Vagueness, Partial Belief, and Logic
Hartry H. Field · Oxford University Press eBooks · 2016
A standard sorites argument holds that, since someone with $50,000,000 is rich and someone with 57¢ isn’t, the following conclusion obtains: (Cut) for some n, someone with n¢ is rich but a person with n-1¢ isn’t. As Schiffer says, the premises seem determinately true, but the conclusion (Cut) neither determinately true nor determinately false. Schiffer concludes that the argument is neither determinately valid nor determinately invalid. But on an alternative conception of validity, it’s determinately invalid. One advantage of that alternative: modus ponens comes out determinately valid, whereas on Schiffer’s it doesn’t; indeed virtually no inference does. In addition, Schiffer’s division of partial beliefs into two kinds, governed by different laws, to characterize borderline belief states is questioned. Schiffer’s main contribution—showing that the belief states governing borderline cases don’t conform to standard probabilistic laws—stands on its own and doesn’t require the introduction of vagueness-related partial belief.