Abstract
In the second part of this book I will present, put into some systematic order and evaluate attempts at a description and classification of the moment of change which have been made in our century. Chronological order is unimportant now. The texts will be classified according to the four systematic options one has for describing the moment of change: the either/or-option (ch.II,1), the either-way-option (ch.II,2), the both-statesoption (ch.II,3) and the neither/nor-option (ch.II,4). Since exclusive application of just one option will prove to yield unsatisfactory results, a further chapter (ch.II,5) will present a good compromise: a mixed description using the neither/nor- and the either/or-option, which is known by the somewhat misleading name of ‘Neutral Instant Analysis’.
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Notes
In the first version of his article ‘Aristotle on the Instant of Change’, Sorabji still views his own suggestion as an interpretation of the relevant passages in Aristotle. The reason for this is that in this version he favours the opinion that Aristotle allowed talk of rest and motion at instants. He abandoned this position in the second and third version (ch.26 of ‘Time...’).
Sorabji: Time..., p.405.
Ibid., pp.406f.
Sorabji: Aristotle... [second version], p.72.
lbid.: “We must make a recommendation [...] It would be reasonable but not mandatory. Reasonableness is all we need in order to escape the charge of arbitrariness.”
lbid.
Sorabji: Time..., pp.405f.
Moody shows that the concept of momentary velocity developed gradually in the late Middle Ages and was by no means a sudden revolution brought about by a few Renaissance physicists. Of special importance were the contributions of some logicians of Merton College, Oxford, among them Willam Heytesbury. Cf. Ernest A. Moody: Laws of Motion in Medieval Physics, in: Studies in Medieval Philosophy, Science and Logic, Collected Papers 1933–1969, University of California Press, Berkeley 1975, pp.189–201.
Frank Jackson/Robert Pargetter: A Question about Rest and Motion, in: Philosophical Studies 53 (1988), pp.141–146.
Cf. Ibid., p.143, point (vi).
Ibid., p.142.
Ibid., p.144.
Ibid., p.141.
Jackson/ P argetter are right in remarking (p.141): “ W e might have specified X ’s position over time by : s= 0 for t 0, s= t for t > 0 . This specification and the original one are precisely equivalent. They put X in exactly the same positions at the same times.”
Ibid., p.144.
Ibid.
Ibid., p.146.
Definition: An object a moves ‘uniformly’ throughout a period c if the proportion of the distance covered by a in c to the duration of c equals the proportion of the distance covered by a in any subperiod c 1 of c to the duration of c 1 , or (which amounts to the same) the local function of a is linear with respect to the interval of all instants which fall within c.
In this case the proportion of the distance covered in c to the duration of c does not equal the proportion of the distance covered in any subperiod c1 of c to the duration of c 1 and the local function of a is not linear with respect to the interval of all instants which fall within c.
Jackson/ Pargetter, p.141.
The question also arises whether the importance of the difference between abrupt and smooth change of ‘momentary velocity’ might not be exaggerated if it is assigned such a crucial role for the description of the moment of change. This difference does not seem to have anything to do with the questions from which philosophers started out (Plato and Aristotle had no idea of this difference). That it might be problematic to lay very strong emphasis on this difference can be seen in Chris Mortensen’s ‘The Limits of Change’ (Australasian Journal of Philosophy, March 1985, Vol. 63 No.1, pp.1–10). It contains valuable criticism of other authors on the moment of change; and this initially appears to be the article’s intended theme. However unfortunately then Mortensen becomes hopelessly entangled in the question “Is Change Continuous?”without thereby obtaining any result about the moment of change.
Peter Thomas Geach: God and the Soul, London 1969, pp.71f.
Betrand Russell: The Principles of Mathemathics, London 1964 (first edition 1903), §442.
Ibid.
Cf.Geach: God and the Soul, pp.91, 99. This criticism is the core of a debate about how one might amend the Cambridge-Criterion in such a way that the difference between mere ‘relational change’ on the one hand and ‘real change’ on the other hand is reflected by it. In my view, all attempts to do so have shown no more than that Russell’s original formula is inadequate for this (this is also Geach’s opinion in loc.cit.). Cf. for this debate Carol Cleland: The Difference between mere Cambridge Change and Real Change, in: Philosophical Studies 60 (3), Nov. 1990, pp.257ff.; Paul Helm: Are Cambridge Changes Non-Events?, in: Analysis 1975, pp.140–144; and: Zum Problem der Veränderung und ihrer Feststellung, in: Ratio 14 (Nov. 1977), pp.35–39; Frederick Schmitt: Change, in: Philosophical Studies 34 (1978); P.T. Smith: On the applicability of a criterion for change, in: Ratio 15 (1973), pp.312–319.
A.J. Ayer, Russell and Moore — The Analytical Heritage, London 1971, p.17.
Peter Thomas Geach: Truth, Love and Immortality, London 1979, p.91.
V.Wright introduced the T-operator in his article ‘And next’ for discrete time (Acta Philosophica Fennica Bd. 18, 1965, p.293–304), for continuous time in ‘And then’ (Commentationes Physico-Mathematicae of the Finnish Society of Sciences, vol. 32, No 7, 1966). The discrete version is of no interest here. A very readable introduction about the Toperator is ch.2 of his ‘Norm and Action’ (London 1963). The T-operator also plays an important role in ‘Time, Change and Contradiction’ (Philosophical Papers vol. 2, London 1983).
V.Wright calls the propositions which the T-operator takes ‘generic propositions’. They are, as his description makes clear, just what is usually called ‘temporally indefinite propositions’. v Wright has a very complicated classification of propositions according to the kinds of facts they reflect, which I shall neglect here.
According to Galton, both statements have logically nothing in common with the sentence ‘I write a book’.
The examples are all taken from the introduction to Galton’s ‘Logic of Aspect’; for an impression of how event logic works one should read at least the first three chapters of it.
Galton: The Logic of Aspect, pp.5f.
This might mean a lot of things: is it taking place if I do not finish the book? Is it taking place during my coffee break? Galton tries to catch the various possible meanings of ‘is just taking place’ in the last chapters of ‘The Logic of Aspect’ by different versions of Prog. We can neglect those (otherwise important) details here.
I am grateful to Bertram Kienzle for suggesting this expression (German: ‘Präsenslücke’).
Galton: The Logic of Aspect, p.5.
Ibid., p.15. There is obviously some sort of parallel here between ‘event’ and ‘res successiva’ as well as between ‘state’ and ‘res permanens’. Galton himself draws a connection between ‘event’ and kívησtS as well as between ‘state’ and ε vɛpγεa (which I find less convincing).
Ibid., p.18.
One should note that Galton views the state/event-dichotomy not as an ontological difference but as a difference in describing the world: “The main difference between these two ways of presenting the situation is that in presenting it as an event we regard Jane’s swimming as a unitary whole with a definite beginning (when she starts swimming) and a definite end (when she stops), wheras if we present it as a state we do not treat it in this way.” (Galton: The Logic of Aspect, p.24).
It is quite surprising that the first operator which Galton introduces deals with a kind of event which is untypical and does not agree with the intuition concerning events from which Galton originally motivated his project.
Ibid., p.61.
(Def. P*) P*α = a v Pa. (Def a v Fa.
Galton: The Logic of Aspect, p.50.
Ibid., p.33. Galton provides a second argument as to why a ‘ p/p-change’ must be ‘ instantaneous’ :“...although the change can only be located within an interval, and not at a moment, it is still an instantaneous change because there is no lower limit to the length of intervals which contain it.” (Logic of Aspect, p.34). This is rather cryptic. Galton’s reasoning seems to be: ‘Instantaneous’ means ‘has no duration’. Whatever has a duration must have a definite duration by ‘filling’ a certain interval. But for any interval in dense time which contains a change there is another interval which is shorter and contains the change, too. So an interval which contains a change may be chosen to be arbitrarily short. An interval which is to contain an event of definite duration cannot be chosen to be arbitrarily short. Therefore a change has no duration, but is instantaneous. This reasoning is definitely weaker than the first one. Kienzle is right in criticizing: “Da er [Galton] die Instantaneität eines Wahrheitswertwechsels [...] damit erläutert, daß die Länge der Intervalle, die ihn enthalten, keine untere Grenze haben [...], sollte man eigentlich annehmen, daß sie von Null verschieden ist.” (“Since Galton explains the instantaneity of a truth-value change [.. by saying that ] that there is no limit as to the shortness of intervals which contain it, [...] one should expect it to be greater than zero.) Cf.Bertram Kienzle: Cambridge-Wechsel, Prima Philosophia 1991, p.108).
Ibid., p.100.
It is important to remember that combining version C of the logical reconstruction, which avoids a violation of the LEM, with Plato-1 does not make any sense.
Galton: The Logic of Aspect, p.34. Similar, but also similarly unclear: v Wright’s treatment of change taking place ”...at the ‘point of division’...during the interval in question” (Time, Change and Contradiction XIV, p.128).
Antony Galton: The Logic of Occurrence in: Antony Galton (ed.) Temporal Logics and their Applications, London 1987, pp.169–196. Page references here refer to the authorized German translation in ‘Die Logik des Vorkommens’ by Bertram Kienzle in: Bertram Kienzle (ed.): Zustand und Ereignis, Frankfurt am Main 1994, pp.377–412. The Vs and Ns in the names of the sets are taken from the translation, too. They are derived from ‘before’ (German ‘vorher’) and ‘after’ (German ‘nachher’).
Galton: Die Logik des Vorkommens, p.387f.
Ibid., p.388.
Ibid., p.389.
In ‘The Logic of Occurrence’ Galton also introduces a simultaneity-operator for events. By means of it, he tries to reduce talk of instants to talk of the simultaneity of events (Cf. a similar project in Charlton’s ‘Analytic ambition’). The definition of this operator involves some commitment as to how to describe the moment of change. Galton’s ‘solution’ is to assign a first instant and deny a last instant to every event (this is due to a in the definition on p.406) which can hardly be taken seriously. Galton himself views the part of his article in which this definition occurs rather as the presentation of a project than as its elaboration (cf.p.412) .
Galton: Die Logik des Vorkommens, p.406.
lbid.
This property is also called ‘convex’. The following is characteristic of it: if t lies between t’ and t”, and t’ nd t” are elements of v, then t is also an element of v
Cf. Kienzle: Cambridge-Wechsel, definition 5, p.110.
Ibid., p.111.
Ibid., p.112.: “[Ein Cambridge-Wechsel läßt sich]... durchaus als etwas in der Zeit Vorkommendes auffassen. Jedenfalls sind die Cambridge-Übergänge, aus denen ein solcher Wechsel besteht, zeitlich ausgedehnte Prozesse. Und [...es] gibt [...] in einer kontinuierlichen Zeit tatsächlich keine untere Grenze für die Länge der Intervalle, die einen solchen Übergang enthalten.”
Kienzle calls Cambridge-transitions ‘processes’, using the word in a different sense to that in which I use it.
I am grateful to Bertram Kienzle for a very detailed discussion of his approach and my criticism. I could not have formulated it as clearly as this without his support and explicit encouragement.
If he wanted to express this in an Aristotelian manner, he might very well say that an ‘occurrence’ in Kienzle’s sense is an_εv ώI of the taking place of a change, but no ɛv ω πpέτε, of which he could still claim that it does not exist. Cf.ch. I, 2.4.2.
In Aristotelian terminology: for every C-transition there is another C-transition which is superior to the first one with respect to the taking place of the change.
Taking, of course, ‘aspect’ in its original, concrete sense: the way of looking at something; not ‘aspect’ as an abstract noun or as a technical term of grammar.
In this sense, aspects correspond to ‘Gegebenheitsweisen‘ in Frege’s sense. Cf. about ‘Gegebenheitsweisen’ (aspects in the concrete sense) Bertram Kienzle: Identität und Erkenntniswert — eine fast fregesche Deutung, in: Allgemeine Zeitschrift für Philosophie 10/1985, pp.27–40.
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Strobach, N. (1998). The Either/or-Option. In: The Moment of Change. The New Synthese Historical Library, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9127-0_6
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