lawfully sufficient

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In the first place, we might say that X is lawfully sufficient for Y, if there are some laws of nature L such that (X and L) is logically or analytically sufficient for Y (where neither X nor L alone is logically or analytically sufficient for Y).
We need this last qualification to restrict NESSs to nonredundant parts of lawfully sufficient conditions for Y.
It seems to us most plausible to suppose that the concept of necessity on which Wright's definition relies is logical or analytic necessity; the sense of sufficiency on which his definition relies is lawful sufficiency [36] In short, X is a NESS for Y when there is some state of affairs N of which X is a logical constituent, and where N is a lawfully sufficient condition for Y, yet the state of affairs (N X) that would result from subtracting X from N would not be lawfully sufficient for Y.
Consider some state of affairs that is lawfully sufficient for the fire in my basement.
If there really is a problem here, the solution is to be more specific about the sense in which a NESS must constitute a nonredundant part of a lawfully sufficient condition.
A fact X is lawfully sufficient for a fact Y when the proposition made true by X is lawfully sufficient for the proposition made true by Y.
Clearly, the bullet was a nonredundant part of a set of conditions that is lawfully sufficient for Jones's death, and had such a role even if it is true that Jones would have died even had the bullet not been fired.
Given the way in which we define lawful sufficiency, nothing is ever lawfully sufficient for anything in a radically indeterministic universe.
The problem is that, to get a set of conditions that is genuinely lawfully sufficient for some outcome, the set must contain indefinitely many conditions.
And all we need to establish to reach the conclusion that it was is that it was part of a complex set of conditions that was lawfully sufficient for the ship not making it to the relevant port; it was.
Here Carroll proposes that for any two actual states of affairs, P and Q, if (1) If P hadn't obtained, Q wouldn't have obtained, or (2) P was lawfully sufficient for Q, then P and Q are causally linked.
Here P is lawfully sufficient for Q, P raises the chance of Q, and Q counterfactually depends on P (if we hadn't measured the left particle and found spin up, the state of the right particle wouldn't have changed).