[PHI 1000] Being free with a brain?

Here's a simple argument for causal determinism:

1. The human brain is a causally determined system (i.e., a system in which effect E necessarily follows from cause C given the initial conditions and the laws of nature).
2. If the human brain is a causally determined system, then human actions are causally determined.
3. Therefore, human actions are causally determined.

Evidence for premise (1) comes from neuroscience. The famous case of Phineas Gage, for example, shows that injuries in certain regions of the brain bring about certain changes in behavior.

Is this argument sound? And if so, is there any room for free will?