A quick heuristic for testing conjunctive accounts

Suppose someone proposes an account of some concept A in conjunctive form:

• x is a case of A if and only if x is a case of A₁ and of A₂ and ... of A_n.

It may seem initially plausible to you that anything that is a case of A is a case of A₁,...,A_n. There is a very quick and simple heuristic for whether you should be convinced. Ask yourself:

• Suppose we can come up with a case where it's merely a coincidence that x is a case of A₁,A₂,...,A_n. Am I confident that x is still a case of A then?

In most cases the answer will be negative, and this gives you good reason to doubt the initial account. And to produce a counterexample, likely all you need to do is to think up some case where it's merely a coincidence that A₁,A₂,...,A_n are satisfied. But even if you can't think of a counterexample, there is a good chance that you will no longer be convinced of the initial account as soon as you ask the coincidence question. In any case, if the answer to the coincidence question is negative, then the initial account is only good if there is no way for the conditions to hold coincidentally. And so now the proponent of the account owes us a reason to think that the conditions cannot hold coincidentally. The onus is on the proponent, because for any conditions the presumption is surely that they can hold coincidentally.

Consider for instance someone who offers a complicated account of knowledge:

• x knows p if and only if (i) x believes p; (ii) p is true; (iii) x is justified in believing p; (iv) some complicated further condition holds.

Without thinking through the details of the complicated further condition, ask the coincidence question. If there were a way for (i)-(iv) to hold merely coincidentally, would I have any confidence that this is a case of knowledge? I suspect that the answer is going to be negative, unless (iv) is something weaselly like "(i)-(iii) hold epistemically non-aberrantly". And once we have a negative answer to the coincidence question, then we conclude that the account of knowledge is only good if there is no way for the conditions to hold coincidentally. So now we can search for a counterexample by looking for cases of coincidental satisfaction, or we can turn the tables on the proponent of the account of knowledge by asking for a reason to think that (i)-(iv) cannot hold coincidentally.

Most proposed accounts crumble under this challenge. Just about the only account I know that doesn't is:

• x commits adultery with y if and only if (i) x or y is married; (ii) x is not married to y; (iii) x and y have sex.

Here I answer the coincidence question in the positive: even if (i)-(iii) are merely coincidentally true (e.g., x believes that he is married to y but due to mistaken identity is married to someone else), it's adultery.