Maxwell–Boltzmann Statistics And The Metaphysics Of Modality

Abstract

Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical partition functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics.