In debates about criteria for human death, several camps have emerged, the main two focusing on either loss of the “organism as a whole” (the mainstream view) or loss of consciousness or “personhood.” Controversies also rage over the proper definition of “irreversible” in criteria for death. The situation is reminiscent of the proverbial blind men palpating an elephant; each describes the creature according to the part he can touch. Similarly, each camp grasps some aspect of the complex reality of death. The personhood camp, in contrast to the mainstream “organism” camp, recognizes that a human organism can still be a biological living whole even without brain function. The mainstream camp, in contrast to the personhood camp, recognizes that a person can be permanently, even irreversibly unconscious, and still be a living person so long as his/her body is alive. The author proposes that hylomorphic dualism incorporates both these key insights. But to complete the picture of the entire “death elephant,” a fundamental paradigm shift is needed to make sense of other seemingly conflicting insights. The author proposes a “semantic bisection” of the concept of death, analogous to the traditional distinction at the beginning of life between “conception” and “birth.” To avoid the semantic baggage associated with the term “death,” the two new death-related concepts are referred to as “passing away” (or “deceased”) and “deanimation,” corresponding, respectively, to sociolegal ceasing-to-be (mirror image of birth) and ontological/theological ceasing-to-be of the bodily organism (mirror image of conception). Regarding criteria, the distinguishing feature is whether the cessation of function is permanent (passing away) or irreversible (deanimation). If the “dead donor rule” were renamed the “deceased donor rule” (both acronyms felicitously being “DDR”), the ethics of organ transplantation from non–heart-beating donors could, in principle, be validly governed by the DDR, even though the donors are not yet ontologically “deanimated.” Thus, the paradigm shift satisfies both those who insist on maintaining the DDR and those who claim that it has all along been receiving only lip service and should be explicitly loosened to include those who are “as good as dead.” Even so, a number of practical caveats remain to be worked out for non–heart-beating protocols.