‘Now’ and ‘Then’ in Tense Logic

Journal of Philosophical Logic 38 (2):229-247 (2009)
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Abstract

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

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Ulrich Meyer
Colgate University

Citations of this work

Expressive Power of “Now” and “Then” Operators.Igor Yanovich - 2015 - Journal of Logic, Language and Information 24 (1):65-93.
Times in Tense Logic.Ulrich Meyer - 2009 - Notre Dame Journal of Formal Logic 50 (2):201--19.
Tense Logic.Ulrich Meyer - 2015 - Philosophy Compass 10 (6):406-419.
Temporal Reference in Linear Tense Logic.M. J. Cresswell - 2010 - Journal of Philosophical Logic 39 (2):173-200.

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References found in this work

From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
On what there is.W. V. Quine - 1953 - In From a Logical Point of View. Cambridge, Mass.: Harvard University Press. pp. 1-19.
Time and modality.Arthur N. Prior - 1955 - Westport, Conn.: Greenwood Press.
Symposium: On What there is.P. T. Geach, A. J. Ayer & W. V. Quine - 1948 - Aristotelian Society Supplementary Volume 25 (1):125-160.

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