All incompatibilists are not necessarily libertarians

Before van Inwagen then, incompatibilists were libertarians, opposing the idea that free will is compatible with determinism.

But after van Inwagen, the new emphasis on "incompatibilism" drew attention to the idea that that James' "hard" determinists were also incompatibilist in the sense of denying compatibilism.
Unfortunately for the clarity of the dialectic, this new category of incompatibilism is very confusing, because it now contains two opposing concepts, libertarian free will and hard determinism!
And like determinism versus indeterminism, compatibilism versus incompatibilism is a false and unhelpful dichotomy. J. J. C. Smart once claimed he had an exhaustive description of the possibilities, determinism or indeterminism, and that neither one neither allowed for free will. (Since Smart, dozens of others have repeated this standard logical argument against free will.)

The Consequence Argument and Mind Argument

Van Inwagen has his own terminology for the two-part standard argument, dividing it into the Consequence Argument and the Mind Argument.

Van Inwagen defines determinism very simply.

"Determinism is quite simply the thesis that the past determines a unique future." (Essay on Free Will, p.2)

He concludes that such a Determinism is not true, because we could not then be responsible for our actions, which would all be simply the consequences of events in the distant past that were not "up to us."

This approach, known as van Inwagen's Consequence Argument, is the perennial Determinism Objection in the standard argument against free will.

Note that in recent decades the debates about free will have been largely replaced by debates about moral responsibility. Since Peter Strawson, many philosophers have claimed to be agnostic on the traditional problem of free will and determinism and focus on whether the concept of moral responsibility itself exists. Some say that, like free will itself, moral responsibility is an illusion. Van Inwagen is not one of those. He hopes to establish free will.

Van Inwagen also notes that quantum mechanics shows indeterminism to be "true." He is correct. But we still have a very powerful and "adequate" determinism. It is this adequate determinism that R. E. Hobart and David Hume have recognized we need when they say that "Free Will Involves Determination and is Inconceivable Without It." Our will and actions are determined. It is the future alternative possibilities in our thoughts that are undetermined.
Sadly, many philosophers mistake indeterminism to imply that nothing is causal and therefore that everything is completely random. This is the Randomness Objection in the standard argument.