However, upon further consideration, it seems that what’s of prime importance in this scenario is not “liberty,” but “life.” After all, we are essentially saying that one person’s liberty is more important than another’s. This seems rather obvious — of course a person’s liberty to not be sexually mutilated overrides a person’s liberty to sexually mutilate. Still, it would be accurate to say that liberty is not prime, whereas innocent life is.
This depends on a misunderstanding of the classical liberal conception of the individual and individual rights. Chris is assuming that the right to life, liberty and property are wholly separate and distinct rights, ones that can be violated or respected without offending on the others. That is, that we can violate a person’s right to property (take their car, say) without impinging on their right to liberty (to live their life how they choose).
That isn’t the case. For classical liberals, the individual is just that—distinct and separate, not part of some greater mechanism or organism (say, society), but unique.1 There is no overlap between individuals. You cannot say, “I can’t quite tell where Betty ends and Don begins.”
The individual is herself inviolable, and she has full control over herself. Only she has literal direction over herself—in what actions she chooses, and in what she owns.2 Because every individual has that right, by their very nature as an individual, others cannot (morally) choose to violate someone else’s right. Someone cannot choose to, as Chris asked, sexually mutilate someone, because that violate their right to control their life.
What this means is that there are no distinct rights. There is no right to life, or right to liberty, or right to property. Those are approximations used to understand the natural rights of the individual. I only have a right to direct my own life, in all senses. My decisions cannot violate someone else’s same right.
This doesn’t mean we are placing restrictions on someone’s rights by not allowing them to harm others, because they never had that right to begin with. Short hand for this is “my right to swing my fist ends where your nose begins,” and it’s apt.
If you haven’t, I highly suggest reading John Locke’s Two Treatises of Government. Political theory has moved far beyond it, obviously, but it’s incredible just how insightful it is. Some works only become more important as the centuries pass.