- (Premise) Frankfurt's example shows that if compatibilism is true, then the Principle of Alternate Possibilities is false.
- (Premise) The Principle of Alternate Possibilities is true.
- Therefore, compatibilism is false.
It is worth noting that (2) was accepted by classic compatibilists like Hume and Ayer (with a compatibilist reading of "able to do otherwise"). Of course, they might well have abandoned the Principle of Alternate Possibilities given Frankfurt's example. But perhaps they shouldn't have. For the Principle is deeply plausible. Instead, they should have abandoned compatibilism.
A potential response is to modify the Principle in a flicker-of-freedom way. This is open to compatibilists as well as incompatibilists.