"In principle, both are intentional causing injury: actions intrinsically bad." Here's where we disagree. Dropping her to a likely injury is surely physical harm, but there is nothing morally bad about it, no --- zero ----moral offense, if these two conditions are simultaneously met:
- the injury is not directly intended. (The sincerity of this could be tested by asking three questions: if there were a less harmful alternative, would you take it? Would you try to minimize the harm beforehand, e.g. by providing a softer landing? Would you try to remediate the harm afterward, e.g by dragging the woman to safety and treating all injuries?)
- the harm is justly proportionate (in this case, causing injury vs. saving lives.)
I don't think these are equivocations. I think they happen every day; we just don't analyze them every day. Let's see if I can list some off the top of my head.
- Your toddler is frantically upset because another toddler has taken his toy. He finds a fork and goes after the other kid with the apparent intent of stabbing him in the hand. (You have kids? Then you know: this happens.) You grab him and pull him back sharply, yelling "No!" He drops the fork and is yelling hysterically. You've injured his arm. *Harm, foreseeable but not directly intended.*The end was proportionate.
- Your older daughter is carrying your baby daughter in her arms at a farmers' market. Distracted, she doesn't realize there's a produce truck backing up towards her; the truck driver apparently doesn't notice either. You shout, grab her and literally throw her out of the way. She ends up with bruises. You have done objective harm. * But the harm you inflicted was not directly intended. *The end was proportionate: life-saving.
- Measles vaccination. The risk of lasting harm to a child from measles is very low, but occasionally child-to-adult transmission occurs, with grave harm if the adult is a pregnant woman whose measles can gravely injure the unborn child. Therefore vaccination is almost universal. So all children are, often against their will, literally injected with disease organisms, not principally for the individual child's own good, but for the overall protection of public health. * The harm inflicted --- pain, fear, various injection risks---is foreseen, but not directly intended. *The end is proportionate: life-saving.
I think many of the myriad things GOOD parents do, plus the everyday actions of GOOD doctors and GOOD defense/security/law enforcement, turn out, if you analyze them, to be examples of double effect, where the harm done is foreseeable, proportionate, and not directly intended. In such cases, it's not a mitigated moral offense, it's NO moral offense.
In all your recent examples both the harm and the benefit accrue to the same person, as well as perhaps another: the child pushed out of the way is the same child protected from the psychological scar of causing injury (plus, of course, the other child is protected from the injury itself); the other two are exactly the same person getting both sides of the double effect.
I do not see how injuring a woman before her death in the fire is intrinsically good or neutral. It is intrinsically a moral bad.
It is only the huge imbalance between the injury: merely a broken bone a minute before painful death and the good: the rescue of a child from the fire that obscures the analysis.
Remember there are three components to invincible double effect:
1. Intrinsic nature of the act is good or neutral.
2. Intent is good.
3. Harm is outweighed by the good.
In your principal example, (1) is lacking. If the firefighter pushed her out of the way of the fire, but caused an injury, that would be an intrinsic good like in your three recent examples, but that was not your original case. If he pushed her around while still unable to remove her from the fire, that would be intrinsically neutral. But he, a firefighter capable of evaluating the odds, injures her; injuring people is intrinsically bad.
Yes, I have children and understand the realism of the three recent examples. I also still remember nearly poking the eye of my play-fencing childhood mate and shudder at the thought.