'Now' and 'Then' in Tense Logic

Journal of Philosophical Logic 38 (2):229-247 (2009)
According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now” and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic
Keywords Quantified tense logic  “Now” and “then”  Actuality operator
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DOI 10.1007/s10992-008-9090-6
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Igor Yanovich (2015). Expressive Power of “Now” and “Then” Operators. Journal of Logic, Language and Information 24 (1):65-93.
Ulrich Meyer (2015). Tense Logic. Philosophy Compass 10 (6):406-419.
M. J. Cresswell (2010). Temporal Reference in Linear Tense Logic. Journal of Philosophical Logic 39 (2):173 - 200.

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