The Journal of Philosophy: Vol. 111, No. 8, August 2014.
Strong Axioms of Infinity and the Debate About Realism, KAI HAUSER and W. HUGH WOODIN
One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality. That interpretation is contested by antirealists seeking to explain the convergence as an artifact of the language of set theory. This paper shows that the reductionist view is flawed by exhibiting examples of arguably natural strong axioms of infinity that are demonstrably incomparable. It also examines the question to what extent our examples support the case for mathematical realism.
The Impossibility of Pure Libertarianism, MATTHEW BRAHAM and MARTIN VAN HEES
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|Title Annotation:||Philosophical Abstracts|
|Publication:||The Review of Metaphysics|
|Date:||Jun 1, 2015|
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