- Necessarily, a punishment of x is only just if the occurrence of the punishment is at least partly explained by something x is culpable for. (Premise)
- Necessarily, if x is guilty of having committed a horrific crime, x is unrepentant and unforgiven, and we believe on overwhelming evidence that x is guilty of the crime, then it is ceteris paribus just to punish x on the basis of the evidence. (Premise)
- If compatibilism holds, it is possible to believe on overwhelming evidence that x is guilty of having committed a crime, without that belief or evidence being even partly explained by anything x is culpable for. (Premise)
- If compatibilism holds, it is possible to justly punish x without the punishment being even partly explained by anything x is culpable for. (Premise, justified by 2 and 3 and some uncontroversial modal intuitions)
- But the consequent of (4) is false. (By 1)
- Therefore, compatibilism is false. (By 4 and 5)
The intuition behind (1) is that the punishment needs to be a result of the crime. Part of the intuition behind (2) is that what matters for justice is that the evidence be good, not what sort of evidence it is. But (3) observes that if compatibilism were true, we could have cases where our overwhelming evidence for a crime is the state of the world prior to the agent's coming into existence.
One might want to modify (1) by subjectifying it: justice only requires that one believe that the punishment would be a result of the crime. That's fine—the rest of the argument adapts to that version of (1).
This argument has an interesting consequence. It implies that one could not be criminally culpable for an action if that action follows with overwhelming probability from a prior state that one is not culpable for. This means that not only does the full causal determination of a wicked deed by an earlier state one is not culpable for take away culpability, but overwhelmingly strong probabilification will significantly decrease culpability.
The argument also rules out some Molinist views (I am grateful to Trent Dougherty for pointing out basically this)—namely those on which the truth values of the conditionals of freedom are never explained by the truth values of the consequents.
If I were a compatibilist, I think I'd deny (2). I'd insist that at least some of the evidence of the crime be explanatorily posterior to the crime. Not for epistemological reasons, but to ensure the "resultingness" of the punishment. This would, however, have the odd consequence that a person might become justly convictable by a piece of evidence that lowers the probability that she committed the crime. For suppose that all the evidence that has been given was about the state of the universe long prior to the defendant's crime, and that this evidence made it 99.99999999999% likely that the defendant committed the crime. We could now imagine a piece of testimony by an eyewitness to the crime that simultaneously defeats some of the evidence from the previous state of the universe and replaces it with slightly weaker evidence that is, nonetheless, explanatorily dependent on the crime, so that now the evidence makes it only 99.9999999998% likely that the defendant committed the crime. Since that's a probability high enough for conviction (at least in a non-capital case), and since now we have the explanatory connection requirement satisfied, it follows that this evidence which lowered the probability of guilt has made the criminal justly convictable.