Incompatibilism is the view that a deterministic universe is completely at odds with the notion that people have a free will; that there is a dichotomy between determinism and free will where philosophers must choose one or the other. This view is pursued in at least three ways: libertarians deny that the universe is deterministic, the hard determinists deny that any free will exists, and pessimistic incompatibilists (hard indeterminists) deny both that the universe is determined and that free will exists. Some of these incompatibilistic views have more trouble than the others in dealing with the standard argument against free will.
Incompatiblism is contrasted with compatibilism, which rejects the determinism/free will dichotomy. Compatibilists maintain free will by defining it as more of a 'freedom to act' - a move that has been met with some criticism.
Metaphysical Libertarianism argues that free will is real and that determinism is false. One might defend the view of a mind that is metaphysically free. Such dualism risks an infinite regress however; if any such mind is real, it is still subject to the standard argument against free will. Yet another alternative remains philosopher Robert Kane's model.
Robert Kane (editor of the Oxford Handbook of Free Will) is a leading incompatibilist philosopher in favour of free will. Kane seeks to hold persons morally responsible for decisions that involved indeterminism in their process. Critics maintain that Kane fails to overcome the greatest challenge to such an endeavor: "the argument from luck". Namely, if a critical moral choice is a matter of luck (indeterminate quantum fluctuations), then on what grounds can we hold a person responsible for their final action? Moreover, even if we imagine that a person can make an act of will ahead of time, to make the moral action more probable in the upcoming critical moment, this act of 'willing' was itself a matter of luck.
Libertarianism in the philosophy of mind is unrelated to the like-named political philosophy. It suggests that we actually do have free will, that it is incompatible with determinism, and that therefore the future is not determined. For example, at this moment, one could either continue reading this article if one wanted, or cease. Under this assertion, being that one could do either, the fact of how the history of the world will continue to unfold is not currently determined one way or the other.
One famous proponent of this view was Lucretius, who asserted that the free will arises out of the random, chaotic movements of atoms, called "clinamen". One major objection to this view is that science has gradually shown that more and more of the physical world obeys completely deterministic laws, and seems to suggest that our minds are just as much part of the physical world as anything else. If these assumptions are correct, incompatibilist libertarianism can only be maintained as the claim that free will is a supernatural phenomenon, which does not obey the laws of nature (as, for instance, maintained by some religious traditions).
However, many libertarian view points now rely upon an indeterministic view of the physical universe, under the assumption that the idea of a deterministic, "clockwork" universe has become outdated since the advent of quantum mechanics. By assuming an indeterministic universe libertarian philosophical constructs can be proposed under the assumption of physicalism.
There are libertarian view points based upon indeterminism and physicalism, which is closely related to naturalism. A major problem for naturalistic libertarianism is to explain how indeterminism can be compatible with rationality and with appropriate connections between an individual's beliefs, desires, general character and actions. A variety of naturalistic libertarianism is promoted by Robert Kane, who emphasizes that if our character is formed indeterministically (in "self-forming actions"), then our actions can still flow from our character, and yet still be incompatibilistically free.
Alternatively, libertarian view points based upon indeterminism have been proposed without the assumption of naturalism. Although at the time C. S. Lewis wrote Miracles, Quantum Mechanics (and physical indeterminism) was only in the initial stages of acceptance, he stated the logical possibility that if the physical world was proved to be indeterministic this would provide an entry (interaction) point into the traditionally viewed closed system, where a scientifically described physically probable/improbable event could be philosophically described as an action of a non physical entity on physical reality (noting that under a physicalist point of view the non physical entity must be independent of the self identity or mental processing of the sentient being). Lewis mentions this only in passing, making clear that his thesis does not depend on it in any way.
Others may use some form of Donald Davidson's anomalous monism to suggest that although the mind is in fact part of the physical world, it involves a different level of description of the same facts, so that although there are deterministic laws under the physical description, there are no such laws under the mental description, and thus our actions are free and not determined.
Hard determinism 
Those who reject free will and accept Determinism are variously known as "hard determinists", hard incompatibilists, free will skeptics, illusionists, or impossibilists. They believe that there is no 'free will' and that any sense of the contrary is an illusion. Of course, hard determinists do not deny that one has desires, but say that these desires are causally determined by an unbroken chain of prior occurrences. According to this philosophy, no wholly random, spontaneous, mysterious, or miraculous events occur. Determinists sometimes assert that it is stubborn to resist scientifically motivated determinism on purely intuitive grounds about one's own sense of freedom. They reason that the history of the development of science suggests that determinism is the logical method in which reality works.
William James said that philosophers (and scientists) have an "antipathy to chance." Absolute chance, a possible implication of quantum mechanics and the indeterminacy principle, implies a lack of causality. This possibility often disturbs those who assume there must be a causal and lawful explanation for all events.
Moral implications 
As something of a solution to this predicament, it has been suggested that, for the sake of preserving moral responsibility and the concept of ethics, one might embrace the so-called "illusion" of free will. This, despite thinking that free will does not exist according to determinism. Critics argue that this move renders morality merely another "illusion", or else that this move is simply hypocritical.
The Determinist will add that, even if denying free will does mean morality is incoherent, such an unfortunate result has no effect on the truth. Note, however, that hard determinists often have some sort of 'moral system' that relies explicitly on determinism. A Determinist's moral system simply bears in mind that every agent's actions in a given situation are, in theory, predicted by the interplay of environment and upbringing. For instance, the Determinist may still punish undesirable behaviours for reasons of behaviour modification or deterrence.
Pessimistic incompatibilism 
While hard determinism clearly opposes the concept of free will, some have suggested that free will might also be incompatible with non-determinism. This is pessimistic incompatibilism, and has been used as an argument against Libertarian incompatibilism.
Under the assumption of naturalism and indeterminism, where there only exists the natural world and that the natural world is indeterministic — events are not predetermined (e.g., for quantum mechanical reasons) and any event has a probability assigned to it — no event can be determined by a physical organism's perceived free will, and nor can any event be strictly determined by anything at all.
Hard incompatibilism differs from hard determinism in that it does not commit to the truth of determinism. Typically, supporters of hard incompatibilism accept both libertarian critiques of compatibilism and compatibilist critiques of libertarianism.
Experimental research 
In recent years researchers in the field of experimental philosophy have been working on determining whether ordinary people, who aren't experts in this field, naturally have compatibilist or incompatibilist intuitions about determinism and moral responsibility. Some experimental work has even conducted cross-cultural studies. The debate about whether people naturally have compatibilist or incompatibilist intuitions has not come out overwhelmingly in favor of one view or the other. Still, but there has been some evidence that people can naturally hold both views. For instance, when people are presented with abstract cases which ask if a person could be morally responsible for an immoral act when they could not have done otherwise, people tend to say no, or give incompatibilist answers, but when presented with a specific immoral act that a specific person committed, people tend to say that that person is morally responsible for their actions, even if they were determined (that is, people also give compatibilist answers).
See also 
- Daniel Dennett's Freedom Evolves
- Daniel Dennett's Elbow Room
- Dilemma of determinism
- Lucretius's On the Nature of Things
- Philosophical zombie
- Why Naturalists Should Mind about Physicalism, and Vice Versa Williams, Peter Quodlibet Journal, Volume 4 Number 2-3, Summer 2002
- summary of Kane's views by the Stanford Encyclopedia of Philosophy
- Kane, Robert. “Free Will: New Directions for an Ancient Problem.” (2003). In Free Will, Robert Kane (ed.) (2003) Malden, MA: Blackwell
- Lewis, C.S (1947). Miracles.
- Sosa -- Free Mental Causation! (MS Word)
- Saul Smilansky, Free Will and Illusion, Oxford, 2000
- William James, The Dilemma of Determinism, p.153
- Pereboom, Derk. 2001. Living Without Free Will. Cambridge: Cambridge University Press. ISBN 0-521-79198-7
- Eddy Nahmias, Stephen Morris, Thomas Nadelhoffer,and Jason Turner. (forthcoming).Incompatibilism Intuitive?,” Philosophy and Phenomenological Research.
- Hagop Sarkissian, Amita Chatterjee, Felipe De Brigard, Joshua Knobe, Shaun Nichols, Smita Sirker (forthcoming)."Is belief in free will a cultural universal?" Mind & Language
- Shaun Nichols and Joshua Knobe. (forthcoming).“Moral Responsibility and Determinism: The Cognitive Science of Folk Intuitions.” Nous.