# Uncertainty and Persistence: a Bayesian Update Semantics for Probabilistic Expressions

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## Abstract

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are *not* persistent (i.e. beliefs that won’t necessarily survive the addition of new information that is compatible with all previous information), whereas propositions express beliefs that *are* persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave.

## Keywords

Modality Dynamic semantics Update semantics Belief revision## Notes

### Acknowledgments

Thanks above all to Pranav Anand for countless hours of productive and enjoyable conversation, without which this paper would not exist. For reading and commenting on this paper in various incarnations, thanks to Adrian Brasoveanu, Donka Farkas, Dan Lassiter and Margaret Kroll. Thanks also to Floris Roelofsen, for helpful discussion and a pleasant walk, and especially grateful thanks to Chris Barker & Dylan Bumford, who were this paper’s saviors at one point in its history. Finally, thanks to Frank Veltman and an anonymous reviewer for JPL for efficiently shepherding this paper to publication, and improving it substantially in the process. All errors are mine.

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