There is a very good article on the logic of personhood as beginning at conception at nationalreviewonline. It's written by Patrick Lee of Franciscan University of Steubenville and Robert P. George of Princeton.
Consider this excerpt: "In defending embryonic human life, we have pointed out that every human adult was once an embryo, just as he or she was once an adolescent, and befofre that a child, and before that an infant, and before that a fetus. This is not a religious claim or a piece of metaphysical speculation. It is a human fact. The complete human organism - the whole living member of the species Homo sapiens - that is, for example, you the reader, is the same human individual that at an earlier point in his or her life was an adolescent, a child, an infant, a fetus, am embryo."
"Human embryos do not differ in kind from (other) human beings; rather, they differ from other human beings merely in respect of their stage of development."
Thus, there is no "point in time" (such as the moment of "viability") where suddenly the fetus "becomes a person."
The argument against abortion then runs logically like this:
1. The fetilized egg is a person.
2. Every person has a right to life.
3. Therefore the fertilized egg has a right to life.