On Friday Oct 24th, Paul Portner (Department of Linguistics, Georgetown University) will present to the workshop from 11:00am-1:00pm in the Landahl Linguistics Research Center (in the basement of Social Sciences). The title and abstract for the talk are below.

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Scales of Probability

Paul Portner

 

Expressions of necessity and possibility are standardly analyzed as operators with meanings of the kind familiar from modal logic, that is as quantifiers over possible worlds, and Kratzer (1981) extends this treatment to a wider variety of expressions.  In particular, she is able to give an account not only of It is necessary that and It is possible that, but also such forms as It is probable that, There is a good possibility that, and There is a slight possibility that.  However, as pointed out by Portner (forthcoming), it seems that the formal theory she develops – involving two paramters of interpretation, the modal base and ordering source, and multiple modal forces defined in terms of these – is unable to explain the open-ended nature of the distinctions:  there is no limit to the number of grades of probability we need to recognize:

 

possible, somewhat possible, quite possible, entirely possible, probably, extremely probable, 60% probability that, 61% probability that, chance, slight chance, good chance, really good chance, incredibly good chance, two in three chance, necessary, somewhat necessary, completely necessary, absolutely necessary ….

 

Another feature these Probability and Possibility Expressions (PPEs) is that they are more or less normal adjectives, adverbs, and nouns;  as such most (if not all) of them are gradable.  Thus somewhat possible stands in need of an analysis parallel to somewhat tall.  (In this, they differ from modal auxiliaries and modal particles.)  Whatever deep account we give of the meanings of PPEs, whether it involves possible worlds or some other device, it must fit into the syntactic and semantic mechanics of the theory of gradable expressions (e.g. Kennedy 2007).  In particular, gradale PPEs must be given analyses using scales.

 

I will briefly describe two approaches to developing a scale-based semantics for PPEs.  The first is based on probability theory:  scales for PPEs are constructed out of the probability scale, i.e. the interval [0,1].  The second is based on modal semantics;  in particular, we derive scales of propositions from the modal base/ordering source framework of Kratzer, as sketched in Portner (forthcoming;  see also Villalta 2007).  In this talk, I’ll spend more time developing the ideas behind the second approach, working out the theoretical details to the extent that time permits.