I know that Traditional Natural Law theorists and New Natural Law theorists disagree on this important issue: If you cause another person's death but you didn't intend his death as an end or as a mean, is this sufficient to make your act licit?
I'm quoting from Dr. Feser's blog:

"One notorious example concerns craniotomy and abortion.  Again, NNLT writers are opposed to intentionally killing an unborn child.  However, some of them have argued that crushing a fetus’s skull so as to remove it from the mother’s body and thereby end the pregnancy need not reflect an intention to kill the fetus even though this procedure will in fact kill it.  It could reflect instead merely an intention to alter the shape of the fetus’s skull so as more easily to remove it, and in some cases be in principle justifiable (by the principle of double effect) on that basis.  This reflects the NNLT’s distinctive analysis of intention, which is very different from the traditional Thomistic analysis, and (unsurprisingly) it has generated considerable controversy among Catholic moral theologians".

Moreover, I've read that Finnis considers stabbing a lethal aggressor in the heart a licit form of self-defence, while thomists would disagree. So my question is: what is, exactly, the thomistic understanding of the Principle of Double Effect? How do you distinguish a licit way to indirectly cause one person's death from what is really DIRECTLY causing one person's death.

I have some questions about genus and essential definition.

1) How does the scholastic concept of genus differ from the mathematical concepts of class and set?
In mathematics, a set is any collection of objects which can be proven to exist from the ZFC axioms. A class is an even more general kind of thing. Every collection of objects which have a given property make a class. For example, there is a class of all the x such that x is ( (a fish & red) or (a horse and not blue) ). I guess that such a  feature does not make a genus. Moreover, there are sets/classes which are defined just enumerating their elements. But I guess there is no genus such as G= { Archangel Michael, Archangel Gabriel, Archangel Raphael } .

2) An essential definition is a definition of the proximate-genus-specific-difference kind. Now, my question is: is the essential definition of an essence unique? It seems to me that it's not. Let's say that there is an essence such as being A&B&C. I could say that the genus is being A&B and the specific difference is being C. Or I could say that the genus is being A&C and the specific difference is being B. So there could be a lot of different essential definition for one essence. But there is probably something wrong with my argument; otherwise, it seems strange that man is always defined as rational animal and is never defined in another way.