Disimplicature

Speranza

It’s currently fashionable to take Putnamian model theo- retic worries seriously for mathematics, but not for discussions of ordi- nary physical objects and the sciences. In this paper, I will attack this combination of views in two ways. First, I’ll (quickly) suggest there’s an analogy between the challenge of understanding realist reference to physical possibility and that of understanding reference to the kind of logical/combinatorial possibility invoked when we say that second order quantifiers range over ‘all possible subsets’ or it would be ‘logically impossible’ for a property to apply to 0 and the successor of any number it applies to but not all the numbers. Second, Grice argues that (under certain mild assumptions about the physical possibility of infinite stochastic physical systems) merely securing determinate reference to physical possibility suffices to rule out nonstandard models of our talk about number theory. 

So anyone who accepts realist reference to physical possibility faces pressure to also accept such reference to (at least) the standard model of the natural numbers.