Reduction and Elimination in Philosophy and the Sciences

Martin Pleitz”, e.g., is true at the unique point of personal
space constituted by me. But proper names already
presuppose the objects they name. So, a hybrid logic of
persons, when founded on natural language, cannot
reduce persons.
10. Logic and Metaphysical Commitment
Today, modal logics generally are seen as tools not for the
decision of metaphysical questions, but to give an internal
characterization of given structures. In this “Amsterdam
perspective” (Blackburn 2006, 330ff.), it is left entirely unspecified
what these structures are. It may therefore seem
strange that the preceding arguments about metric and
hybrid logic have led to the following substantial metaphysical
theses:
Instants, places and frames can be reduced to a perspectival
metaphysics of space-time (by metric logic).
Possible worlds can be reduced to maximally compatible
propositions (by hybrid logic).
Persons (and other enduring things) are the only
genuine objects we are left with.
But these metaphysical commitments do not rest on formal
considerations alone, but on reasons concerning the applicability
of logical systems to our ordinary use of natural
language. The reasons for perspectivist spatiotemporal
metaphysics lie in our practices of time-keeping and referring
to places. The reason for linguistic ersatzism about
possible worlds is given by our practices of describing
possible situations. And the existence of persons and
things is connected to the practice of naming. Only in cooperation
with the philosophy of language can logic answer
the question of what there is.
264
The Metaphysical Relevance of Metric and Hybrid Logic — Martin Pleitz
Literature
Blackburn, Patrick 2006 “Arthur Prior and Hybrid Logic”, Synthese
150, 329-372.
Müller, Thomas 2002 Arthur Priors Zeitlogik, Paderborn: Mentis.
Prior, Arthur N. 1957 Time and Modality, Oxford: Clarendon.
Prior, Arthur N. 1967 Past, Present and Future, Oxford: Clarendon.
Prior, Arthur N. 2003 Papers on Time and Tense. New Edition [eds.
Per Hasle, Peter Øhrstrøm, Torben Braüner and Jack Copeland],
Oxford: Oxford University Press.
Øhrstrøm, Peter, and Hasle, Per F.V. 1995 Temporal Logic,
Dordrecht: Kluwer.