The main champion of an ontology of events has been Donald Davidson. Davidson's argument for an ontology of events is that an ontology of events lets us give a good analysis of certain sorts of sentences, particularly action sentences.

Consider the following two sentences. "Brutus stabbed Caesar with a knife." "Brutus stabbed Caesar." Obviously, the first of these sentences entails the second. But if we treat these sentences in the way which we all learn in introductory logic, this entailment is completely mysterious. In introductory logic, we learn to symbolize the first sentence using a three-place predicate, "x stabbed y with z." We learn to symbolize it as follows: (Ez)(z is a knife, and Stabbed(Brutus, Caesar, z) ). The second sentence, however, we learn to symbolize using a two-place predicate, "x stabbed y": Stabbed(Brutus, Caesar). But ordinary first-order logic treats these as two different predicates, and thus, given these symbolizations, we cannot show, by constructing a derivation, that the first of these sentences entails the second.

We might try to solve this problem by symbolizing the second sentence with the same three-place predicate, (Ex)(Stabbed(Brutus, Caesar, x) ). Then we may show by constructing a derivation that the first entails the second. But what about "Brutus stabbed Caesar with a knife at noon"? In order to show that this entails "Brutus stabbed Caesar" (using ordinary logic) we shall have to symbolize the latter using a four-place predicate, "x stabbed y with z at t". And what about "Brutus stabbed Caesar with a knife at noon in the Forum"? In order to show that this entails "Brutus stabbed Caesar," we shall have to symbolize the latter using a five-place predicate "x stabbed y with z at time t and place p." What about "Brutus stabbed Caesar in his back with a knife at noon in the forum"? We need to use a six-place predicate to show the relevant entailment! And it seems possible that we could keep tacking adverbial modifiers indefinitely, so that we may need to use a seven, eight, or nine-place predicate. There's got to be a better way, says Davidson.

Davidson proposes that we treat predicates of action as containing an single-extra place for variables that range over events. Thus to symbolize "Brutus stabbed Caesar", we make use a three-place predicate meaning "x is a stabbing of y by z." Using this predicate, we may then show that all the above entailments hold. We symbolize "Brutus stabbed Caesar" as (Ex)Stabbing(x, Brutus, Caesar). We symbolize "Brutus stabbed Caesar at noon" as (Ex)(Stabbing(x, Brutus, Caesar) and x occurred at noon." The latter is derivable from the former in ordinary first-order logic. Thus by treating action predicates as containing an extra place (i. e. one more than the surface grammar would lead us to expect), and by symbolizing adverbial modifiers as predicates that are true of events, we may show these entailments to be a matter of first-order logic.

A second sort of sentence that Davidson wishes to analyze using an ontology of events is sentences using the "by"-locution, such as "I signaled to the auctioneer by waving my hand." This sentence clearly entails "I signaled to the auctioneer" and "I waved my hand", which will be symbolized, following Davidson, as (Ex)(x is a signaling by me to the auctioneer), and (Ey)(y is a hand-waving by me), respectively. But the conjunction of the latter two sentences does not entail the former, even if we add that the signaling and the hand-waving occurred at the same time. What needs to be added to the conjunction of the latter two to entail the former, i. e. how are we to symbolize "I signaled to the auctioneer by waving my hand", so that ordinary logic will show the relevant entailments? Obviously we need to add that some relation holds between the signaling and the hand-waving. Davidson maintains that this relation is identity. Thus, according to Davidson, we should symbolize "I signaled to the auctioneer by waving my hand" as (Ex)(Ey)(x is a signaling by me to the auctioneer, y is a hand-waving by me, and x=y), or equivalently (Ex)(x is a signaling by me to the auctioneer, and x is a hand-waving by me).

Aside from propounding these analyses, Davidson has not said much about the nature of events, e. g. whether they are in some sense reducible to other objects in our ontology. But Jaegwon Kim has. According to Kim, an event is "an exemplification of a property by a substance at a time." Following Kim, we may designate an event as follows: [x, P, t], where "x" refers to a substance (material objects, and immaterial souls, if such there be, are substances), "P" refers to a "constitutive property", and "t" refers to a time. Kim proposes the following as identity conditions for events: event [x, P1, t1] is identical to event [y, P2, t2] just in case x=y, P1=P2, and t1=t2. (To take the mystery some have complained about out of the functional operator "[...]", Kim proposes that we treat "is an event" as a predicate true of certain triples of substances, properties, and times: <x, P, t is an event iff x has property P at time t. The identity conditions Kim proposes then follow from the set-theoretic axiom of extensionality. Events are then no less mysterious than sets, for whatever that's worth.)

A couple of notes on this proposal of Kim's. First, Kim acknowledges the existence of relational events. A relational event will consist of an ordered n-tuple of substances, an n-place relation, and a time. Second, Kim acknowledges that this theory of events doesn't do well as a theory of the nature of such events as comings-to-be and ceasings-to-be. For such events, we need a different treatment, although there is no reason, according to Kim, to expect that we can achieve a unified treatment of all things we wish to call events. Third, I think that Kim should have said that exemplifications of properties at times are "basic events," out of which other events are composed, for surely every sum of events is itself an event. A football game is an event, composed of many events of shorter duration, which may be Kim's exemplifications of properties at times.

Davidson has criticized Kim's theory of events on the ground that these entities cannot serve the proper role in the analyses he has proposed. Thus Davidson's criticism of events is analogous to Lewis's criticism of ersatzism about possible worlds: just as Lewis says that if worlds are consistent stories, the analyses of modal statements don't come out right, Davidson says that if events are as Kim claims, his analyses of sentences don't come out right. Since it is these analyses that are our prime motivation for admitting events into our ontology, events cannot be what Kim claims they are.

It should be noted that Kim has a lot of leeway in his theory concerning what property (or relation) counts as the "constitutive property" of an event. Thus Kim may accept many of Davidson's analyses (which he does). Kim may render "Brutus stabbed Caesar at noon" as (Ex)(x is a stabbing of Caesar by Brutus, and x occurs at noon). Kim might say that the value of x for which the open sentence following the quantifier is true is the event [<Brutus, Caesar, stabbing, noon]. The substances of the event are Brutus and Caesar, the constitutive property of the event is the relation of stabbing, and the time is noon. So far, Davidson has no objection to Kim's theory. And if Kim were willing to be extremely flexible about what counts as the constitutive property of an event, he could make all of Davidson's analyses work.

But Kim takes seriously such locutions as "The collapse was caused, not by the bolt giving way, but by the bolt giving way suddenly." Davidson would symbolize "The bolt gave way" as (Ex)(x is a giving way by the bolt), and would symbolize "The bolt gave way suddenly" as (Ex)(x is a giving way by the bolt, and x is sudden). Given that the bolt only gave way once, we may derive from these two sentences "The giving way of the bolt is identical to the giving way suddenly of the bolt", i. e. in Davidson's symbolization, (the x such that (x is a giving way by the bolt) = the x such that (x is a giving way by the bolt, and x is sudden). But the sentence at the beginning of the paragraph, on the face of it, entails by Leibniz' Law that the giving way of the bolt is not identical to the giving way suddenly of the bolt, for one, but not the other, was a cause of the collapse. Kim maintains that this distinction is a distinction between the constitutive properties of the two events (since both involve the same substance and occurred at the same time): one event is [the bolt, giving way, t], and the other is [the bolt, giving way suddenly, t]. It follows from this that Kim cannot consistently accept Davidson's symbolization of these sentences.

How then, Davidson asks, can Kim explain the entailment of "The bolt gave way" by "The bolt gave way suddenly"? (Furthermore, Kim's reasoning also seems to by inconsistent with Davidson's analysis of "Brutus stabbed Caesar with a knife" and "Brutus stabbed Caesar", for one might wish to say "It was not Brutus's stabbing Caesar that caused Caesar's death, but Brutus's stabbing Caesar with a knife (for if he had stabbed him with a carrot, his death would not have ensued)."

Furthermore, Kim's proposed identity conditions for events may prevent general application of Davidson's analysis of "by" sentences. Suppose that the constitutive property of my signaling the auctioneer is the two-place relation "signals", and that the constitutive property of my hand-waving is the one-place property "waves a hand." These presumably are not identical properties. If this is so, then Kim is barred from accepting Davidson's analysis of "I signaled the auctioneer by waving my hand," for Davidson's analysis entails that the event of my signaling the auctioneer is identical to my waving my hand, and Kim insists that identical events have identical constitutive properties. What then, Davidson may ask, is the relationship between these two events that makes it true that I signaled to the auctioneer by waving my hand?

In an attempt to counter these problems, Kim has made an appeal to a relation between events he calls inclusion. "The bolt gave way suddenly" entails "The bolt gave way" in virtue of the fact that the bolt's giving way suddenly includes the bolt's giving way. If all events of type A include events of type B, then any sentence that entails the existence of an event of type A entails the existence of an event of type B. Kim might also make use of this relation of inclusion in analysing "by" sentences. Perhaps the additional sentence we need to add to "I waved my hand" and "I signaled to the auctioneer" to entail "I signaled to the auctioneer by waving my hand" is "My signaling includes my hand-waving."

Davidson would reply that this makes the relevant entailment more than a matter of mere logic. In addition to the principles of logic, we must add certain axioms stating that events of one type necessarily include events of another type. This is not unprecedented, of course. Mere logic will not suffice to show that "Ted is a bachelor" entails "Ted is not married", or that "This candle is red" entails "This candle is colored." What Kim owes us, then, is an account of these axioms.

What Davidson owes us, on the other hand, is an account of sentences such as "The collapse was caused, not by the bolt giving way, but by the bolt giving way suddenly." Since on the face of it this sentence entails by Leibniz Law that the bolt's giving way is not identical the bolt's giving way suddenly, Davidson must give us some alternate analysis of such sentences. Davidson's general strategy, which I will not go into in detail, is to understand such sentences as being about causal explanation, and not about causation per se. That the bolt gave way suddenly explains why the collapsed occurs, although that the bolt gave way does not.

References Davidson, Donald. "The Individuation of Events," in Essays on Actions and Events. Oxford, 1980.

"The Logical Form of Action Sentences," in Essays on Actions and Events, op. cit.

Kim, Jaegwon. "Events as Property Exemplifications," in Supervenience and Mind. Cambridge, 1993.