Accidental generalizations that accidentally support counterfactuals

One of the long-standing problems in philosophy of science is how to distinguish accidental generalizations, such as that all the coins in Sam's pocket are nickels when this is a mere coincidence, from non-accidental generalizations, such as that all electrons are charged.

A standard observation is that non-accidental generalizations support counterfactuals. If there were another electron, it too would be charged. But it is not true that if there were another coin in the pocket, it too would be a nickel. Or so the story goes.

But in fact one can make accidental generalizations accidentally support counterfactuals as well. Sam and Jenny are on a lifeboat. Sam has five nickels in his pocket and Jenny has two nickels and three dimes, all due to chance. And that's all the money around for miles. Jenny accidentally drops the three dimes in the sea. Hours pass. At this point the following counterfactual seems true:

• If another coin came to be present in Sam's pocket, it would be one of Jenny's nickels.

This is intuitively correct, and obviously right on Lewisian semantics. After all, worlds where a quarter comes into existence ex nihilo in Sam's pocket, or one of Jenny's dimes flies out of the ocean, or even ones where several hours back Jenny did not drop the dime in the ocean and now gives it to Sam, are all more distant from our world than a world where Jenny just hands Sam another nickel and he puts it in his pocket. And so, plausibly:

• If another coin came to be present in Sam's pocket, it would be a nickel.

So, the accidental generalization that Sam has five nickels has started to support counterfactuals. But it's still accidental, and its support of counterfactuals is but an accident.