Maxwell-Boltzmann Statistics and the Metaphysics of Modality

Synthese 133 (3):393-417 (2002)
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ABSTRACT. Two arguments have recently been advanced that Maxwell-Boltzmann particles are indistinguishable just like Bose-Einstein and Fermi-Dirac particles. Bringing modal metaphysics to bear on these arguments shows that ontological indistinguishability for classical (MB) particles does not follow. The first argument, resting on symmetry in the occupation representation for all three cases, fails since peculiar correlations exist in the quantum (BE and FD) context as harbingers of ontic indistinguishability, while the indistinguishability of classical particles remains purely epistemic. The second argument, deriving from the classical limits of quantum statistical partition functions, embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a third argument is considered that attempts to deflate metaphysical concerns altogether by showing that the phase-space and distribution-space representations of MB-statistics have contrary haecceitistic import. Careful analysis shows this argument to fail as well, leaving de re modality unproblematically grounding particle identity in the classical context while genuine puzzlement about the underlying ontology remains for quantum statistics



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Bruce Gordon
Northwestern University (PhD)

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