How Many there Are Isn’t

Abstract

A world where there exists exactly n concrete things is a count-determinate world. The orthodox assumption is that count-determinacy is necessary; if to be is to be the value of a variable and the domain of quantification is enumerable, count-determinacy follows (Schaffer 2009, Van Inwagen 2002, 2009). Against this I argue how many there are can be indeterminate; count-indeterminacy, I argue, is metaphysically possible and likely actual- even assuming existence is determinate. Notably, the argument includes rebuttals of Evans’ reductio against indeterminate identity and the Lewis/Sider ‘argument from vagueness’. Count-indeterminacy should therefore be recognized as another basic form of genuine metaphysical indeterminacy, in addition to types recently defend by Barnes (2013, 2014), Williams (2008), and Wilson (2013, 2016).