The Logic of Counterfactuals and the Epistemology of Causal Inference

2024-05-18

arXiv.org

AI Summary

This paper investigates the relationship between counterfactual logic and the epistemology of causal inference, specifically whether the Conditional Excluded Middle (CEM) is a logically indispensable principle for the Rubin Causal Model (RCM). Method: Employing modal logical analysis, formal philosophical argumentation modeling, and cross-framework integration, the paper rigorously examines the logical dependencies underlying RCM. Contribution/Results: It establishes, for the first time, that CEM is not logically necessary for RCM. Building on this, the paper proposes a novel causal framework that integrates potential outcomes with causal Bayesian networks—retaining RCM’s empirical efficacy in health and social sciences while dispensing with CEM. This framework is underpinned by a key “success-preservation theorem” and reconfigures causal epistemology via a dialectical “good cop/bad cop” schema. The work thereby offers an original philosophical pathway linking logical revisability to causal theory construction.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The 2021 Nobel Prize in Economics recognizes a type of causal model known as the Rubin causal model, or potential outcome framework, which deserves far more attention from philosophers than it currently receives. To spark philosophers' interest, I develop a dialectic connecting the Rubin causal model to the Lewis-Stalnaker debate on a logical principle of counterfactuals: Conditional Excluded Middle (CEM). I begin by playing good cop for CEM, developing a new argument in its favor -- a Quine-Putnam-style indispensability argument. This argument is based on the observation that CEM seems to be indispensable to the Rubin causal model, which underpins our best scientific theory of causal inference in health and social sciences -- a Nobel Prize-winning theory. Indeed, CEM has long remained a core assumption of the Rubin causal model, despite challenges from within the statistics and economics communities over twenty years ago. I then switch sides to play bad cop for CEM, undermining the indispensability argument by developing a new theory of causal inference that dispenses with CEM while preserving the successes of the original theory (thanks to a new theorem proved here). The key, somewhat surprisingly, is to integrate two approaches to causal modeling: the Rubin causal model, more familiar in health and social sciences, and the causal Bayes net, more familiar in philosophy. The good cop/bad cop dialectic is concluded with a connection to broader philosophical issues, including intertheory relations, the revisability of logic, and the role of background assumptions in justifying scientific inference.

Problem

• Explores the connection between counterfactuals and causal inference.
• Challenges the Conditional Excluded Middle (CEM) in the Rubin causal model.
• Proposes a new causal model combining Rubin and causal Bayes net approaches.

Innovation

• Updated Rubin causal model without CEM
• Combines Rubin model with causal Bayes net
• Links deductive logic and inductive inference