The first two sections consider whether there is any way to strengthen the DN model to deal with the problem cases without relying on the notion of causation or on elements of a nonconditional analysis of causation. The third section provides proofs underlying the conclusions drawn in §8.5.

Nomic Sufficient Conditions and Explanations

In his essay “The Direction of Causation and the Direction of Conditionship” David Sanford offers an account of causal priority in terms of a nonsymmetrical relation among propositions, “is a causal condition of.” If his account succeeds, then he has provided the core of a purely conditional analysis of causation. Sanford also implicitly offers an account of scientific explanation. Sanford does not claim to have done so much, because his account also relies on an unanalyzed notion of “causal connection in a direct line.”

Let us, following Sanford, say that “A is nomically sufficient for B in circumstances C” (or “B is nomically necessary for A in circumstances C”) if and only if “A&∼B&C&L” is logically inconsistent where A, B, C, and L are all propositions, the conjunction is strongly nonredundant, and L is a (conjunction of) law(s) of nature. A and B state that events with properties A and B occur (1976, pp. 200–1). The exposition differs here from Sanford's in four significant ways: (1) Sanford's exposition is more general and applies to other sorts of necessity. (2) Sanford uses the notion of a logical impossibility rather than the narrower one of logical inconsistency.