Logical Investigations of Causal Models and Counterfactual Structures

There is little doubt that causal reasoning and counterfactual reasoning (about what would or might be the case if things were different) are closely related. It is thus reasonable to expect that successful formal tools for the former and those for the latter should bear interesting and illuminating relationships. In this project we aim to carry out in-depth investigations into the relationship between two such formal tools and explore the philosophical implications of our results. Both objects of our study are influential: one is the framework of structural equation models (SEMs), which is widely used to model causal systems and is gaining ground in the philosophical literature; the other is the Stalnaker-Lewis possible-world semantics for counterfactual conditionals, which remains one of the most popular and best known semantics for counterfactuals in philosophy.

Broadly speaking, we will pursue two approaches in our investigations. The first is a standard semantical approach, where the two frameworks are compared with respect to what logics of counterfactuals they validate. There are already a few interesting results of this kind in the literature, but most of them are restricted to a special class of SEMs, known as recursive causal models. A distinction of our inquiry is to also consider non- recursive causal models, which are commonly seen in practice. Building on some preliminary results that the PI has established, we plan to attack a number of questions, including at least two questions that we believe may interest a wide audience: (1) Are there methodological justifications for the constraints on SEMs that the PI has identified, and to what extent do the models used in practice conform to them? (2) How to extend SEMs to model non-causal determination (such as "supervenience") alongside causal determination?

The second approach will take our inquiry to a higher level of generality and abstraction. We will examine the two formalisms from a category theoretic perspective. Roughly speaking, category theory is the mathematical study of transformations between structures, both within a category (which consists of objects and mappings between objects) and across categories. We aim to construct categories of SEMs and of possible- world models, respectively, and study their relationship by investigating whether certain transformations exist between the categories (called "adjoint functors") that reflect a close relationship. We expect that this mathematically sophisticated approach will also deliver philosophical payoffs by, for example, revealing new and plausible constraints on theorizing about the relationship between causation and counterfactuals.