CfP special issue of the journal "Theoria" on Thin Objects

In his recent book 'Thin Objects: An Abstractionist Account' (Oxford University Press, 2018), Øystein Linnebo claims that mathematical objects are thin in the sense that "very little is required for their existence". Linnebo articulates this view in terms of Fregean abstraction principles, arguing that it is sufficient for abstract objects to exist that some nonabstract objects, or pluralities thereof, stands in the appropriate equivalence relations. Linnebo set up, among others, a defence of predicative vis-á-vis impredicative abstraction, and articulates a 'dynamic' approach to abstraction itself, on which abstraction is taken to extend the domain of objects available for quantification, and predicative abstraction is iterated over larger and larger domains.

The goal of this Special Issue is to bring together contributions addressing both the philosophical and the technical aspects of Linnebo's book, also in connection to similar proposals in the philosophy of mathematics and logic. Contributions to the Special Issue should consist in short papers (4000-6000 words). Øystein Linnebo will contribute a précis of his book, opening the issue, and a 'Reply to Critics', closing the issue.