Truth in Fiction via Non-Standard Belief Revision
Christopher Badura
Abstract:
Fiction operators such as ‘In the fiction f,' (In_f,) have seen applications particularly in philosophy of fiction, but more broadly in any ontological/metaphysical debate. For example there are fiction operator approaches towards modality, mathematics and morality. Giving a suitable analysis for when a sentence of the form ⌜Inf_{f,φ}⌝ is true, is hence of importance. The most famous approach has been David Lewis's analysis. However, it has certain shortcomings, especially when applied to inconsistent fictions in which not everything is true. We start by taking Lewis's (1978) Analysis 2 and give it a formal interpretation that takes into account impossible worlds and ideas from belief revision theory. Our formal framework comprises multiagent plausibility models with a domain of possible and impossible worlds, ordered by a group plausibility ordering. This gives rise to Grove-style sphere models which are known to be models for the AGM axioms. We extend these models to an impossible world setting.
Then, a sentence of the form ⌜Inf_{f,φ}⌝ is true under our interpretation of Analysis 2 iff. for any world that is, after revising with the explicit content of the fiction, at least as plausible as any common belief world and that makes the explicit content of the fiction true, it also makes φ true.