Penelope Maddy has defended a modified version of mathematical platonism that involves the perception of some sets. Frederick Suppe has developed a conclusive reasons account of empirical knowledge that, when applied to the sets of interest to Maddy, yields that we have knowledge of these sets. Thus, Benacerraf's challenge to the platonist to account for mathematical knowledge has been met, at least in part. Moreover, it is argued that the modalities involved in Suppe's conclusive reasons account of knowledge can be (...) handled without recourse to either laws of nature or possible worlds, and that this approach is preferable. (shrink)

Imagine a model of the universe that, if true and known to be true, would solve the following philosophical problems: the direction and flow of time, an ontology for laws of nature, the interpretation of quantum mechanics, the interpretation of probability, a semantics for counterfactuals, trans-world and trans-temporal identity, essentialism and natural kinds, and free will and responsibility. The successful solution to these problems would convince most of us that we should, at the very least, give this model serious consideration. (...) This is the argument of Storrs McCall's A Model of the Universe: Space-Time, Probability, and Decision. Assume that the branched-tree model of the universe is true, and all these problems are solved. Thus, the branched-tree model should at least be a plausible candidate for the true model of the universe. (shrink)