Indivisible Temporal Boundaries from Aristophanes until Today

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This paper provides a short historical and systematic survey of parameters, problems, and proposals concerning the theoretical treatment of indivisible temporal boundaries throughout the ages. A very early trace of thinking about them is identified in Aristophanes’ comedy The Clouds. The approach of logicians in the late Middle Ages is placed in a broad context. Links of this topic to the issues of vagueness, modality, space and quantized time are discussed.


A Journal for Medieval and Early-Modern Philosophy and Intellectual Life




N. Belnap, “Branching Space-Time,” Synthese 92/3 (1992), 385-434; N. Strobach, Alternativen in der Raumzeit (Berlin, 2007).


Strobach, The Moment of Change, 2-7.


Strobach, The Moment of Change, 124-145. Cf. R. Sorabji, “Aristotle on the Instant of Change,” Proceedings of the Aristotelian Society, Supplementary Volume 50 (1976), 69-91, revised reprint in Articles on Aristotle, vol. iii, ed. J. Barnes, M. Schofield and R. Sorabji (London, 1979), 159-178, and R. Sorabji, Time, Creation and the Continuum (Chicago, 1983), ch. 26, “Stopping and Starting,” 403-421; F. Jackson and R. Pargetter, “A Question about Rest and Motion,” Philosophical Studies 53 (1988), 141-146; A. Galton, The Logic of Aspect (Oxford, 1984).


Strobach, The Moment of Change, 171-182. Cf. C.L. Hamblin, “Starting and Stopping,” The Monist 53 (1969), 410-425; cf. also C.L. Hamblin, “Instants and Intervals,” Studium Generale 24 (1971), 127-134.


Strobach, The Moment of Change, 146-160. Cf. F. Brentano, Philosophische Untersuchungen zu Raum, Zeit und Kontinuum (Hamburg, 1976); R.M. Chisholm, “Beginnings and Endings,” in Time and Cause, ed. P.V. Inwagen (Dordrecht, 1980), 17-25; B. Medlin, “The Origin of Motion,” Mind 72 (1963), 155-175.


Cf. Strobach, The Moment of Change, 161-170, 109-110.


G. Priest, “To Be and Not To Be: Dialectical Tense Logic,” Studia Logica 41 (1981), 249-268.


S. Knuuttila, “Remarks on the Background of Fourteenth Century Limit Decision Controversies,” in The Editing of Theological and Philosophical Texts from the Middle Ages, ed. M. Asztalos (Stockholm, 1986), 245-266; S. Knuuttila and A. Inkeri Lehtinen, “Change and Contradiction: A Fourteenth Century Controversy,” Synthese 40 (1979), 189-207.


Strobach, The Moment of Change, 198-234.


Detailed discussion: Strobach, The Moment of Change, 20-46.


Bostock, “Plato on Change and Time,” 229-242.


C. Strang, “Plato and the Instant,” Proceedings of the Aristotelian Society, Supplementary Volume 48 (1974), 63-79.


Such a rule is sketched in Strobach, The Moment of Change, 206-224. Within the framework that is presupposed there, there is nothing wrong with that. However, conceptual frameworks themselves, although they are indispensable for structuring a discussion, should not go unquestioned.


A. Rumberg, “Transition Semantics for Branching Time,” Journal of Logic, Language and Information 25/1 (2016), 77-108; A. Rumberg, Transitions Toward a Semantics for Real Possibility (Utrecht, 2016).


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