Stephen Schiffer

SI is a paradox because it presents four appearances that cannot all be veridical: first, it appears to be valid—after all, it’s both classically and intuitionistically valid; second, its sorites premiss, (2), seems merely to state the obvious fact that in the sorites march from 2¢ to 5,000,000,000¢ there is no precise point that marks the cutoff between not being rich and being rich; third, premiss (1), which asserts that a person with only 2¢ isn’t rich, is surely true; and fourth, the conclusion (3), which asserts that a person with 5,000,000,000¢—i.e. $50 million—isn’t rich, is surely false.

Pleonastic entities are entities whose existence is secured by something-from-nothing transformations, these being conceptually valid inferences that take one from a statement in which no reference is made to a thing of a certain kind to a statement—often a pleonastic equivalent of the first statement—in which there is a reference to a thing of that kind. The possibility of pleonastic entities is further explained in terms of the notion of one theory being a conservative extension of another. Propositions are pleonastic entities, and the way in which they are individuated shows how pleonastic propositions are both fine-grained and unstructured.

I. Vague Properties and the Problem of Vagueness The philosophical problem of vagueness is to say what vagueness is in a way that helps to resolve the sorites paradox. Saying what vagueness is requires saying what kinds of things can be vague and in what the vagueness of each kind consists. Philosophers dispute whether things of this, that, or the other kind can be vague, but no one disputes that there are vague linguistic expressions. Among vague expressions, predicates hold a special place in the problem of vagueness, for it’s their vagueness that is soritesgenerating. That puts the vagueness of predicates at the hub of the problem of vagueness, and there can be little doubt that we’ll be a short step from home if we can account for it. Any account of vagueness will of course require commitment to theses that are themselves foci of philosophical debate, but one can’t expect to get anywhere without taking on some as working hypotheses and then striving to say something that will be plausible if those hypotheses are plausible. One of the working hypotheses of this paper is that propositional attitudes and propositional speech acts are relations to propositions of some stripe or other, in the generic sense in which a proposition is an abstract, mind- and language-independent entity that has a truth condition, and has that truth condition both essentially and absolutely (i.e. without relativization to anything).1 The existence of propositions requires the existence of properties, in the generic sense in which a property is an abstract, mind- and language-independent entity that has an instantiation condition, and has that instantiation condition both essentially and absolutely. For present purposes it will be harmless to pretend that the propositions we believe and assert are Russellian propositions---structured entities whose basic constituents are the objects and properties our beliefs and speech acts are about. When a propositionalist speaks in loosey-goosey mode, she is apt to say that a sentence token is true just in case the proposition expressed in its utterance is true.