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.
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, 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.
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.
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.