Now is the time

Australasian Journal of Philosophy 84 (3):311 – 332 (2006)
The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only 'real' time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the other. I shew that this translation is preserved at the metalinguistic level, so that equivalent truth conditions can be defined in a tensed metalanguage or an indexical metalanguage. I then make some remarks about the connection between proofs of relative consistency and metaphysical truth; and some historical remarks about Arthur Prior's use of formal logic in expressing his presentist views.
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DOI 10.1080/00048400600895805
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M. J. Cresswell (2010). Temporal Reference in Linear Tense Logic. Journal of Philosophical Logic 39 (2):173 - 200.
Takashi Yagisawa (2008). Modal Realism with Modal Tense 1. Australasian Journal of Philosophy 86 (2):309-327.

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