1 Several things should be said about (1). (a) I am not much concerned, here, with whether existence is a property. (1) can be read either as exists . (b) The sense of necessity operant here is the sense of necessity in quantified S5 given a Kripkean semantics in which the Barcan formual fails. (c) I prefer (1) as it is, i.e., because the latter commits one, on a natural interpretation, either to the view that all objects which exist exist in all possible worlds or to the view that objects have their essences in worlds in which those objects do not exist. To avoid confronting this issue, I adopt the weaker former over the latter (which implies the former).

2 Every property which is an essence, in my sense, will be an essential property in Plantinga's (except perhaps for existence, if it's a property at all), though not every essential property is an essence. Tautological properties, like being either green or non-green, are essences for me; but I don't mind that, for I am interested in what I shall call kinds and metaphysical categories; and those concepts will require the addition to (1) and (2) of condition (3), below, which will rule out tautological properties as being essences of kinds or metaphysical categories (if there is more than one kind of thing — and that I am, in this paper, taking for granted).

3 What I mean here is that if there is more than one kind of abstract entity, that is, abstract entities which are, say, propositions, sets, properties, then we could get, for a criterion of identity for abstract entities construed as such, nothing better than

where the expressions of the form ‘R(x,y)’, ‘R’(x,y)’, ‘R”(x,y)’, etc. each give a criterion of identity for the abstract entities which are propositions, sets, properties, etc., respectively. Criteria of identity of the form displayed I wish to call “disjunctive”, and I mean to rule out any class of objects, as forming a metaphysical category of thing or a kind of thing, whose members can have nothing better than a disjunctive criterion of identity. Of course, an acceptable criterion of identity for a class having an essence ф must meet other conditions as well (e.g., it must not contain, after ‘if and only if’, the identity sign flanking terms whose references are фs), but non-disjunctiveness is the only one that really concerns me here.

4 So, if the ф is a metaphysical category, then ф is a kind (but not necessarily vice versa), and if ф is a kind, then ф is an essence (but not necessarily vice versa).

5 A fourth possibility is that we've not been clever enough. This is different from the third case, for in this case, we might know perfectly well that we've got a kind on our hands and know what that kind's essence is, but Just not have been smart, lucky, or diligent enough to hit on the right criterion of identity. This possibility is, from a metaphysical point of view, uninteresting. And attacks on entities, based on Quine's dictum, when this possibility describes the actual state of the situation, are similarly uninteresting, though it might be difficult to say when that is the case.

6 This argument is Davidson's and it appears in his paper, “The Individuation of Events”, in Rescher, N. et al. (eds.), Essays in Honor of Carl G. Hempel (Dordrecht: D. Reidel, 1969), pp. 224-25.CrossRefGoogle Scholar

7 In Rescher, N. (ed.), The Logic of Decision and Action (Pittsburgh: University of Pittsburgh Press, 1967), pp. 96–103.Google Scholar Davidson's paper is to be found in that volume as well, pp. 81-95.

8 Ibid., pp. 116-17.

9 Brand, Myles has continued it in his paper, “Particulars, Events, and Actions”, in Brand, and Walton, (eds.), Action Theory (Dordrecht: D. Reidel, 1976).CrossRefGoogle Scholar

10 If we say (1) that an event, e, is located at a place, p, at a time, t, if and only if all objects, o, which are involved in e at t are in p at t, and (2) that an object, o, is involved in e at t if and only if it is the case that if e occurs (or is occurring) at t, then o changes (or is changing) at t, and a change in o at t is identical with e at t, then we can define ‘the minimal location of e at t’ as ‘the location of the smallest object a change in which is identical with e at t’. See “The I ndividuation of Events”, p. 228.

11 I am excluding, here, changes such as coming into existence and going out of existence. And I would also like a restriction placed in the choice of properties such that it will not be the case that something changes Just because it has and then lacks a property the having and then lacking of which is Just what that object's persisting consists in. Also, it should be noted that not every object which is the subject of some change, according to the criterion of change Just employed, is ipso facto the subject of some event. This distinction is discussed in the appendix to this paper. But, so far as the main body of the paper is concerned, one should understand talk of changes as talk of events.

12 A change, say, from being F to being G, takes place during t, if t is an interval of long enough duration to include the time at which the changing thing was F and the time at which it was G. A change takes place at t, if t is the shortest interval during which it takes place.

13 So, when I later speak of an object's exemplifying or having some dynamic property at a time t, t must be construed as an interval of time, not as an instant. Of course, an object can exemplify a static property or an instantaneous dynamic property at successive instants (and, hence, over an interval). And so, some property-expressions may be ambiguous with respect to its picking out a dynamic or an instantaneous dynamic property. But, no object can have a dynamic property at an instant; for to have a dynamic property at t is to have and then lack a static property, and that takes “two” times at least.

14 I want, here, to acknowledge my thanks to David Kaplan, for it was in discussion with him that the idea of a quality space in which things change arose. I do not know, however, whether or not he would approve of what I've done with this idea, or even how I have explicated it.

15 My thanks go to Alexander Rosenberg for this last observation which was made in the course of his comments on my paper, “Events and Quality Spaces”, read at the APA, Western Division, Meetings, 1 May 1976. The effects of this observation are felt in the second and third paragraphs of section V which were motivated by an example of Rosenberg's. Sections Ill and IV of this present paper are revisions of parts of my APA paper.

16 This and the previous paragraph might show what it is that is so plausible about, irrespective of the eventual outcome of, a criterion of identity for events given in terms of sameness of causes and effects.

17 The definitions which follow, particularly (D3), are motivated in addition by my interest in giving an account of events as the exemplifyings by objects of dynamic properties at times (which are intervals). This account comes in Section VI, and is ultimately motivated by my sketch in Section IV of the idea that events are movements through quality spaces by objects, where I take that idea to capture the idea that events are changes.

18 The objects which are to serve, in my view, as atomic are objects which are extended in time and have no temporal parts. Thus, when I speak of an object's exemplifying a property at a time (either an instant or an interval), I do not mean that some object, x-at-t, has timelessly some property P. Nor do I mean that the object, x, has the property of being P-at-t. I take ‘has the property P at t’ to express a two-place relation holding between objects and times.

19 The complication in (D3), which begins with (b), is needed because we will not want to say that two events, one consisting of a movement by an object from having P_i to having P_k “directly”, and one consisting of a movement by an object from having P_i to having P_j to having P_k, are two events of the same type. With the complication, we can have an atomic event which consists of an atomic object's movement from having P_i to having P_j to having P_k. But, if a movement is one such that if its subject passes through P_j in getting from having P_i to P_k. and it does so only contingently, then that movement cannot be atomic and must be construed as a sequence of atomic movements. One price which must be paid for this is that some atomic events will be construable as temporal sequences of atomic events as well. But with the complication, though it may be the case that some atomic events have atomic events among their parts, atomic events “of the same type” must always have exactly the same atomic event parts. As an example, no movement (in a flat two-dimensional space, say) from a point p₁ to a point p₂ can be atomic, if one instance of that “type” can be straight and another curved. The restriction (b) in (D3) makes the “directionality” (in general) of a movement (change) part of the essence of such movements (changes). The result of all this, as will be clear, is that some events may have more than one canonical description; this, however, will not imply that some events may have more than one essence, in the sense of ‘essence’ to be discussed. So, in what follows, I shall speak of the canonical description of an event; but, though some events can have more than one, this simplification will be harmless, since from a canonical description of an atomic event construed as a sequence we can, by consulting the relevant quality space, derive the canonical description of the event construed as not being a sequence. For if we know that an atomic event is being construed as a sequence, we know automatically what that sequence must be. The restriction in (D3) shows us that, for it shows that the only sequences which can be atomic events are those events which must (according toT) pass certain points in the quality space in getting from P_i to P_k.

20 I suspect that not every combination of simultaneous atomic events will be a non-atomic event; there seems to be no event which consists of this pot of water's boiling at t and an eruption of a volcano on Jupiter at t. Similarly, not every group of atomic and non-atomic events occurring over a stretch of time counts as a sequence; there seems to me to be no event which consists of this pot of water's boiling at t and then Jupiter's turning on its axis at t'. Surely, there must be some restrictions dealing with which combinations of events constitute events. But it is not my intention, here, to delve into this question.

21 ‘Rots’ also might pick out an instantaneous dynamic property (if it were an atomic event verb), for it would be true of the wood at each instant during which the wood is rotting, and its being true of the wood at any such instant would imply that at different surrounding instants the wood had different static properties. But then it would also have a dynamic sense, in which it picks out a property of the wood which the wood would have at the time of the whole interval of time at which the wood was rotting (viz. the property of first being wholly unrotten and then completely rotten). And it is the latter, dynamic, property that is of concern here. Of course, the fact that the wood has the dynamic property of rotting is not independent of the fact that it has at instants in the interval of the rotting the instantaneous dynamic property of rotting.

22 The event types to which events which are not atomic belong can be derived from the atomic event types to which their atomic constituents belong.

23 See, for example, Kim's “Events and Their Descriptions”, in Essays in Honor of Carl G. Hempel, pp. 198-215, his “Events as Property Exemplifications”, in Action Theory, pp. 159-77, and Goldman's A Theory of Human Action (Englewood Cliffs: Prentice-Hall, 1970). It might be noted here that my canonical descriptions cannot be descriptions of states, but only of events. I am inclined not to lump events and states into one category of thing, since, it seems to me, there are important differences between events and states, and I don't see any overriding motive for ignoring those differences. But this is not the place to go into this issue.

24 It is, of course, to be understood here that what is contingent or not must be relativized to the theory against the background of which events are given their canonical descriptions.

25 Of course, two atomic events of the same type involving the same subject can occur during a certain period of time, but not at a certain period of time. An event occurs at t when t is the shortest interval of time during which that event occurs.

26 Of course, two or more events of the same type which are not atomic could occur simultaneously; but for that to be the case, at least some of their atomic constituents must be different.

27 In “On Events and Event-Descriptions”, Fact and Experience, ed. J. Margolis, (Oxford: Blackwells, 1969), p. 81.

28 I am not especially concerned here with the fact that ‘x ф ed at t’ is general with respect to фings by x at t, while ‘x's exemplifying ф at t occurred’ is not.

29 Thus, one can define ‘e is a ф ing by x at t’ as follows: an event, e, is a ф ing by x at t if and only if there is an object, x, and an interval of time, t, such that either (a) e is x's exemplifying ф at t, where being a ф ing is not the essence of e, or (b) e is x's exemplifying ф at t, where being a ф ing is the essence of e. Note that if e is an atomic event and being a ф ing is the essence of e, then e = [x, ф,t], but not otherwise. Also, it seems as if the Kim-Goldman definition of 'e is a ф ing by x at t’ would delete alternative (a).

30 See my paper, “Actions, Results, and the Time of a Killing”, Philosophia 8 (1978), for a defense of a version of this analysis.

31 See Goldman, op. cit., pp. 25-26.

32 Another class of identity claims, typified by ‘Sebastian's stroll = Sebastian's leisurely stroll’, gets dealt with in a different way. The issue here, it seems to me, has to do with events and vectors of events. It seems unlikely that being a leisurely stroll should be the essence of any event, even if being a stroll were. Being leisurely seems to be better construed as a property of events (rather than being a leisurely stroll being construed as a property of strolling things); and being a leisurely one seems clearly to be a contingent property of such events.

33 See Kim's “Noncausal Connections”, Nous 8 (1974), pp. 41-52, and my “Events, Changes, and the Non-extensionality of ‘Become’”, Philosophical Studies 28(1975), pp. 131-36.

34 See my just cited paper for the suggestion, and Kim's for the reasons.

35 In “Events and Quality Spaces”.

36 This criterion is motivated and defended in my paper, “Relational Change and Relational Changes”, Philosophical Studies (1978).

37 I would like to express my gratitude to Michael McKinsey with whom I spent a great deal of time (a lot of his patience) talking about the issues discussed in this paper. He made some very valuable suggestions (especially in section I, but elsewhere as well), and tried to make me less muddled. I am certain that his suggestions were valuable; but I am not certain that he succeeded in making me less muddled, though that was not his fault. And my thanks also go to Lawrence Powers for some helpful suggestions. I am also indebted to the editors and referees at the Canadian Journal of Philosophy whose suggestions and criticisms forced me to make this paper better than it would otherwise have been. I am, of course, solely responsible for what is in this paper.