Noonan's Argument

Noonan's Argument

A try at Nooan's argument:

  1 It is morally wrong to harm another human being without sufficient reason.  
  2 Except in cases of cancerous uterous and ectopic (tubal) pregnancy, abortion harms another human being without sufficient reason.  
3 Except in cases of cancerous uterous and ectopic pregnancy, abortion is morally wrong.  

This is a good first approximation of Noonan's argument. But it is clear upon closer reading that his argument is much more complicated. For example, Noonan is awfully concerned to justify the assumption that the human conceptus is a human being--alternatively, that the fetus is a person. But this assumption is nowhere to be seen in the above argument. Hence we have more work to do:

Noonan's Argument
  1 If x is an act of harming a human being and x has no sufficient reason, then x is morally wrong.  
  2 If x is an abortion then x is an act of harming a human conceptus (embryo, fetus).  
  3 A human conceptus is a human being.  
4 If x is an abortion then x is an act of harming a human being. 2&3
  5 If x is an abortion then, if x is not a case of cancerous uterous or ectopic pregnancy, then x has no sufficient reason.  
6 If x is an abortion and x is not a case of cancerous uterous or ectopic pregnancy, then x is an act of harming a human being and x has no sufficient reason. 4&5
7 If x is an abortion and x is not a case of cancerous uterous or ectopic pregnancy, then x is morally wrong. 1&6

Here we have Noonan's argument in fuller detail. Notice that we've uncovered a number of assumptions in the process of expanding his argument. The argument is valid, so our question now is whether it is sound. Are all of Noonan's assumptions--premises (1), (2), (3), and (5), specifically--true?