Agreed; it seems likely that the axiom system of the typical pro-life defender[0] is closer to "It's always wrong to end an innocent life"; this requires the inclusion of a set of axioms defining innocence (and thus probably invoking some combination of free will, and an absolute moral axis. A convenient framework for this includes a soul). This way you preserve the ability to defend yourself, to take the life of an enemy soldier, etc, while still being able to justify a pro-life position. It also allows for the death sentence for murderers.
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0. there are, of course, different sets of axioms that arrive at superficially similar conclusions. For example, the category of pacifist that believes that any loss of life is not justifiable; this kind of person will reject both abortion and ownership of weapons, war, etc.
It could also be that either side of these debates are unknowingly using abductive reasoning for how they feel about a stance that conflicts. Perhaps the proposed axioms come after to explain how people feel about controversial issues.
Funny enough, this conversation could also be a form of abductive reasoning. We're inferring that people are using abductive reasoning because people often hold conflicting moral views, though using abductive reasoning wouldn't necessarily guarantee conflicting views.
yes, and you'd also end up with an outright ban on civilian ownership of automatic weapons, amongst other safety measures. But you don't often see those two together. I think that the axioms are a layer or two below that, and might involve concepts like "individual responsibility" and "greater good"