Abstract
“Three, two, one, zero...” the countdown ends. “Ready, steady..” — we are waiting attentively for the “go!”. We wait for a certain position of the hands of the clock or for an announcement on the radio, until, sure of having passed a certain boundary in time to which we have attached some meaning, we wish each other a happy new year. We conjure up time by conjuring up the moment of change. Doing so is a way of becoming aware of time. This can be felt especially when we notice that our becoming conscious of the beginning of the new year is always a little late with respect to the beginning itself. So, suddenly, we are facing questions of metaphysics. What is time? What is the relation between time and present? How can a boundary in time be conceived and experienced?
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Notes
Introduction 1 (Content)
Graham Priest: Inconsistencies in Motion, American Philosophical Quarterly Vol. 22, No.4, October 1985, p.339.
Roderick Chisholm: Beginnings and Endings, in: Peter van Inwagen (ed.): Time and Cause, Dordrecht 1980, p. 17.
David Bostock: Plato on Change and Time in the ‘Parmenides’, Phronesis 1978, p.238.
Brian Medlin: The Origin of Motion, Mind April 1963, p.155.
A11 talk of rest and motion in what follows is talk about rest and motion with respect to some freely chosen reference frame. With this in mind we can forget about Special and General Relativity for the rest of the book. As will be seen, the prominence of the change between rest and motion is a bit of a problem, since here the question of how to define rest and motion is involved and makes this change an exceptionally complicated example.
The ‘C’ stands for ‘Cambridge’, because this type of change is called ‘Cambridge change’, since Bertrand Russell first drew attention to it. Cf. Bertrand Russell: The Principles of Mathematics, London 1964 [first edition 1903], §442.
Richard Sorabji: Aristotle on the Instant of Change, Proceedings of the Aristotelian Society, Suppl. Vol. 50 (1976) [first version], p.69.
Even the mere existence of instants is extraordinary for some authors, though (probably, e.g., for Plato, cf. ch. 1,1.). Extreme opinions on this point are that talk of instants is reducible to talk of periods (Hamblin) or even to talk of simultaneity of events (William Charlton). Cf. C. Hamblin: Instants and Intervals, in: Studium Generale 24 (1971), pp. 127–134
W. Charlton: The Analytic Ambition, Oxford 1991, pp.83–87.
Strangely enough, it has sometimes been thought that the existence of such changes can be excluded a priori by uttering the words”natura non facit saltus“.
A useful summary of this debate is, e.g., found in Ralf Stoecker: Was sind Ereignisse?
Cf. L. Lombard: Relational Change and Relational Changes, in: Philosophical Studies 34 (1978); a similar opinion is found in Carol Cleland: The Individuation of Events.
Galton: The Logic of Aspect, Introduction.
The situation for temporally extended events apart from instantaneous ones: temporally extended events are typically heterogeneous (a property which can be characterized rather precisely, cf. introduction 2 and Galton loc.cit.). The difficulties are in the realm of events which do not take time. Unfortunately, if changes are events, they are events which take no time.
That both Plato and Aristotle had something to say about the moment of change has always been clear. However, so far only G.E.L. Owen has paid any attention to the fact that the relevant texts are very closely related. Cf. G.E.L. Owen: Tithenai ta Phainomena, in: J. Barnes/M. Schofield/R. Sorabji (eds.): Articles on Aristotle, vol.l, London 1975.
To my knowledge, the term ‘Neutral Instant Analysis’ was introduced by Norman Kretzmann in: Incipit/Desinit, in: Machamer/Turmbull (eds.): Motion and Time, Space and Matter, Columbus (Ohio) 1976, p. 114.
Introduction 2 (Form)
About the possibility of regarding tense logic as a logic of predicates, cf. Bertram Kienzle: Zustand und Ereignis, Frankfurt 1994, p. 10 and the translation of Prior’s ‘Tense Logic and the Logic of Earlier and Later’, p. 103 (original in A.N. Prior: Papers on Time and Tense, Oxford 1968). The ‘classic’ text of tense logic is Prior’s ‘Past, Present and Future’, Oxford 1967.
Prior’s (loc.cit.)”time a is p-ing“expresses this intuition especially clearly.
In my view, it would be wrong to think that they have ‘indefinitely short’ (or, worse, ‘infinitesimal’) duration. I cannot make any sense of that, since I think that whatever has an extension has a definite extension. My view has not been altered by learning about so-called non-standard analysis. It may be a formally satisfactory theory. The problem is in the realm of interpretation: only in interpreting the formal system does one commit oneself to talk about something which has an extension but no definite extension. Cf. about non-standard analysis: William Me Laughlin and Sylvia L. Miller: An Epistemological Use of Nonstandard Analysis to Answer Zeno’s Objections against Motion, in: Synthese, vol. 92, pp.371–384; Edward Nelson: Internal Set Theory — A New Approach to Nonstandard Analysis, in: Bulletin of the American Mathematical Society, vol. 83 (Nov. 1977), pp. l165–1198
Alain Robert:, Nonstandard Analysis, New York 1988.1 am grateful to Eva Maria Krause for telling me about non-standard analysis and for (controversial) discussions about it.
These expressions should be taken cum grano salts. There are good reasons for claiming that duration in the strict sense is peculiar to events, e.g. William Charlton’s idea that, since events have a duration in time, periods of time, if they had duration would have to have it in some kind of Super-Time. So in order to be very precise one should perhaps rather talk of the ability of a period to contain an event of a certain duration than of the duration of a period. Cf. William Charlton: The Analytic Ambition, pp.83–86.
Cf. C. Hamblin: Starting and Stopping, in: The Monist 53 (1969), pp. 410–425 and C. Humberstone: Interval Semantics for Tense Logic, in: Journal of Philosophical Logic 8 (1979), pp. 171–196. A sceptical evaluation of the project of Interval Semantics is found in Pavel Tichy: ‘Do we need Interval Semantics?’ (in: Lingusitics and Philosophy 8 (1985), pp.263–282) and in Antony Galton: ‘The Logic of Aspect’, Oxford 1984, ch.l.
loc.cit.
Cf. Hamblin: Instants and Intervals, pp.l27f.
Ibid., p. 131.
Ibid., p. 130.
Cf. Hamblin: Starting and Stopping, p. 130.
I here follow a suggestion for which I am grateful to Eva Maria Krause. Hamblin’s definition of containment is a little more complicated in using an O(verlap)’ relation between periods. A ?-relation as defined above intuitively represents containment in most imaginable kinds of branching time (an exception would be a rather odd time in which time branches can reunite after splitting up). Hamblin’s ?-relation does not, because his O’-relation does not intuitively represent overlap for branching time. I am grateful to Bertram Kienzle for pointing this out to me.
Hamblin: Instants and Intervals, p. 132. Another approach working with both instants and periods is found in Alexander Bochmann: Concerted Instant Interval Semantics I + II, Notre Dame Journal of Formal Logic Summer/Fall 1990, pp.404–414/580–601. An informal plea for this kind of time ontology is found in Richard Swinburne’s ‘God and Time’, and apparently also in Chisholm’s ‘Beginnings and Endings’ as well as in his ‘On Metaphysics’ (compare the chapter on ‘Boundaries’).
This distinction may look strange to the mathematician or logician. However, I really think that an instant is no more a pair of periods than a single child is a pair of parents, although in both cases a mention of the pair can be used for uniquely identifying the entity. Mentioning an entity A in order to uniquely identify an entity ? is not the same as identifying A with B.
Cf. Hamblin: Instants and Intervals, p. 132:“The double use of and’causes no ambiguity since we use [different...] letters for instants and for intervals”.
This convention is the exact opposite of a convention stated by Hamblin in ‘Instants and Intervals’. According to Hamblin, a temporal predicate satisfies a period only if what it is about is the case throughout the period. This convention is reflected in axioms 9 and 10 of his interval semantics in ‘Instants and Intervals’. Both conventions are formally possible. So one can decide which to use for practical reasons. It will be seen that, especially for reconstructing arguments of Aristotle in ch.1,2.,the opposite convention to Hamblin’s will be more practical in the context of this book.
Galton maintains that this is even characteristic of all events, and marks them off from states. It is, however, difficult to see how instantaneous events can be heterogeneously structured.
One should note, however, that *-~-P(c) does not hold C being a negation prefix equivalent to—i1). There is, of course, a period contained in ? which satisfies P, i.e. ? itself.
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Strobach, N. (1998). Introduction. In: The Moment of Change. The New Synthese Historical Library, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9127-0_1
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