Citations of:
A Natural Model of the Multiverse Axioms
Notre Dame Journal of Formal Logic 51 (4):475-484 (2010)
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f The purpose of this paper is to investigate categoricity arguments conducted in second order logic and the philosophical conclusions that can be drawn from them. We provide a way of seeing this result, so to speak, through a first order lens divested of its second order garb. Our purpose is to draw into sharper relief exactly what is involved in this kind of categoricity proof and to highlight the fact that we should be reserved before drawing powerful philosophical conclusions (...) |
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The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe (...) |
