The incompatibilists believe that free will refers to genuine (i.e., absolute, ultimate, physical) alternate possibilities for beliefs, desires, or actions, rather than merely counterfactual ones. Compatibilism is sometimes called soft determinism (William James's term) pejoratively.
Compatibilism is determinism with a slight modification for the sake of appearances and for our language use. It is a position taken because of the perceived need to have some idea of accountability or responsibility for human behavior.
Soft Determinism (also called Compatibilism and Self-determinism): Though determinism is true, that does not rule out freedom and responsibility. In contrast to hard determinism (which claims that determinism is incompatible with freedom), soft determinism says that we are determined and are nonetheless still free.
Compatibilism, most famously championed by Hume, is a theory that suggests that free will and determinism are in fact compatible. According to Hume, free will should not be understood as an absolute ability to have chosen differently under exactly the same inner and outer circumstances.
The belief is that their God's providence is "compatible" with voluntary choice. Soft theological determinism is known as theological compatibilism (see figure, top right).
Thus, hard determinism is quite literally a form of compatibilism. Therefore, assuming that libertarianism is false, compatibilism is the only remaining account of free will, and must be the one we endorse.
Also, some philosophers use the term 'compatibilism' to refer to the view that determinism is compatible with moral responsibility or with free will understood in a sense according to which free will is necessary for moral responsibility.)
Compatibilists state such a compatibility, whereas incompatibilists deny it. Libertarians are those incompatibilists who postulate the actual existence of free will (and are thus committed to deny the truth of determinism).
Compatibilism, as the name suggests, is the view that the existence of free will and moral responsibility is compatible with the truth of determinism.
The determinist approach proposes that all behavior has a cause and is thus predictable. Free will is an illusion, and our behavior is governed by internal or external forces over which we have no control.
A substantial body of the free will debate is about the relationship between free will and determinism in science. In fact, indeterminism has no place at all in an understanding of human free will. Indeterminism is the false presupposition of the free will debate.