Incompatibilism was historicaly the position in the taxonomy of free will debates that says determinism is incompatible with human freedom. It is a complex idea, because it is not committed to the truth or falsity of determinism. But how does this idea of "incompatibilism" differ from the normal idea that free will does not exist if determinism is true? The answer is that incompatibilism was invented by Peter van Inwagen as a new free will position that denies the truth of "compatibilism." It is an "anti-compatibilism" that is more subtle than the question of the existence of free will or determinism. When we recall that compatibilism itself is a "wretched subterfuge" (Immanuel Kant) and a "quagmire of evasion" (William James), it is perhaps no surprise that incompatibilism is a tortured and muddled concept that gives rise to contorted logistical and linguistic debates. If compatibilism is a quagmire, incompatibilism is even darker and deeper, perhaps a "tarpit of confusion." It is arguably the worst recent coinage in a philosophical field that is already crowded with conflicted terminology. To be sure, libertarians have always denied the nonsense of compatibilism, and accepted the idea that free will is incompatible with determinism. Simple enough. But there is another view, that of determinists who agree that determinism is incompatible with free will. So there are two kinds of incompatibilists, those who deny human freedom (usually called "hard" determinists), and those who assert it (often called voluntarists, free willists, or metaphysical libertarians - to distinguish them from political libertarians). As a result, incompatibilism is a very confusing term in the free will debates. Adding to the confusion, indeterminism is also said to be incompatible with human freedom, or at best provides an incoherent and unintelligible account of freedom.
If the proximate cause of our actions is undetermined - for example, the result of an uncaused quantum mechanical event in the mind - it would not be freedom of a kind worth having and we should disavow responsibility.
Some incompatibilists feel (correctly) that there must be a deterministic or causal connection between our will and our actions. This allows us to take responsibility for our actions, including credit for the good and blame for the bad.
Compatibilists accept the view of a causal chain of events going back indefinitely in time, consistent with the laws of nature, with the plan of an omniscient God, or with other determinisms. As long as our own will is included in that causal chain, we are free, they say. So what exactly is incompatibilism? It's either to deny the strict causal chain and allow free will, or to deny free will and accept strict determinism. Such an ambiguous concept is one of the reasons that the free will debate has been so muddled.
Let's look at the taxonomy of deterministic positions and see where incompatibilism fits.
Recently, incompatibilists have staked out nuanced versions of the familiar positions with new jargon, like semicompatibilism, hard incompatibilism, and illusionism.
Broad compatibilists think both free will and moral responsibility are compatible with determinism. Narrow compatibilists think free will is not compatible, but moral responsibility is compatible with determinism. Semicompatibilists are narrow compatibilists who are agnostic about free will and determinism.
Hard incompatibilists think both free will and moral responsibility are not compatible with determinism. Illusionists are incompatibilists who say free will is an illusion.
Soft incompatibilists think both free will and moral responsibility are incompatible with strict determinism, but both are compatible with an adequate determinism.
Let's also look at the taxonomy of indeterministic positions and see where incompatibilism fits.
Incompatibilists who are indeterminists (denying determinism) generally accept the view that random events (most likely quantum mechanical events) occur in the world. Whether in the physical world, in the biological world (where they are a key driver of genetic mutations), or in the mind, randomness and uncaused events are real. They introduce the possibility of accidents, novelty, and human creativity.
Although random quantum mechanical events break the strictly deterministic causal chain, which has just one possible future, they nevertheless are causes for successive events. They start new unpredictable causal chains. They generate unpredictable futures. They are said to be causa sui.
Soft causalists are event-causalists who accept causality but admit some unpredictable events that are causa sui and which start new causal chains.
While microscopic quantum events are powerful enough to deny determinism, the magnitude of these events is generally so small, especially for large macroscopic objects, that the world is still overwhelmingly deterministic. We call this "adequate determinism."
Our Cogito model places "soft" causality and adequate determinism in the critical apparatus of the Macro Mind. From the Micro Mind, and from the external world including other minds, come surprising and unpredictable events to feed the Agenda of possible thoughts and actions. The Cogito is compatibile with both an adequate determinism and uncertainty. It lives in Eddington's "halfway house."
The old incompatibilism explains freedom. It cannot explain the will. A new "soft" incompatibilism gets us both free (random) and will (adequately determined).
The Cogito is genuine free will.