The Groundedness Approach to Class Theory

Inquiry: An Interdisciplinary Journal of Philosophy 57 (2):244-273 (2014)
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Abstract

Kripke showed how to restrict Tarski’s schema to grounded sentences. I examine the prospects for an analogous approach to the paradoxes of naive class comprehension. I present new methods to obtain theories of grounded classes and test them against antecedently motivated desiderata. My findings cast doubt on whether a theory of grounded classes can accommodate both the extensionality of classes and allow for class definition in terms of identity

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Jonne Kriener
Birkbeck College

Citations of this work

Term Models for Abstraction Principles.Leon Horsten & Øystein Linnebo - 2016 - Journal of Philosophical Logic 45 (1):1-23.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1973 - Atlantic Highlands, NJ, USA: Elsevier.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
Believing the axioms. I.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):481-511.

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