An Indeterminate Universe of Sets
Published in Synthese, 2020
Recommended citation: Scambler, Chris. (2020). "An Indeterminate Universe of Sets." Synthese. 197, 545–573. https://link.springer.com/article/10.1007/s10992-019-09520-0
In this paper, I develop a view on set-theoretic ontology I call Universe-Indeterminism, according to which there is a unique but indeterminate universe of sets. I argue that Solomon Feferman’s work on semi-constructive set theories can be adapted to this project, and develop a philosophical motivation for a semi-constructive set theory closely based on Feferman’s but tailored to the Universe-Indeterminist’s viewpoint. I also compare the emergent Universe-Indeterminist view to some more familiar views on set-theoretic ontology.