Incompatibilism
The philosophical term incompatibilism was coined in the 1960s, most likely by philosopher Keith Lehrer, to name the view that the thesis of determinism is logically incompatible with the classical thesis of free will. The term compatibilism was coined (also by Lehrer) to name the view that the classical free will thesis is logically compatible with determinism, i.e. it is possible for an ordinary human to exercise free will (the freedom-relevant ability to do otherwise) even in a universe at which determinism is true. These terms were originally coined for use within a research paradigm that was dominant among academics during the so-called "classical period" from the 1960s to 1980s, or what has been called the "classical analytic paradigm". Within the classical analytic paradigm, the problem of free will and determinism was understood as a Compatibility Question: "Is it possible for an ordinary human to exercise free will (classically defined as an ability to otherwise) when determinism is true?" Those working in the classical analytic paradigm who answered "no" were incompatibilists in the original, classical-analytic sense of the term, now commonly called classical incompatibilists; they proposed that determinism precludes free will because it precludes our ability to do otherwise. Those who answered "yes" were compatibilists in the original sense of the term, now commonly called classical compatibilists. Given that classical free will theorists (i.e. those working in the classical analytic paradigm) agreed that it is at least metaphysically possible for an ordinary human to exercise free will, all classical compatibilists accepted a compossibilist account of free will (i.e. a compossibilist interpretation of the ability to do otherwise) and all classical incompatibilists accepted a libertarian (a.k.a. libertarianist) account of free will (i.e. a libertarian/libertarianist interpretation of the ability to do otherwise).
The classical analytic paradigm has fallen out of favor over the last few decades, largely because philosophers no longer agree that free will is equivalent to some kind of ability to do otherwise; many hold that it is, instead, a type of sourcehood that does not require an ability to do otherwise. The number of philosophers who reject the classical assumption of anthropocentric possibilism, i.e. the view that it is at least metaphysically possible for a human to exercise free will, has also risen in recent years. As philosophers adjusted Lehrer's original (classical) definitions of the terms 'incompatibilism' and 'compatibilism' to reflect their own perspectives on the location of the purported "fundamental divide" among free will theorists, the terms 'incompatibilism' and 'compatibilism' have been given a variety of new meanings. At present, then, there is no standard meaning of the term 'incompatibilism' (or its complement 'compatibilism').
On one recent taxonomy, there are now at least three substantively different, non-classical uses of the term 'incompatibilism', or (if one prefers) three different types of incompatibilism, namely: neo-classical incompatibilism, post-classical incompatibilism (a.k.a. incompossibilism), and anti-classical incompatibilism; correspondingly, there are neo-classical, post-classical (compossibilist), and anti-classical versions of compatibilism as well. Neo-classical incompatibilism is a two-tenet view: (1) incompossibilism is true (i.e. it is metaphysically impossible for an ordinary human to act freely when determinism is true), and (2) determinism-related causal/nomological factors preclude free will (which explains why incompossibilism is true). Correspondingly, neo-classical compatibilism is the two-tenet view that (1) the negative, non-explanatory tenet of neo-classical incompatibilism is false (i.e. compossibilism is true), and (2) the positive, explanatory tenet of neo-classical incompatibilism is false. Anti-classical incompatibilism is the explanatory thesis of neo-classical incompatibilism; anti-classical incompatibilism is neutral on the truth-value of incompossibilism. Correspondingly, anti-classical compatibilism is the negation of neo-classical incompatibilism's positive tenet, i.e. anti-classical compatibilism is the contradictory of anti-classical incompatibilism. Post-classical incompatibilism is just the negative, non-explanatory thesis of neo-classical incompatibilism; this view is neutral on whether the positive, explanatory thesis of neo-classical incompatibilism is truIe. (Put another way, on the post-classical redefinition of 'incompatibilism', it is just an alternative name for incompossibilism, a view which is completely silent on whether determinism-related causal factors are relevant to free will or are a total red herring in discussions of free will.) Correspondingly, post-classical compatibilism is identical to compossibilism (i.e. on the post-classical redefinition of 'compatibilism', it denotes mere compossibilism).
The ambiguity of 'incompatibilism' can be a source of confusion because arguments with very different (even inconsistent) conclusions are currently lumped together under the umbrella phrase "arguments for incompatibilism." For example, it is easy for the casual reader to overlook that some arguments for post-classical incompatibilism (a.k.a. incompossibilism) are not arguments for neo-classical incompatibilism on the grounds that the argument does not aim to support the latter's explanatory tenet (a.k.a. anti-classical incompatibilism). Other arguments support post-classical incompatibilism (a.k.a. incompossibilism) but conclude that neo-classical incompatibilism is false on the grounds that its explanatory tenet (a.k.a. anti-classical incompatibilism) is false. Arguments in the last category conclude that people lack free will when determinism is true but not at all because determinism is true (i.e. not at all because certain causal/nomological factors obtain); most propose that the real threat to free will is that people lack adequate control over their own constitutive properties, or what is often called their "constitutive luck" (as opposed to causal luck).