Abstract: This chapter concentrates on philosophical theories of laws of nature that take for granted certain concepts of possibility, possible worlds, necessity, or physical probability. The accounts of Wilfrid Sellars, Storrs McCall, Peter Vallentyne, and Robert Pargetter are criticized. Crucial to any such account that draws on a notion of objective chance or probability is the ’horizontal-vertical problem’ (of accounting for statistical predictions based on assumptions about chance). It is argued that if the metaphysical point of view is maintained, then this problem is unsolvable.

Keywords: chance, horizontal-vertical problem, Storrs McCall, necessity, Robert Pargetter, possibility, possible worlds, probability, Wilfrid Sellars, Peter Vallentyne,