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Edited by Frédéric Goubier and Magali Roques

Since antiquity, philosophers have investigated how change works. If a thing moves from one state to another, when exactly does it start to be in its new state, and when does it cease to be in its former one? In the late Middle Ages, the "problem of the instant of change” was subject to considerable debate and gave rise to sophisticated theories; it became popular and controversial again in the second half of the twentieth century. The studies collected here constitute the first attempt at tackling the different aspects of an issue that, until now, have been the object of seminal but isolated forays. They do so in through a historical perspective, offering both the medieval and the contemporary viewpoints.
Contributors are Damiano Costa, Graziana Ciola, William O. Duba, Simo Knuuttila, Greg Littmann, Can Laurens Löwe, Graham Priest, Magali Roques, Niko Strobach, Edith Dudley Sylla, Cecilia Trifogli and Gustavo Fernández Walker.

Can Laurens Löwe

Abstract

This paper examines the accounts of limit decision advanced by Hervaeus Natalis and Durand of St. Pourçain in their respective discussions of the sanctification of the Blessed Virgin. Hervaeus and Durand argue, against Aristotle, that the temporal limits of certain changes, including Mary’s sanctification, should be assigned in discrete rather than continuous time. The paper first considers Hervaeus’ discussion of limit decision and argues that, for Hervaeus, a solution of temporal limits in terms of discrete time can coexist with an Aristotelian continuous time solution because Hervaeus takes continuous and discrete time to be two non-intersecting, but correlated time-series. The paper next examines Durand’s account of limit decision and argues that Durand rejects Hervaeus’ correlation assumption as well as Aristotle’s continuous time solution.

Simo Knuuttila

Abstract

Hugh of Novocastro, Landolfo Caracciolo, John Baconthorpe, and some other medieval authors argued that there are real contradictions in nature. The background of this early fourteenth-century theory was the Aristotelian question of how to determine the instant of change between p and ~p. The argument was that these are simultaneously true at the temporal instant of change if it is an instant of changing. The author’s aim is to discuss the background of this view in Henry of Ghent’s theory of instantaneous change from potentiality to actuality at that very instant.

Graham Priest

Abstract

Instantaneous changes may well be thought to give rise to contradiction. If one endorses an explosive logic, where contradictions entail everything, this is entirely unacceptable. However, if one deploys a paraconsistent logic, which keeps contradictions under control, one may give perfectly coherent and precise models of such changes. In In Contradiction the author showed how and he explored the philosophical implications of the model. Here, the author revisits the issue in the light of a recent critique by Greg Littmann.

Greg Littmann

Abstract

Graham Priest has argued that changes occur at a moment of change in which objects are in a contradictory state, being in both the state changed from and the state changed to. In “Moments of Change,” the current author rejected this model on the grounds that every change would require an infinite number of other changes, and that for similar regress problems, the model is not compatible with the Leibniz Continuity Condition that Priest appeals to in the model’s support. In “Contradiction and the Instant of Change Revisited,” Priest rightly points out in response that any regress can be stopped by allowing that some changes can occur without a moment of change and that there are some exceptions to the LCC in the case of change.

It is argued here that while the regress can be stopped by allowing for exceptions to the rules, the more exceptions that must be allowed and the more similar the excepted cases are to cases of supposed contradiction, the less attractive both the contradictory account of change and the LCC should be. Secondly, it is argued that the intuitions that make the contradictory account of change seem appealing are likely to disappear if we adopt an eternalist model of spacetime, which we should do in any case in order to best accommodate the special theory of relativity. In particular, eternalism undermines our intuitions that there must be a moment of change in order for change to occur, that contradictory moments are required to allow for a Laplacian universe, that motion must be intrinsic to an object at a time, and that change obeys the LCC.

Niko Strobach

Abstract

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.

Frédéric Goubier and Magali Roques

Damiano Costa

Abstract

The author argues that medieval solutions to the limit decision problem imply four-dimensionalism, i.e., the view according to which substances that persist through time are extended through time as well as through space and have different temporal parts at different times.

Graziana Ciola

Abstract

In this paper, the author offers an introduction to Marsilius of Inghen’s treatment of expositiones of sentences de incipit and de desinit in his treatise on Consequentiae, with an analysis of the various modi exponendi presented by Marsilius and an edition of the text. The author argues that, in the split between physical and logical approaches to the issues arising in analyses of incipit and desinit, Marsilius’ theory presents some hybrid features, but tends towards the logical end of the spectrum.

Edith Dudley Sylla

Abstract

In his De primo et ultimo instanti, Walter Burley paid careful attention to continuity, assuming that continua included and were limited by indivisibles such as instants, points, ubi (or places), degrees of quality, or mutata esse (indivisibles of motion). In his Tractatus primus, Burley applied the logic of first and last instants to reach novel conclusions about qualities and qualitative change. At the end of his Quaestiones in libros Physicorum Aristotelis, William of Ockham used long passages from Burley’s Tractatus primus, sometimes agreeing with Burley and sometimes disagreeing. How may this interaction between Burley and Ockham be understood within its historical context?