For simplicity, suppose all utilities are commensurable.
No finite amount of utility justifies killing a being with moral standing. Take this to be stipulative of moral standing, and further take it as a substantive thesis that adult humans have moral standing. For any being x at a time t, let u(x,t) be the greatest (finite or infinite) number u with the property that if u' is any number smaller than u, then it is wrong to destroy x at t to produce u' units of utility. For instance, if the units of utility are average human lives, maybe u(adult dog, now) is 0.0001—it would be wrong to kill a dog to produce less than 0.0001 times the value of an average human life, but it would not be wrong to kill a dog to produce 0.00011 times that value. The exact calibration will be obviously controversial, and some people will say that the right number for a dog is 0.1 or 0.5 or even 1. We could call u(x,t) the "moral significance of x at t". Note that x has moral standing at t if and only if u(x,t) is infinite.
Now consider the following plausible assumptions:
- No earthly critter changes at all significantly in its natural properties over a period of time in its life that does not exceed the Planck time (5.4x10−44 seconds).
- If x is an earthly critter, and u(x,t) changes very significantly over a period of time, then x changes at least somewhat significantly in its natural properties over that period.
- If u(x,t2)>100u(x,t1)+100, where the units are average human life utilities, then u(x,t) has changed very significantly between t1 and t2.
- If x is an earthly critter that has moral standing at some time in its life, then x has moral standing at all times in its life.
- I was once a fetus.
- I now have moral standing.
- The fetus I have grown out of had moral standing.
This argument is based on this argument by Mike Almeida.