Libertarianism
The incompatibilist free will position is much harder to defend than compatibilism. 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.
Read more about this topic: Incompatibilism