Abstract
This article advances the first semantics that is neither for nor against a default implicational link between the progressive and perfective forms, when it comes to solving the imperfective paradox. Depending on the doxastic context of its use, we contend that the progressive form sometimes allows and sometimes does not allow the inference of the corresponding simple form. In other words, the preparatory phase of an event might or might not be believed to lead to its culmination. Indeed, the context can put constraints on beliefs about the time of the culmination and whether or not it allows this inference to be made. From a formal perspective, this new solution to the imperfective paradox combines a specific modal approach with an event-structure analysis originating in event semantics. Finally, this approach solves the associated difficulties (e.g., pauses, past futures, interruptions and sensibility to description) that have plagued the most well-known theories in this field.
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Notes
Some are rather neutral on this point, such as Binnick (1991).
Inertia worlds are possible worlds identical to the actual world up to the time in question and whose future development is the most compatible with the past events.
Dowty (1979).
On a more technical level, Baggio and van Lambalgen draw on the Event Calculus framework elaborated in van Lambalgen and Hamm (2005).
Baggio and Lambalgen (2007).
This difference between the two theories could be tested experimentally, for instance, by observing whether there is a correlation between the difficulty or the duration of an accomplishment and the belief that it will terminate, without the need of explicit disabling conditions.
Michaelis (2003).
Parsons (1989) provides another important formulation of this same view but the differences are not relevant to our argument.
Parsons (1989) similarly maintains the following: “The difference between a progressive and a non-progressive event sentence is, roughly, whether the sentence requires for its truth that the eventuality picked out by the verb culminates, or whether it only needs to ‘go on’ for a while [to ‘hold’ in Parsons’ terms]”.
Dowty (1979).
Notice that Reichenbach also uses the reference point in his analysis of perfect tenses. For instance, in the sentence John had run, we do not speak directly about the event time at which John runs but instead use an intermediate point \(t_{R}\) for the event time preceding this reference time, which itself occurs before the speech time. However, we will not deal with perfect tenses in this article and instead focus exclusively on progressive tenses.
(Naumann and Piñón 1997) already insisted on the importance of considering the beliefs of the speaker in an analysis of the imperfective paradox.
(Priest 2008) is a good manual for an introduction to semantics associating possible worlds with more than two truth-values.
For a similar though distinct move, see the distinction between objective and subjective truth argued in (Wulf 2000).
This is what is defended by (Dowty 1979) with the inertia worlds.
As suggested by some reviewers, improvements of this semantics could be carried, for instance by formally distinguishing the different agents or by using intervals of time.
Quantification in natural language is sufficiently lax to allow for the domain of quantification to not correspond exactly to the whole set of times constituting the previous day.
This analysis could be extended to deal with unicorns and other non-existent objects. Several solutions exist within the possible world approach: for instance, see Priest (2005).
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We would like to thank three anonymous referees for their valuable comments that greatly helped to improve the paper.
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All the concepts, theses and discussions that form the content of this paper sprang from a genuine collective work of both authors. Since he wrote down the whole formal part of the paper which presents the core of our solution, Mathieu Vidal’s name features in first position.
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Vidal, M., Perrin, D. A default-free solution to the imperfective paradox. Synthese 196, 273–297 (2019). https://doi.org/10.1007/s11229-017-1474-0
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DOI: https://doi.org/10.1007/s11229-017-1474-0