Hume’s famous attack on causation, making it out to be nothing more than an idea formed from the observation of constant conjunction, seems to undercut models of one-way determinism.
Determinism says that from any earlier state and the laws, the later states logically follow. Two-way determinism adds that from any later state and the laws, the earlier states logically follow.
~Pruss, Darwinian Evolution and Determinism
In fact, it is difficult to see that anything could logically follow from any earlier state given some laws, since on the Humean account, any projections we make inductively about ‘x causing y’ are inherently stipulated absent logical necessity. There is no logically necessary connection between x and y, such that x is a necessary or sufficient condition for y, and given x, y. Instead, we observe that experience y follows experience x in such a consistent way that we form the idea of causal connection between x and y – but such an account cannot provide the foundation for strict physical/Naturalistic determinism. In fact, the Humean can only at best describe what is likely to occur (by which they don’t actually mean that it ‘is’ likely to occur, but only that we have reason or precedence to suspect it will), and no state has any causal relation with any successive state.
I think this means that a Humean Naturalist cannot consistently be a determinist. This poses an interesting problem I think, since the Naturalist should not appeal to ‘randomness’ as an alternative to determinism without greatly undermining all inductive reasoning in principle. Moreover, on a Naturalistic account of the world, what other option is there? Maybe with appeal to some proximate teleology a Naturalist could get away from this trouble. If teleology is admitted then two-way determinism (or something like it) might be admitted without having to admit of true causes. The only difference perhaps is that nothing ever logically follows from one state to another (whether prior to, simultaneous with, or after the first). Rather, constant conjunction is ordered towards ends which provide a rationale for normativity across successive states of time.
If this argument were successful and further developed, it might demonstrate that the Humean Naturalist must choose between the alternatives of Naturalism in combination with something like Intelligent Design on the one hand, and Theism on the other. That would be an impressive and legitimate ad hominem argument.