During the Modern era, philosophers such as Descartes and Locke developed the notions of material substance and immaterial substance. Material substance, or matter, was primarily defined as being extended and spatially located. Descartes, and other thinkers, also took the view that material substance could not think. Immaterial substance was taken to lack extension and to not possess a spatial location. Most importantly, immaterial substance was regarded as having thought as its defining attribute. While these philosophers are long dead, the influence of their concepts lives on in philosophy and science.
In philosophy, people still draw the classic distinction between dualists and materialists. A dualist holds that a living person consists of a material body and an immaterial mind. The materialist denies the existence of the immaterial mind and accepts only matter. There are also phenomenonalists who contend that all that exists is mental. Materialism of this sort is popular both in contemporary philosophy and science. Dualism is still popular with the general population in that many people believe in a non-material soul that is distinct from the body.
Because of the history of dualism, free will is often linked to the immaterial mind. As such, it is no surprise that people who reject the immaterial mind engage in the following reasoning: an immaterial mind is necessary for free will. There is no immaterial mind. So, there is no free will.
Looked at positively, materialists tend to regard their materialism as entailing a lack of free will. Thomas Hobbes, a materialist from the Modern era, accepted determinism as part of his materialism. Taking the materialist path, the argument against free will is that if the mind is material, then there is no free will. The mind is material, so there is no free will.
Interestingly enough, those who accepted the immaterial mind tended to believe that only an immaterial substance could think—so they inferred the existence of such a mind on the grounds that they thought. Materialists most often accept the mind, but cast it in physical terms. That is, people do think and feel, they just do not do so via the mysterious quivering of immaterial ectoplasm. Some materialists go so far as to reject the mind—perhaps ending up in behaviorism or eliminative materialism.
Julien La Metrie was one rather forward looking materialist. In 1747 he published his work Man the Machine. In this work he claims that philosophers should be like engineers who analyze the mind. Unlike many of the thinkers of his time, he seemed to understand the implications of mechanism, namely that it seemed to entail determinism and reductionism. A few centuries later, this sort of view is rather popular in the sciences and philosophy: since materialism is true and humans are biological mechanisms, there is no free will and the mind can be reduced (explained entirely in terms of) its physical operations (or functions).
One interesting mistake that seems to drive this view is the often uncritical assumption that materialism entails the impossibility of free will. As noted above, this rests on the notion that free will requires an immaterial mind. This is, perhaps, because such a mind is said to be exempt from the laws that run the material universe.
One part of the mistake is a failure to realize that being incorporeal is not a sufficient condition for free will. One of Hume’s many interesting insights was that if immaterial substance exists, then it would be like material substance. When discussing the possibility of immortality, he claims that nature uses substance like clay: shaping it into various forms, then reshaping the matter into new forms so that the same matter can successively make up the bodies of living creatures. By analogy, an immaterial substance could successively make up the minds of living creatures—the substance would not be created or destroyed, it would merely change form. If his reasoning holds, it would seem that if material substance is not free, then immaterial substance would also not be free. Leibniz, who believed that reality was entirely mental (composed of monads) accepted a form of determinism. This determinism, though it has some problems, seems entirely consistent with his immaterialism (that everything is mental). This should hardly be surprising, since being immaterial does not entail that something has free will—the two are rather distinct attributes.
Another part of the mistake is the uncritical assumption that materialism entails a lack of freedom. Naturally, if matter is defined as being deterministic and lacking in freedom, then materialism would (by begging the question) entail a lack of freedom. Likewise, if matter is defined (as many thinkers did) as being incapable of thought, then it would follow (by begging the question) that no material being could think. Just as it should not be assumed that matter cannot think, it should also not be assumed that a material being must lack free will. Looked at another way, it should not be assumed that being incorporeal is a necessary condition for free will.
What, obviously enough, seems to have driven the error is the conflation of the incorporeal with freedom and the material with determinism (or lack of freedom). Behind this is, also obviously enough, the assumption that the incorporeal is exempt from the laws that impose harsh determinism on matter. But, if it is accepted that a purely material being can think (thus denying the assumption that only the immaterial can think) it would seem to be acceptable to consider that such a being could also be free (thus denying the assumption that only the immaterial can be free).