Counterfactual Analysis by Algorithmic Complexity: A metric between possible worlds

TL;DR

This paper introduces a novel approach to analyzing counterfactuals using algorithmic complexity, offering new insights into philosophical debates and addressing issues like vagueness and context-dependence.

Contribution

It proposes a new method based on algorithmic complexity for interpreting counterfactuals, bridging logic, philosophy, and AI.

Findings

Provides a new interpretation of the Lewis-Stalnaker possible worlds framework

Offers solutions to vagueness and non-monotonicity in counterfactuals

Enhances understanding of counterfactual reasoning through complexity analysis

Abstract

Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a new form of analysis for counterfactuals: analysis by algorithmic complexity. Inspired by Lewis-Stalnaker's Nicholas Corr\^ea 2 Manuscrito-Rev. Int. Fil. Campinas, 2022. Possible Worlds Semantics, the proposed method allows for a new interpretation of the debate between David Lewis and Robert Stalnaker regarding the Limit and Singularity assumptions. Besides other results, we offer a new way to answer the problems raised by Goodman and Quine regarding vagueness, context-dependence, and the non-monotonicity of counterfactuals. Engaging in a dialogue with literature, this study will seek to bring new insights and tools to this debate. We hope our method of analysis can make counterfactuals more understandable in an intuitively plausible way, and a philosophically justifiable manner, aligned with the way we usually think about counterfactual propositions and our imaginative reasoning.