The category of achievements forms one of the four cornerstones of Vendler's (1967) aspectual classification. In Vendler's words, achievements "occur at a single moment" (p. 103) and "involve unique and definite time instants" (p. 107). Two examples of achievement verbs are given in 1.
(1) a. Rebecca reached the summit at 12:00 sharp. b. I recognized Katja as soon as she entered the room.
In 1a, Rebecca's reaching of the summit occurred exactly at noon-- it did not last several moments, the final of which was the transition to 12:00. Of course, she may have climbed towards the summit for a long time, but this 'development phase' should not be confused with her actual reaching of the summit. It may be vague as to how far she had to climb in order to be counted as reaching the summit, but once a threshold is stipulated, her reaching of the summit occurs at an instant. Other examples of achievement verbs are win, die, arrive, convince, persuade, discover, notice.
Broadly speaking, there have been two approaches to achievements in the aspectual literature since Vendler, pragmatic and semantic. The pragmatic approach denies that there is a semantic distinction between accomplishments and achievements. Specifically, achievements are said to be nothing but (what we conventionally take to be) very short accomplishments-- the difference is quantitative rather than qualitative and can shift if our conventions change. Verkuyl (1993, 2.4) advocates this view most explicitly, claiming that "[t]he length of the event does not seem to be a linguistic matter" and that "there appear to be no grounds for distinguishing Achievement terms from Accomplishment terms" (p. 49). Egg (1995, 4.2) strongly concurs with Verkuyl, arguing that the feature 'punctual' is a "minor feature" whose assignment is heavily influenced by pragmatic factors. Parsons (1990, p. 24) writes in a similar vein: "I assume that "Achievements," such as 'reaching the summit', are not essentially different from Accomplishment-events."
In order for the pragmatic approach to be viable, it isn't enough to argue that there are short accomplishments-- one must also argue that there are long achievements (i.e., that achievements can last longer than an instant in certain contexts). Without this second half of the argument, the qualitative difference between accomplishments and achievements is by no means eliminated. Rather, it is at best the case that short accomplishments behave in certain respects like achievements. None of the advocates of the first approach argue that there are long achievements, and I claim that any such argument would fail precisely because achievements are essentially short. In fact, I claim that although achievements are located in time (1), they don't fill or take up any time at all (2-3).
(2) a. # Rebecca reached the summit for a fraction of an instant. b. # I recognized Katja for a split second. (3) a. Rebecca reached the summit in a fraction of an instant (or: in five hours). b. I recognized Katja in a split second (or: in five minutes).
Note that the in-adverbials in 3 don't specify the minimal interval during which the achievement described takes place. Rather, they specify an interval after the passing of which the achievement takes place. This is supported by the fact that the sentences in 4 paraphrase those in 3.
(4) a. Rebecca reached the summit after a fraction of an instant (or: after five hours). b. I recognized Katja after a split second (or: after five minutes).
I conclude that the pragmatic approach, far from eliminating the semantic distinction between achievements and accomplishments, actually fails to provide any account of achievements.
The semantic approach takes achievements to be a category in their own right, not reducible to accomplishments. This was Vendler's view, of course, and it is affirmed in different ways by Lys and Mommer (1986), Mittwoch (1991), and C. S. Smith (1991), to mention but a few. Lys and Mommer (p. 221) state that achievement verbs "represent a situation type that includes only a culmination point." C. S. Smith (p. 58) similarly proposes that achievements are "instantaneous events that result in a change of state." While the intuitions behind this approach seem correct, they stand in need of explicit characterization. For example, it is difficult to see how it follows from the intuitive notion of a 'culmination point' or an 'instantaneous event' that achievements are located in time but don't fill time, as I argued above. Moreover, it is also unclear how such 'instantaneous events' are related to larger events.
In this paper, I offer a semantic analysis of achievements that addresses these issues. I propose that achievements be analyzed as a new type of event in an event semantics. Specifically, I claim that achievements are boundaries of processes or states. In saying this I mean to introduce boundaries as concrete particulars into a temporal ontology for aspectual semantics. Boundaries as such exhibit three properties that achievements also exhibit. First, boundaries are extremely thin objects, so thin in fact they don't fill space (in three dimensions) or time (in one dimension). Second, boundaries are ontologically dependent objects: they require for their existence the existence of that which they bound. Boundaries do not stand alone. Third, boundaries-- at least the external boundaries of objects-- are asymmetrical: they bound only in one direction.
If achievements are boundaries, as I claim, then they should also have these properties, and in fact they do. First, achievements are extremely thin: they don't fill time (2-4). Second, achievements are ontologically dependent on processes (1 a) or states (1 b) . In 1 a, for example, it would have been impossible for Rebecca to have reached the summit without there having been a process in which she climbed towards it. Her reaching of the summit was ontologically dependent on her climbing towards it. Third, achievements are typically asymmetrical: they bound to the left (la) or the right (lb), but not in both directions at once. In la, for example, Rebecca's reaching of the summit bounded her climbing towards the summit, but it didn't bound (in the same sense) the sum of all other processes and states that followed her climbing.
I formalize my analysis of achievements using a mereotopology, viz., a mereology (or a theory of parts) enhanced by topological notions (on mereotopology, see Varzi 1993, Pianesi and Varzi 1994, B. Smith 1994, Asher and Vieu 1995, Eschenbach 1995). The reason for using a mereotopology is that the notion of boundary as intended here is not definable within a (classical) mereology. Specifically, I aim for a distinction between extensive (or thick) parts and non-extensive (or thin) parts-- boundaries are the latter. The mereotopology that I adopt is closest to that proposed by B. Smith (1994). The idea is to complement the primitive relation of proper part of mereology with a primitive relation of interior part. The latter is a topological notion: intuitively, if a part x of an object z is completely internal to z, not overlapping (from the inside) an outermost extent of z, then x is an interior part of z. It is then possible to define an object x as being a boundary of an object y iff x is a part of y and every object z that x is an interior part of is such that z overlaps y but is not a part of y. Put another way, if an object x is a boundary of y, then x is a part of y and x doesn't overlap any interior part of y. Applying this formal notion of a boundary, I provide an event semantics for achievement verbs as denoting external boundaries of processes or states. For example, I analyze the verb reach as denoting right external boundaries of motion processes of traversal (in 1 understood to be a climbing).