Talk (Work in Progress): Marta Esteves (MCMP)

Title:

A logic of graded counterfactuals

Abstract:

Counterfactuals play a central role in many areas from causation to philosophy of science and language. Graded accounts of counterfactuals are particularly relevant as they provide a degree to the central notion of similarity between possible worlds, allowing for a more fine grained account of counterfactual reasoning. Here, we propose an axiomatization of a logic of graded counterfactuals inspired by Lewis's (1973) well-known formulation. We start by axiomatizing a multi-modal logic $L_{\square_\epsilon}$ of graded similarity, and show that it is sound and complete with respect to the class of ultra-metric spaces. We suggest an understanding of possible worlds as infinite sequences of events and propose that two worlds are more similar the longer they share their event histories.

Finally, we derive a gradual counterfactual from this notion of similarity and axiomatize the corresponding logic $L_{\square_\epsilon \rightarrow}$, which we prove to be sound and complete with respect to the class of ultra-metric $\alpha-models$ (see Rosella and Ugolini (2024)).

This account provides us with a topological semantics for a modal logic of similarity between possible worlds and a derived logic of graded counterfactuals, where the ultra-metric distance aligns with the graded approach to counterfactual reasoning.