P1.  Microphysical Causal Closure:  Every microphysical property/object/event has a sufficient microphysical causal history.

P2.  Microphysical Supervenience:  All of reality supervenes on microphysical reality.

C1.  Human actions are effects that supervene on (are constituted by? identical to?) some microphysical conditions. (By P2)

P3.  Causal Realization Principle:  Causing the realization/supervenience base for some higher-level property is both necessary and sufficient for causing that higher-level property.

C2.  Human actions have sufficient microphysical causes.  (By P1, C1, and P3)

P4.  Exclusion Principle:  Except in rare cases of causal overdetermination, one sufficient cause for an effect excludes other independent, sufficient causes for that same effect.

P5.  Non-reduction of the Mental:  Intentional mental properties (or predicates) are not reducible to microphysical properties (or predicates).  Causal relations backed by laws, counterfactuals, etc. that make essential use of intentional mental properties (or predicates) are independent of causal relations backed by laws, counterfactuals, etc. that makes essential use of only microphysical properties (or predicates).

C3.  The presence of sufficient microphysical causes of human actions and the microphysical conditions on which they supervene excludes the causal efficacy of intentional mental properties (with respect to human actions and the microphysical conditions on which they supervene).  (By C2, P4, and P5)

This conclusion (Epiphenomenalism) seems unacceptable.  What should we do?  P1 and P2 are basic Physicalist assumptions.  In order to preserve the causal efficacy of the mental, the Physicalist must deny P3, P4, or P5, or else deny the validity of one of the inferences.

Deny P3?:  Some counterfactual analyses.  Dual explanandum approaches.

Deny P4?:  Yablo argues that properties related as determinable-determinate are exceptions to such principles.  Others (e.g., Sider) reject exclusion principles altogether.

Deny P5?:  In various ways, Lewis, Kim and Robb pursue this line.

Deny the inference to C3:  Davidson?