Here is a plausible principle:
- If p explains q1 and p explains q2, then p explains the conjunction of q1 and q2.
Now suppose that
p says that persons
x1,
x2,...,
x100 were the buyers of tickets to a fair lottery, with each buying one ticket. Let
qi be the proposition that person
xi did not win. Suppose that in fact
x100 won. Then
p explains
q1 with a perfectly fine 99/100 stochastic explanation. And by the same token
p explains
q2, and so on up to
q99. So by (1),
p explains the conjunction of
q1,...,
q99. But the probability of that conjunction being true given
p is only 1/100. So we have a stochastic explanation despite a low probability.
One can even rig cases where one has a stochastic explanation despite zero probability if (1) extends to infinite conjunctions.
2 comments:
Perhaps this is more true:
1a. If p explains q1 and p explains q2, and q1 is causally independent from q2, then p explains the conjunction of q1 and q2.
Example: If my painting a white chair explains why it is now entirely red and my painting the chair explains why is is now entirely blue, it does not follow the chair can be both entirely red and blue at the same time because of my painting it.
That p explains q entails that both p and q true. But the chair isn't both entirely red and entirely blue.
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