Libertarian free will has been espoused in many different flavors, ture. And I personally don’t subscribe to libertarian free will being completely devoid of determinants and thereby of reasons for what it does (which could be construed in certain such variants of the concept). That said, this is to me the very crux of the issue:
One might phrase (b) as causal inevitability, or determinism, or an instance of the principle of sufficient reason. I'm actually leaning towards that latter phrasing lately - that determinism inside a universe means everything that happens in that universe has sufficient reason to happen. — flannel jesus
“Determinism” to most will necessarily entail what in former days was termed “necessarianism” and what today is coined as “causal inevitability” – in both cases, potential subtleties aside, everything that happens happens necessarily. Thereby disallowing for any possibility of libertarian free will.
It’s why I explicitly specified (b) as “causal inevitability”. Which is in no way equivalent to “everything that happens holds an ontically occurring reason for it so happening”. To exemplify this, in the libertarian free will that I sponsor, every possible decision will need to hold at the very least one intent which one intentions as the particular decision’s ontically occurring reason for its occurrence. And this intent is of itself construed to be a teleological determinant - an ontically occurring teleological reason - for the decision between options which was made. For any choice one makes, one will – at the very least when in the right frame of mind – be able to affirm why one made the choice: e.g. so as to get rich, or so as to find love, etc. All these being intents that determine that option which one chooses via one’s libertarian free will. Due to this, the principle of sufficient reason here fully applies – but it in no way translates into “the decisions I/you make are causally inevitable”.
I fully know and acknowledge that such a reality wherein the PSR holds for all choices made would be one in which all choice made via libertarian free will (as it was previously defined) are nevertheless determined by some determinant. However, when one does X for the sake of Z, Z (the end pursued) will not of itself causally determine X – but will instead teleologically determine X; this without in any way nullifying the lack of metaphysical constrains one has in choosing one of the options toward Z as intended outcome.
All this is not determinism as the term is understood today, such that it entails causal inevitability, while nevertheless yet being a reality wherein everything is yet determined by some or other determinant and, therefore, wherein the PSR holds for all events. One's of libertarian free will fully included.
Causally though, when one entertains libertarian free will, the agent in a large sense becomes an non-causally determined cause of the option chosen as effect - keeping in mind that this agent in its causing of the effect is necessarily teleologically determined by the intent which the agent pursued.
This is of course a very different mindset relative to those commonly held today: such as those wherein everything can only be either causally inevitable or else random. .
But this is the very reason why there is a pivotal difference between a libertarian compatibilism (where libertarian free will is maintained to occur together with the Principle of Sufficient Reason for all choice made), on the one hand, and a deterministic, else non-libertarian, compatibilism (where some non-libertarian understanding of free will is maintained together with the doctrine of universal causal inevitability).
One cannot willy nilly jump back and forth between a libertarian compatibilism and a deterministic, in the sense of non-libertarian, compatibilism on account of both of these being "compatibilism" - for the first mandates the ontic reality of a libertarian free will and the second mandates its very metaphysical impossibility.