Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Logic of Counterfactuals and the Epistemology of Causal Inference

Hanti Lin

TL;DR

The paper interrogates whether the deductive counterfactual principle Conditional Excluded Middle ($CEM$) is indispensable for causal inference, focusing on the Rubin causal framework and its Nobel-winning applications. It first defends $CEM$ via an indispensability argument rooted in health/social-science causal inference, then introduces a stochastic extension of the Rubin model combined with causal Bayes nets to dispense with $CEM$ while preserving the core IV-based inference, reframed as the DATE (degree-of-compliance-weighted average treatment effect). A central result, Theorem 2, shows that DATE is identified by the same observable ratio used to identify $LATE$ in the classic approach, undermining the indispensability claim. The analysis highlights deep links between deductive logic and inductive inference, and raises questions about intertheory relations in causal modeling, with practical implications for how causal conclusions are drawn in science.

Abstract

The 2021 Nobel Prize in Economics recognized an epistemology of causal inference based on the Rubin causal model (Rubin 1974), which merits broader attention in philosophy. This model, in fact, presupposes a logical principle of counterfactuals, Conditional Excluded Middle (CEM), the locus of a pivotal debate between Stalnaker (1968) and Lewis (1973) on the semantics of counterfactuals. Proponents of CEM should recognize that this connection points to a new argument for CEM -- a Quine-Putnam indispensability argument grounded in the Nobel-winning applications of the Rubin model in health and social sciences. To advance the dialectic, I challenge this argument with an updated Rubin causal model that retains its successes while dispensing with CEM. This novel approach combines the strengths of the Rubin causal model and a causal model familiar in philosophy, the causal Bayes net. The takeaway: deductive logic and inductive inference, often studied in isolation, are deeply interconnected.

The Logic of Counterfactuals and the Epistemology of Causal Inference

TL;DR

The paper interrogates whether the deductive counterfactual principle Conditional Excluded Middle () is indispensable for causal inference, focusing on the Rubin causal framework and its Nobel-winning applications. It first defends via an indispensability argument rooted in health/social-science causal inference, then introduces a stochastic extension of the Rubin model combined with causal Bayes nets to dispense with while preserving the core IV-based inference, reframed as the DATE (degree-of-compliance-weighted average treatment effect). A central result, Theorem 2, shows that DATE is identified by the same observable ratio used to identify in the classic approach, undermining the indispensability claim. The analysis highlights deep links between deductive logic and inductive inference, and raises questions about intertheory relations in causal modeling, with practical implications for how causal conclusions are drawn in science.

Abstract

The 2021 Nobel Prize in Economics recognized an epistemology of causal inference based on the Rubin causal model (Rubin 1974), which merits broader attention in philosophy. This model, in fact, presupposes a logical principle of counterfactuals, Conditional Excluded Middle (CEM), the locus of a pivotal debate between Stalnaker (1968) and Lewis (1973) on the semantics of counterfactuals. Proponents of CEM should recognize that this connection points to a new argument for CEM -- a Quine-Putnam indispensability argument grounded in the Nobel-winning applications of the Rubin model in health and social sciences. To advance the dialectic, I challenge this argument with an updated Rubin causal model that retains its successes while dispensing with CEM. This novel approach combines the strengths of the Rubin causal model and a causal model familiar in philosophy, the causal Bayes net. The takeaway: deductive logic and inductive inference, often studied in isolation, are deeply interconnected.
Paper Structure (17 sections, 22 equations, 2 figures)

This paper contains 17 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A Gentle Introduction to the Rubin Causal Model
  3. Introducing the Card Game
  4. Switching from the ATE to the LATE
  5. Estimating the LATE
  6. Playing Good Cop
  7. A New Argument for CEM
  8. What's the Role of CEM, Exactly?
  9. Wrapping up the Indispensability Argument
  10. Playing Bad Cop
  11. An Expansion Pack: Going Stochastic
  12. The Final Expansion Pack: A Causal Bayes Net
  13. Dispensing with CEM
  14. Closing
  15. Appendices
  16. ...and 2 more sections

Figures (2)

  • Figure 1: The causal structure that captures the Instrumentality assumption
  • Figure 2: The causal Bayes net assumed in Theorem 2