The Principle of Sufficient Reason

____________________________________________

“The Principle of Sufficient Reason.” Journal of Philosophy XCVIII (2001): 55-74.

(published version) [preprint]

Abstract. Ian Hacking once observed that symmetry-driven counterexamples to Leibniz’s Principle of the Identity of Indiscernibles are inherently inconclusive, since one can always deny that the description proffered manages to accurately characterize any possible world, maintaining instead that the only genuine possibility in the neighborhood arises when the qualitatively identical objects of the original description are taken to be numerically identical. I claim that Leibniz’s Principle of Sufficient Reason can be given a similar line of defense: a description of a set of possible worlds which includes pairs of worlds with identical qualitative structures can always be taken to correspond to the sparser set of possibilities which arises when qualitatively identical worlds are identified. This paper falls into two parts, held together by an admittedly loose interpretation of Leibniz: the later sections form a commentary on some theorems concerning symmetries and the structure of the spaces of physical possibilities of classical mechanics; the first few sections are intended to set this discussion in context.

Note: This paper features a very puzzling argument that purports to show that if two states of a Hamiltonian system are related by a Hamiltonian symmetry, then they represent qualitatively indistinguishable states. The claim argued for is false. See “Symmetry and Equivalence.”

_____________________________________________