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The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. In what follows we show that the supervaluationist approach to singular reference, when wedded to the truthmaker idea, yields a framework of surprising power, which offers a uniform set of solutions to a range of problems regarding identity, reference and knowledge, problems which have hitherto been dealt with on an ad hoc basis. 1. The Problem of the Many You make a true judgment to the effect that Amundsen flew to the North Pole. On the theory to be advanced in what follows, it is in first approximation a certain oddly demarcated portion of reality—which might be labeled Amundsen’s flight—which makes your judgment true. Your judgment serves to set into relief this portion of reality against a background of other portions of reality which are traced over. At the same time the designated portion of reality somehow necessitates the truth of your judgment, which is to say: in any possible world in which your judgment and that portion of reality exist, your judgment is true.
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