Matthew Simpson: "'All', 'Every', Supposition, and Stalnaker"

Matthew Simpson, University of Cambridge: "'All', 'Every', Supposition, and Stalnaker"

Abstract
This paper presents a new semantics for the determiners ‘all’ and ‘every’, as they appear in sentences like ‘every glass on the bar was full’, or ‘all contestants received a prize’, inspired by Robert Stalnaker’s semantics for conditionals. On this view, a sentence like ‘all contestants received a prize’ is true if at the closest possible world in which the restrictor ‘contestants’ is satisfied by something, nothing satisfies it without also satisfying the scope ‘received a prize’. I show how this ‘Stalnaker semantics’ gives an excellent explanation of the behaviour of universal generalisations, including some aspects that extant semantic theories cannot easily explain. In particular I argue that it gives the best explanation of uncertainly empty generalisations, generalisations that to a given agent may or may not have empty restrictors. I then discuss some intuitively valid arguments that are invalid on the Stalnaker semantics, and use pragmatic principles to argue that this is not a significant problem for the view.