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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.
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Magali Roques

Abstract

Ockham’s approach to the problem of the instant of change as it is found in the Summa logicae I, chapter 5, and II, chapter 19, is usually described as “purely logical,” narrowing the treatment of “begins” and “ceases” to simplistic cases. The aim of this paper is to complement our knowledge of Ockham’s position on the problem of the instant of change by analysing the treatment of the problem he gives in his questions on the Physics 98-101. In these passages, Ockham adopts a “physical approach” in order to deal with problems related to the continuity of alteration and the production of the form of the mix from elementary qualities. To solve these problems, he is compelled to give up one of the most important claims at the basis of the logical approach that he adopted in the Summa logicae, namely that the distinction between permanent and successive entities is not relevant in the assignment of truth-conditions to propositions containing the aspectual verbs “beginning” and “ceasing.”

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Cecilia Trifogli

Abstract

Walter Burley (ca. 1275-after 1344) is the author of a treatise, entitled De primo et ultimo instanti, which is regarded as the most popular medieval work on the problem of assigning first and last instants of being to permanent things. In this paper, however, the author does not deal with this treatise directly. She looks instead at Burley’s Physics commentary to see how he applies the ideas presented in De primo et ultimo instanti to the solution of an Aristotelian puzzle about the ceasing to be (i.e., to exist) of the present instant (Physics IV, 10). In Burley’s interpretation, the relevant question raised by the puzzle is whether the present instant ceases to be when it is or when it is not. While Aristotle’s argument quickly dismisses the first alternative as absurd, Burley defends it by appealing to the ‘expositions’ of sentences about ceasing (desinit). Given that the sentence ‘this instant ceases to be’ has two expositions—(1) ‘this instant now is and immediately afterwards will not be’ (position of the present and negation of the future) or (2) ‘this instant now is not and immediately beforehand was’ (negation of the present and position of the past)—Burley maintains that the sentence is true in exposition (1) but not true in exposition (2), so that an instant ceases to be when it is and not when it is not.

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William O. Duba

Abstract

In a seminal article, Simo Knuuttila and Anja Inkeri Lehtinen drew attention to a “curious doctrine” holding that contradictories can be true at the same temporal instant, and identified the major defenders of the doctrine as John Baconthorpe, Landolfo Caracciolo, and Hugh of Novocastro. Normann Kretzmann later asserted as fact the suggestion by Knuuttila and Inkeri Lehtinen that the doctrine comes from a misreading of a passage from Aristotle’s Physics. In fact, a study of the relevant texts reveals that Hugh of Novocastro first elaborated the doctrine by building on the Scotist doctrines of synchronic contingency and simultaneous causation. As these doctrines require at the same instant of time an order of priority and posteriority between possibility and actuality, cause and effect, so, Hugh says, there must be prior and posterior different states of affairs. Landolfo Caracciolo made this doctrine notorious outside the Franciscan convent by using it in his principia debates, directly engaging the circle of Cardinal Iacopo Stefaneschi (Thomas Wylton, John of Jandun, and Annibaldo di Ceccano). John Baconthorpe, the first to (mis)cite the Physics passage, did not have any noticeable effect on the development of the doctrine.

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Gustavo Fernández Walker

Abstract

Previously, the author tried to show that some arguments in one of the two versions of Nicholas of Autrecourt’s Quaestio de intensione visionis are taken almost verbatim from the anonymous Tractatus de sex inconvenientibus. This paper concentrates on the arguments themselves in order to consider two main issues: (a) the ‘translatability’ of limit decision problems, manifest in Autrecourt’s juxtaposition of questions de maximo et minimo, de primo et ultimo instanti, and the intension and remission of forms; (b) the importance of Parisian discussions of limit decision problems prior to the adoption of the new analytical languages developed at Oxford. Thus, the paper is divided in two sections, the first concerning some arguments of Autrecourt’s question, the second focusing on the link between one of Autrecourt’s arguments and the medieval tradition of commentaries on Aristotle’s De caelo, in which it is possible to find some antecedents of the analytical approach that later Parisian scholars (Autrecourt among them) would apply to these problems.

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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?

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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.

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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.

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Frédéric Goubier and Magali Roques

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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.