How would you prove with logic that human life is precious? I agree that it is precious, but I'm not sure how I'd prove it.
(I don't love the wording. But the idea is that, just as the greatest painting of a famous artist is precious, likewise the greatest production of evolution is precious. Not air tight, but maybe a start).
As far as I know, the human body is no more complicated than most mammals. However, the human brain does appear to be unique in its capabilities.
So for human life to be precious, does it need to have a fully-functioning brain? Would that make the life of someone with severe learning difficulties, or even someone in a permanently vegetative state, less precious?
Warfare and dealing pain is about dehumanizing. Now those are constructed much harder to defend.
Otherwise you presume either hard equality between everyone (easy to rebuke) and/or omniscience.
Or you revert to consequentialist ethic where only consequences matter. (Not essentialist.) From that place, going from basic utilitarian ethics you can show what sort of value certain human lives had.
However, the logic should be consistent for any bounded cutoff.
You could construct a system where everyone with lower than given value is subjected to some action. Given your (or societal) bounded knowledge you then cannot generalise because you are not omniscient. This means you get to evaluate everyone on their terms. This view is incompatible with stereotypes.
Alternatively you just assign values by axiom, which will likely end up with a big and likely inconsistent philosophy, unreliable guide.
Indeed egoism like this is a valid strategy but not an optimal one in absolute terms. (Tit for tat is stable instead over time.) A philosophy or strategy should be viable in the presence of a mixture of them.
Survival instinct is powerful, it doesn't necessarily follow that exercising it means that you consider your own life precious.
For example, someone in a truly blind rage might go ahead and recklessly kill someone with complete and total disregard for his own life. While observing this act we might say that he does not believe his life to be precious because he acts as if it's not, yet he can nevertheless still be fighting and killing someone because he's driven by dark emotions.
If you have a red cube and a blue cube and a green cube, only one of the cubes is red. It is the reddest cube. Does being the most red make it precious? Is the blue cube precious because it is the most blue? The green cube? If you have a million cubes of all different hues, is each and every one precious because it is the most its-hue of all of the cubes? If each of the cubes is only mostly a cube, but actually deviates from being a cube in some way, is each one precious for being the most its-shape? But this one is the most pumpkin and the most missing-some-atoms-right-there! Ok, great. So what? So now everything is precious, because everything is the most of something? Let's congratulate ourselves and sing along with Monty Python, "Eeevery sperm is saaaacred....".
Or maybe being the most of something doesn't objectively carry any inherent value other than what we decide to put into it.
This is a biased view of evolution. All species today are "the pinnacle of billions of years of evolution". Humans are not especially advanced, at least not in evolutionary terms.
There may be some argument to make about humans being especially intelligent, or something like that, but it has little to do with evolution.
Arguable. It depends on how you define advanced. There are many organisms that live longer, are more numerous and can survive in more extreme environments than humans. It is also conceivable that humans might completely destroy all habitable environments, which would certainly disqualify us from the subjective qualification of "pinnacle of evolution". More importantly however, evolution has no pinnacle or direction.
Even if we grant that humans are "the most advanced creation of evolution", it does not necessarily follow that this causes it to be inherently precious.
To consider human life superior, we need less objective and more problematic criteria, e.g. claiming that we are special because we are sentient.