Synthese 193 (11):3567-3577 (2016)

Martin Pleitz
Westfälische Wilhelms Universität, Münster
I will show how a metaphysical problem of Arthur Prior’s can be solved by a logical tool he developed himself, but did not put to any foundational use: metric logic. The broader context is given by the key question about the metaphysics of time: Is time tenseless, i.e., is time just a structure of instants; or is time tensed, because some facts are irreducibly tensed? I take sides with Prior and the tensed theory. Like him, I therefore I have to deal with a more specific metaphysical question: How can the instants of tenseless time be reduced to tensed facts? This is the point where, on the technical level, hybrid logic and metric logic come in. For present purposes, both can be seen as species of tense logic; and both are creations of Prior. In his argument for the tensed theory of time, Prior used hybrid tense logic to reduce instants. But, as he himself pointed out, this reduction runs into deep problems, because it immediately generalizes to other categories, for example and most importantly to persons. My main aim is to show that metric logic does not run into similar difficulties: It will help the tensed theory reduce instants, but it leaves persons untouched. I will also give reasons for preferring a metric to a hybrid logic of time that are independent of the metaphysical issue of reduction, but concern temporal reasoning, natural language semantics, and the epistemic side of time-keeping.
Keywords Arthur Prior  Tense logic  Metric logic  Hybrid logic  Philosophy of time  Perspectivism  Reduction
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DOI 10.1007/s11229-015-0931-x
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References found in this work BETA

Naming and Necessity.Saul Kripke - 1980 - Harvard University Press.
Past, Present and Future.Arthur Prior - 1967 - Clarendon Press.
Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.
Relatively Unrestricted Quantification.Kit Fine - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. pp. 20-44.

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