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The continuity argument has been used by many writers. Here is C. Everett Koop's version of the argument taken from his The Right to Live the Right to Die. He writes as follows:

My question to my pro-abortion friend who will not kill a newborn baby is this: "Would you kill this infant a minute before he was born, or a minute before that, or a minute before that, or a minute before that?" You see what I am getting at. At what minute can one consider life to be worthless and the next minute consider that same life to be precious? So much for logic.

Here is another version of the argument from an essay by Sidney Callahan.

As embryology and fetology advance, it becomes clear that human development is a continuum. Just as astronomers are studying the first three minutes in the genesis of the universe, so the first moments, days, and weeks at the beginning of human life are the subject of increasing scientific attention. While neonatology pushes the definition of viability ever earlier, ultrasound and fetology expand the concept of the patient in utero. Within such a continuous growth process, it is hard to defend logically any demarcation point after conception as the point at which an immature form of human life is so different from the day before or the day after, that it can be morally or legally discounted as a nonperson. . . .
The same legal tradition which in our society guarantees the right to control one's body firmly recognizes the wrongfulness of harming other bodies, however immature, dependent, different looking, or powerless....
No human can be treated as a means to an end without consent. The fetus is an immature, dependent form of human life which only needs time and protection to develop. Surely, immaturity and dependence are not crimes.

Reference: C. Everett The Right to Live the Right to Die, p. 27. See also the selection from Callahan in the Baird anthology p. 132-33. Callahan's article originally appeared in Commonweal in the April 25, 1986 issue.