In contrast to eminent historical philosophers, almost all contemporary philosophers maintain that slavery is impermissible. In the enthusiasm of the Enlightenment, a number of arguments gained currency which were intended to show that contractual slavery is not merely impermissible but impossible. Those arguments are influential today in moral, legal and political philosophy, even in discussions that go beyond the issue of contractual slavery. I explain what slavery is, giving historical and other illustrations. I examine the arguments for the impossibility of contractual slavery propounded in the Enlightenment and their offspring expounded in recent writings, including those by Barnett, Cassirer, Ellerman, Rawls, Roberts-Thomson, Satz and Steiner. I show that they involve confusions between abilities and rights, free will and freedom, directing and doing, what may be true sequentially and what may be true simultaneously, default rights and universal rights, impermissibility and impossibility, and metaphorical and literal uses of language.