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Incompossibilism
The term 'incompossibilism' was coined in 2012 by philosopher Kristin M. Mickelson to name the view that is the view that it is metaphysically impossible for an ordinary human to exercise free will in a universe at which determinism is true. The term 'compossibilism' (also coined by Mickelson) names the contradictory of incompossibilism, i.e. the view that it is metaphysically possible for an ordinary human to exercise free will in a universe at which determinism is true.

In free-will discourse, incompossibilism may be contrasted with classical, neo-classical, and anti-classical forms of incompatibilism and compossibilism may be contrasted with classical, neo-classical, and anti-classical forms of compatibilism.

Arguments for Incompossibilism
One of the most popular argument strategies in the contemporary free will debate is the so-called "manipulation argument" (a.k.a. "multiple-case argument"). The first major argument of this kind, "The Four-Case Argument" developed by philosopher Derk Pereboom, concluded to neo-classical incompatibilism, the two-tenet view that (1) incompossibilism is true, and (2) determinism-related causal factors preclude—rule out, destroy, undermine—the exercise of free will by normal human beings. . Shortly afterward, philosopher Alfred Mele introduced a new variant of the manipulation argument, his original Zygote Argument. Like its predecessor, the Four-Case Argument, the original Zygote Argument ("OZA-2006") concluded to the incompatibilist thesis that determinism (i.e. deterministic causal laws) precludes the exercise of free will by an ordinary human being. Since this explanatory thesis implies the truth of incompossibilism, the original Zygote Argument (OZA-2006) aimed to support the same neo-classical incompatibilist conclusion as the Four-Case Argument.

However, Mele now promotes a new variant of his original Zygote Argument; this revised Zygote Argument ("RZA-2012")—first proposed by Mickelson in 2012 —concludes to the non-explanatory conclusion of incompossibilism; it does not aim to support neo-classical incompatibilism. That is, unlike the Four-Case Argument and the original Zygote Argument, the revised Zygote Argument takes no stand on what explains the purported fact that it is metaphysically impossible for an ordinary human to exercise free will when determinism is true. Among other things, this means the the revised Zygote Argument may be developed in a variety ways, e.g. as an argument for constitutive-luck impossibilism and against neo-classical incompatibilism. In other words, the revised Zygote Argument (RZA-2012) may be, and has been, used to argue that the neo-classical incompatibilist conclusion of the original Zygote Argument (OZA-2006) is false.

The distinction between arguments for mere incompossibilism and arguments for neo-classical incompatibilism are often overlooked. The history behind this is complex One contributing factor is that some philosophers who once used the term 'incompatibilism' to name neo-classical incompatibilism now define the term in a new way, namely to refer to mere incompossibilism. This has been called the "post-classical" definition of incompatibilism. For example, because Alfred Mele now uses the post-classical definition of 'incompatibilism', he refers to the revised Zygote Argument as an "argument for incompatibilism" even though it—unlike the Four-Case Argument and the original Zygote Argument (OZA-2006)—is not an argument for neo-classical incompatibilism.