The metaphysical equivalence of three and four dimensionalism

I argue that two competing accounts of persistence, three and four dimensionalism, are in fact metaphysically equivalent. I begin by clearly defining three and four dimensionalism, and then I show that the two theories are inter-translatable and equally simple. Through consideration of a number of different cases where intuitions about persistence are contradictory, I then go on to show that both theories describe these cases in the same manner. Further consideration of some empirical issues arising from the theory of special relativity lead me to conclude that the two theories are equally explanatory, and thus finally that they are metaphysically equivalent.