SANDRO ZUCCHI INCOMPLETE EVENTS, INTENSIONALITY AND IMPERFECTIVE ASPECT* I discuss two competing theories of the progressive: the theory proposed in Parsons (1980, 1985, 1989, 1990) and the theory proposed in Landman (1992). These theories differ in more than one way. Landman regards the progressive as an intensional operator, while Parsons doesn’t. Moreover, Landman and Parsons disagree on what uninflected predicates denote. For Landman, cross the street has in its denotation complete events of crossing the street; the aspectual contribution of English simple past (perfective aspect) is the identity function. For Parsons, both complete and incom- plete events of crossing the street can be in the denotation of the base VP; perfective aspect restricts its denotation to the events that culminate. I present a version of Parsons’s theory that avoids the problems raised by Landman, in particular the problem posed for Parsons by creation verbs. The repaired version and Landman’s theory still differ in the way they analyze uninflected predicates. I present evidence from Slavic languages that both theories are needed. Finally, I discuss some evidence that may favor one or the other approach to the semantics of the English progressive. 1. THE P ROBLEM OF I NDIRECT A CCESS In the study of tense and aspect, one runs into statements of the following sort: ‘Carnap flew to the moon’ is true iff ‘Carnap fly to the moon’ is true relative to some time t < now. If ‘Terry build a house’ is true relative to an interval i, there is no proper subinterval of i relative to which ‘Terry build a house’ is true. If ‘Terry be at home’ is true relative to an interval i, then ‘Terry be at home’ must also be true relative to every subinterval of i. * Versions of this paper were presented at the 1995 Annual Conference of the Israel Association for Theoretical Linguistics at Tel Aviv University and at the 1995 Colloque de Syntaxe et Semantique at the Université Paris 7. I thank Andrea Bonomi, Paolo Casalegno, Anita Mittwoch, Arnim von Stechow, and Zoltan Szabo for commenting on previous drafts. I also thank Wayles Brown, Béla Hollósy, Graham Katz, Fred Landman, Peter Lasersohn, Natalia Kondrashova, Mandy Simons, Milena Sheppard, Draga Zec, and Ede Zimmermann for comments and suggestions. Some of the ideas presented here were developed in the course of a conversation with Karina Wilkinson and Roger Schwarzschild at Ithaca’s Coyote loco. My final thanks are thus to Roger and Karina. Natural Language Semantics 7: 179–215, 1999. 1999 Kluwer Academic Publishers. Printed in the Netherlands. 180 SANDRO ZUCCHI As these examples show, in analyzing the meaning of temporal and aspec- tual features, we make assumptions about the truth conditions of uninflected clauses like ‘Carnap fly to the moon’, ‘Terry build a house’ and ‘Terry be at home’. However, we have only indirect evidence of how these sen- tences are interpreted by native speakers, since they do not occur as independent clauses in English. I’ll refer to the problem of determining the truth conditions of the base sentences that are the input to tense and aspect markers as the problem of indirect access in the semantics of tense and aspect. Making hypotheses based on indirect evidence is common practice in the natural sciences and I have no intention of arguing that the task of providing a truth-conditional analysis of temporal and aspectual features is hopeless or misconceived because of the problem of indirect access. I’m interested instead in the relevance of this problem for the analysis of the progres- sive. I’ll argue that the choice between different approaches to the semantics of the progressive that are currently available in the literature involves choosing between different analyses of the meaning of base predicates: to decide which approach to the semantics of the progressive is empirically more adequate, we have to find evidence, even if indirect, that allows us to establish what event types these predicates denote. I’ll proceed as follows. First, I’ll review two competing theories of the progressive: the theory proposed by Parsons (1980, 1985, 1989, 1990) and the theory proposed by Landman (1992). These theories champion two different approaches to the semantics of the progressive: Landman’s theory regards the progressive as an intensional operator, whereas Parsons’s doesn’t. The reasons put forward by Landman in favor of his theory have nothing to do with the problem of indirect access; they focus, mainly, on the dif- ficulties Parsons’s theory runs into with creation verbs. I’ll argue that these difficulties can be overcome by presenting a repaired version of Parsons’s theory that avoids the problems raised by Landman and other problems as well. The repaired version and Landman’s theory still differ in the way they analyze uninflected predicates. First, I’ll present evidence from Slavic languages that both theories are needed. Then, I’ll come back to English and discuss some evidence that may favor one or the other approach to the semantics of the progressive. 2. TWO T HEORIES OF THE P ROGRESSIVE 2.1. Parsons’s Theory Parsons suggests the following analysis of the progressive and of the simple past: INCOMPLETE EVENTS 181 • ‘x is F-ing’ is true iff there is an F-event in development (or holding) to which x bears the relation J, where J is the thematic role associ- ated with the subject of F. • ‘x F-ed’ is true iff there is a culminated (completed) F-event occurring in the past to which x bears the relation J, where J is the thematic role associated with the subject of F. Here are some examples of the translations that Parsons assigns to pro- gressive sentences and simple past sentences: (1) John is crossing the street. (1¢) $e$I$t [I = now ^ t Î I ^ crossing(e) ^ Agent(e, John) ^ Theme(e, the street) ^ Hold(e, t)] (2) John crossed the street. (2¢) $e$I$t [I < now ^ t Î I ^ crossing(e) ^ Agent(e, John) ^ Theme(e, the street) ^ Cul(e, t)] According to this analysis, the events in the denotation of the predicates that are the inputs to the progressive and the simple past need not be completed (culminated) events. For example, the predicate cross the street may have in its denotation both events in which the agent gets across and events that are only partial crossings. The progressive restricts the deno- tation of the predicate to the events that are in development, the simple past to the events that culminate at some past time. I’ll refer to this analysis of the progressive as the incomplete events approach. A desirable predic- tion of this approach is that (1) fails to entail that there is a time at which (2) is true, because (1) does not say that the crossing event culminates. 2.2. Landman’s Theory According to Landman, progressive sentences, unlike simple past ones, relate actual events to possible events: • ‘x is F-ing’ is true iff there is an actual event that has a possible F- event on its continuation branch to which x bears the relation J, where J is the thematic role associated with the subject of F. • ‘x F-ed’ is true iff there is an actual F-event occurring in the past to which x bears the relation J, where J is the thematic role associated with the subject of F. The continuation branch of an event e in a world w is built according to these instructions. Follow the development of e in w and put every event 182 SANDRO ZUCCHI of which e is a stage in the continuation branch. Take the maximal event of which e is a stage in w and go to the closest world w¢ in which this event continues (i.e., in which this event is a stage of a larger event), if there is one. If w¢ is not a reasonable option for e in w, stop; otherwise follow the development of this event in w¢ until you reach the maximal event of which this event is a stage in w¢. Then, go to the closest world in which this event continues, if there is one. And so on, until there is no world in which the event continues or you reach a world that is not a reasonable option for e in the base world w. To see how the definition of continuation branch works, consider the following example. Suppose John starts crossing the street in w. This event is our initial e. Construct the continuation branch for e in w in this way. Follow the development of e in w. If John gets across in w, put the complete crossing in the continuation branch and you are done, since there is no other world in which this crossing event continues. If John does not get across in w, go to the world w1 most similar to w in which the crossing con- tinues. Here you are faced with a choice. If w1 is not a reasonable option relative to e in w, go no further. If w1 is a reasonable option relative to e in w, follow the crossing in w1. If the crossing is completed in w1, add the completed crossing to the continuation branch and stop. Otherwise, go to the closest world in which the crossing is not interrupted, and so on. According to this procedure, every time we follow the development of an event e in a world other than the base world w (the world we started from), we have to check whether the world we jump to is a reasonable option for e in w.