Let p be the proposition that "the mind is always subject to the influence of causal factors".

(1) Assuming p, we lack free will both in a (a) deterministic context [our thoughts are determined from initial conditions], and in a (b) indeterministic context [our thoughts are 'determined' in part at random].

(2) It follows that causality in general is incompatible with free will.

(43 It follows that under the assumption of p, what evidence we favour, propositions we believe true, intuitions we have, axioms we uphold, all thoughts, and any and all beliefs are discerned by [not in the literal sense that an agent discerns something] a blind force of nature [causality].

(4) It follows that under the assumption of p it cannot be said that we are rational in holding our beliefs [our beliefs may be rational and true by accident; but our warrant for our beliefs and the truth of our beliefs are two different things].

(5) It follows that holding any position in favour of p is self-defeating [as it pertains to what the agent can be blamed for believing; not the raw truth of propositions].

(6) We can derive from our perceptual knowledge that causality is an intregal part of the physical world [considering the epistemic goals of believing truth and avoiding error, we have every reason, backed by mountas of evidence, to believe this, and no reason to reject it].

(7) It follows that it cannot be said to be a rationally held position that "the mind is a purely physical phenomena".

To clarify (4):

Causality has no mechanism in where the thoughts 'it' [not to say casuality is literally an entity] 'selects' [not to that it selects things in the manner an agent could] for us is checked against rational standards [unlike a free agent could do]. As free agents, we would be able to check on our beliefs, reflect on our intuitions, and analyze things we take to be axiomatic. Causality would only deliver us belief in true propositions, blindly, by accident. Causality could deliver us valid first principles, but what we ultimately derive from them still could not be said to be rational. How we think about first principles and what we ultimately take from them are, again, discerned by a blind force of nature.

To clarify (5):

One might think that the conclusion is that we are epistemically doomed. However, if accepting p and it's implications, the mere position that p entails that we are epistemically doomed is not a rationally held belief. This objection would assume epistemic doom except for the ability to discern that are epistemically doomed.