Philosophia Mathematica 7 (2):136-163 (1999)

Authors
G. Aldo Antonelli
University of California, Davis
Abstract
This paper is concerned with the way different axiom systems for set theory can be justified by appeal to such intuitions as limitation of size, predicativity, stratification, etc. While none of the different conceptions historically resulting from the impetus to provide a solution to the paradoxes turns out to rest on an intuition providing an unshakeable foundation,'each supplies a picture of the set-theoretic universe that is both useful and internally well motivated. The same is true of more recently proposed axiom systems for non-well-founded universes, and an attempt is made to motivate such axiom systems on the basis of an old and respected ‘algebraic’ intuition
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DOI 10.1093/philmat/7.2.136
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References found in this work BETA

The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Oxford University Press. pp. 176--187.

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