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What is the metaphysical relationship between the fetus/embryo and the pregnant organism? In this paper I apply a substance metaphysics view developed by Barry Smith and Berit Brogaard to argue, on the basis of topological connectedness, that fetuses/embryos are Lady-Parts: part of the maternal organism up until birth. This leaves two options. Either mammalian organisms begin at birth, or we revise our conception of organisms such that mammalian organisms can be part of other mammals. The first option has some advantages: it is numerically neat; aligns with an intuitive picture of organisms as physically distinct individuals; and ties ‘coming into existence’ to a suitably recognisable and important event: birth. But it denies that the fetus survives birth, or that human organisms existed prior to their birth. The second option allows us to recognise that human organisms exist prior to and survive their birth, but at a cost: it leaves the question of when an organism comes into existence unanswered, and demands potentially far-reaching conceptual revision across a range of domains.