Reducing Causality to Functions with Structural Models

TL;DR

This paper proposes a new formal definition of causality using Structural Functional Models (SFM), which map causes to effects and can generate causal statements aligning with human intuition, offering a novel approach beyond traditional probabilistic methods.

Contribution

It introduces a reductive, function-based definition of causality via SFM, demonstrating its effectiveness in causal inference and its compatibility with existing theories.

Findings

SFM can produce causal statements matching human intuition

SFM is compatible with probability theory but not reducible to it

Application of SFM to problems like free will and mental causation

Abstract

The precise definition of causality is currently an open problem in philosophy and statistics. We believe causality should be defined as functions (in mathematics) that map causes to effects. We propose a reductive definition of causality based on Structural Functional Model (SFM). Using delta compression and contrastive forward inference, SFM can produce causal utterances like "X causes Y" and "X is the cause of Y" that match our intuitions. We compile a dataset of causal scenarios and use SFM in all of them. SFM is compatible with but not reducible to probability theory. We also compare SFM with other theories of causation and apply SFM to downstream problems like free will, causal explanation, and mental causation.