# The Problem of Cross-world Predication

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## Abstract

While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of *cross-world predication*, whereby objects in one world are related to (sometimes the same) objects in another world. Extending first-order modal logic to allow for cross-world predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts of cross-world predication all leave something to be desired. I then propose an account of cross-world predication based on *quantified hybrid logic* and show how it overcomes the limitations of these previous accounts. I will conclude by discussing various philosophical consequences and applications of such an account.

## Keywords

Cross-world predication Cross-world quantification Expressive power First-order modal logic Hybrid logic## Notes

### Acknowledgments

Many thanks to Johan van Benthem, Russell Buehler, Balder ten Cate, Sophie Dandelet, Melissa Fusco, Wesley Holliday, Grace Paterson, Justin Vlasits, Kai Wehmeier, and Seth Yalcin for all their helpful comments and suggestions. A version of this paper was presented at the Berkeley-Stanford Circle in Logic and Philosophy in October 2014. A version of this paper was also presented at a C-ALPHA-sponsored talk at UC Irvine in March 2015 and at the Logic Seminar at Stanford in May 2015. I am very grateful for all the helpful comments and discussion from these talks.

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