Review of Symbolic Logic 1 (2):241-266 (2008)

Authors
Stewart Shapiro
Ohio State University
Abstract
_1. Philosophical background: iteration, ineffability, reflection._ There are at least two heuristic motivations for the axioms of standard set theory, by which we mean, as usual, first-order Zermelo–Fraenkel set theory with the axiom of choice : the iterative conception and limitation of size. Each strand provides a rather hospitable environment for the hypothesis that the set-theoretic universe is ineffable, which is our target in this paper, although the motivation is different in each case.
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DOI 10.1017/S1755020308080192
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References found in this work BETA

Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1958 - Atlantic Highlands, NJ, USA: North-Holland.

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Citations of this work BETA

Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
The Company Kept by Cut Abstraction (and its Relatives).S. Shapiro - 2011 - Philosophia Mathematica 19 (2):107-138.

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