Consider this anti-randomness thesis that some compatibilists use to argument against libertarianism:
- If given your mental state you're at most approximately equally likely to choose A as to choose B, you are not responsible for choosing A over B.
Thesis (1) is false. Here's a counterexample. Consider the following family of situations, where your character is fixed between them: You choose whether to undergo x hours of torture in order to save me from an hour of torture. If x=0.000001, then I assume you will be likely to choose to save me from the torture—the cost is really low. If x=10, then I would expect you to be very unlikely to save me from the torture—the cost is disproportionate. Presumably as x changes between 0.000001 and 10, the probability of your saving me changes from close to 1 to close to 0. Somewhere in between, at x=x1 (I suppose x1=1, if you're a utilitarian), the probability will be around 1/2. By (1), you wouldn't be responsible for choosing to undergo x1 hours of torture to save me from an hour of torture. But that's absurd.
Thus, anybody who believes in free will, compatibilist or incompatibilist, should deny (1).
Now, let's add two other common theses that get used to attack libertarianism:
- If a choice can be explained with antecedent mental conditions that yield at most approximately probability 1/2 of that choice, a contrastive explanation of that choice cannot be given in terms of antecedent mental conditions.
- One is only responsible for a choice if one can give a contrastive explanation of it in terms of antecedent mental conditions.
There is an independent argument against (1). The intuition behind (1) is that responsibility requires that a choice be more likely than its alternative. But necessarily God is responsible for all his choices. And surely it was possible in at least one of his choices for him to have chosen otherwise (otherwise, how can he be omnipotent?). If the choice he actually made was not more likely than the alternative, then he was not responsible by the intuition. But God is always responsible. Suppose then the choice he actually made was more likely than the alternative. Nonetheless, he could have made the alternative choice, and had he done so, he would have done something less likely than the alternative, and by the intuition he wouldn't have been responsible, which again is impossible. Thus, the theist must reject the intuition.