On the Plurality of Lewis's Triviality Results

David Lewis introduced a new kind of reductio ad absurdum style of argument: while the claims, suitably formalized, do not lead to outright contradiction, he showed they are tenable only in trivial ways. Lewis proved what are known as triviality results against the claims. The claims are "Probabilities of conditionals are conditional probabilities." "Desires are beliefs about what is good." The author argues that the tenuous connections between the claims go considerably further still: the claims give rise to debates that display a remarkably parallel structure. He brings out their many similarities to illuminate both of them, and to point the way to some promising avenues for future research. He displays structural similarities between the fluctuating fortunes of Stalnaker's Thesis, and those of Desire-as-Belief. Lewis concludes telegraphically by saying that Desire by Necessity is "a form of anti-Humeanism, sure enough, but not the right form of anti-Humeanism"; and that's it.