In so far as all descriptions of physical law are at best probabilistic, all attempts to make real descriptions of the physical world indicate the merely probabilistic nature of the world. As such, the most that scientific nomology can deliver for determinism is a picture of a generally deterministic world, which is to say, science does not avail to support determinism.
Along similar lines, I encourage you to watch the following lecture on neuroconsciousness by Gerald Edelman. Edelman's remarks do not begin until about the 30-minute mark, but once he begins, note his admission both of the stochastic, radically neuron-individualistic (my term of art) nature of the human brain and of his rejection of reductionism. Here are two syllogisms to keep in mind as you listen:
1. If Edelman is right that each neuron is literally unique, and
2. since scientific laws are generalizations about classes which do not apply to individual cases, then
3. there may be literally no formulable laws of neuroscience.
1. the brain is patently both a stochastic and natural entity, and in so far as
2. stochastic causation undermines determinism, then
3. the brain compromises the deterministic closure of the natural world.