Let P be the proposition that "the mind is always subject to the influence of causal factors". P will be mentioned in some premises; it is important to bring the reader to the attention of P in order for some things I say to have meaning and/or be more clear.

(1) Assuming P, we lack free will [libertarian definition] either in a (a) deterministic context [our thoughts & ultimate will are ultimately determined in the sense that they are necessary effects that follows from an unbreakable chain of causality starting from initial conditions], and in a (b) indeterministic context [our thoughts & ultimate will are 'determined' in part at random; not precluding inherently deterministic sequences of causes].

(2) It follows that causality in general is incompatible with free will [libertarian definition].

(3) It follows that under the assumption of P, what evidence we favor, propositions we believe true, intuitions we have, our reflections on these intuitions, axioms we 'choose' to uphold [that is to say, *upon their recognition*, because we tend to apply them with or without consciously recognizing them], all thoughts in general, and so any and all beliefs are discerned by [not in the literal sense in the way an agent could discern something] a blind force of nature [which is causality; please don't think I believe causality is some sort of entity].

(4) It follows that under the assumption of P, it cannot be said that we have rationale [for lack of a better term] in holding our positions [our beliefs themselves may be rational and true by accident; this is different from *what can be said* about our warrant for holding positions].

(5) It follows that holding any position in favour of p is also self-defeating [note this is different from saying a position itself is self-defeating] as these positions share the same consequences of p [I take justification and warrant to pertain to what the agent can or cannot be blamed for believing; I'm not saying this influences the raw truth of propositions and validity of positions in themselves].

(6) We derive from our perceptual knowledge that nothing physical that exists is exempt from causality.

(7) It follows that nothing that which is exempt from causality is physical [this claim is made in the sense that we have every reason to believe this is true and no reason to believe it is false].

(8) It follows that the only position that we can take [with warrant] is that our minds are at least partially non-physical.

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Our justification for [remember: not the same thing as the raw truth of a position] positions being eradicated completely when accepting p includes the mere acceptance of p itself. The fact that [a position for] P implies it's own contradiction gives as good of a reason as any to reject a position for P. So, the conclusion would be that we have no reason to believe P and every reason to believe an alternative hypothesis.

(1) is obviously incompatible with the compatibilist definition of free will. However, I think that regardless of our definition of free will, we need only operate under what the libertarian definition *describes*. We don't necessarily even have to call it free will.

To elaborate a bit more [mostly about premise 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 or implicitly adherent to rational standards [unlike the case of the existence of a free agent]. If we are free agents, we may freely check on beliefs, reflect on our intuitions, and analyze things we take to be axiomatic. Causality could only deliver us belief in true propositions by accident. An agent also can just be right by accident, but the free agent has a mechanism [if you will] for checking their beliefs freely. A helpess agent [for lack of a better term] still has a mechanism as well, but both this mechanism and how they use it, is once again, 'determined' [at least in some sense] by causality [I'd be speaking more accurately if I gave a description of the relevant causal factors].

One could argue that it only matters that causality deliver us objectively true first principles. However, it'd seem the same consequences of (4) would apply.

I've never understood the compatibilist position that we have predetermined desires but we freely choose from those desires. It seems that this definition of free will is meaningless [and useless] because we are the victim of [we being agents that have no control on our desire or how they influence us] the circumstances of our environment which as they are dictate our following actions. Second, I'm not sure how we would freely choose what follows from desires [unless I'm making a huge straw man of the compatibilist position]. Causality in some sense would still [ultimately] dictate all our thoughts and actions [including thoughts/actions that follows from antecedent desires], because are thoughts as physical effects [unless some people hold the position that our minds are non-physical yet still we lack free will]  are things that necessarily behave one way in accordance to antecedent conditions/causes/whatever [I think you get the point].

The argument is not focused on, and indeed has no weight on the truth of any propositions themselves. What is has weight on is what we should [in the epistemic sense] believe, what would be self-defeating to believe; generally what we have no reason to believe and have every reason to believe.