or that neither is. If there is reason to accept the view that the set-theoretic universe is open-ended, that will be because such a view is the most compelling one to adopt on the purely ontological front.

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Author Profiles

Stewart Shapiro
Ohio State University
Salvatore Florio
University of Oslo

Citations of this work

Higher‐order metaphysics.Lukas Skiba - 2021 - Philosophy Compass 16 (10):1-11.
Against Cumulative Type Theory.Tim Button & Robert Trueman - 2022 - Review of Symbolic Logic 15 (4):907-49.
Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.

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References found in this work

The seas of language.Michael Dummett - 1993 - New York: Oxford University Press.
New Foundations for Mathematical Logic.W. V. Quine - 1937 - Journal of Symbolic Logic 2 (2):86-87.

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