Williams argues in his article that humans have self-ownership - that they own themselves. He then makes several arguments that flow from this premise. Unfortunately, so many people have forgotten the true basis for inalienable rights and thus don't even recognize the terrible flaw in this thinking.
The proper viewpoint is that humans are owned by their Creator - God. Thus, murder is definitely a matter of destroying someone else's property, as Williams points out, but it is destroying God's property.
If we own ourselves, then suicide (assisted or otherwise) should be legal. We obviously can't provide criminal penalties to someone who killed himself, but we do stop people from committing suicide, and we do penalize those who help others commit suicide. That makes sense if committing suicide is an act of destroying God's property and thus wrong. It does not make sense to make suicide and euthanasia illegal and try to prevent people from committing suicide if people own themselves.
The idea that a person owns himself is also behind much of the pro-abortion position. The idea seems to be that the woman owns herself and can decide what to do with her body, but the child in the womb can't own himself because he has no concept of ownership - no personhood - and thus is either owned by no one (meaning killing him causes no crime) or is owned by the mother (meaning she can do with him what she pleases). On the other hand, if all human beings are property of God, murder of the unborn - whether committed by the mother or someone else - is a crime against God and violates His right to that child's life.
Williams is correct that if humans own themselves, they should be able to sell their organs. But this idea of selling one's body parts, before or after death, introduces a big can of worms and a lot of ethical problems. The root of the problem, however, is the starting premise. People don't own themselves, and thus have no right to sell their organs. They are God's property, and thus to place a price on their parts and sell them is to usurp God's ownership and sell what does not belong to them. The current ban on buying and selling human body parts is the correct one, though we have apparently forgotten the basis for it.
While animal and plant life does belong to mankind (because God gave them to us), the ownership of humans is retained by God and only He can rightfully transfer or give up those rights. We humans have no ability to give up or transfer certain rights (such as the rights to life or liberty), which is what it means to have inalienable rights. If I own myself, then I can give up that right of ownership to another (slavery), sell my body parts, or kill myself. My rights to life and liberty (along with all other rights which come from these) would be alienable rather than inalienable.
It is because humans belong to God that we have truly inalienable rights, which is really just our perspective of God's ownership of us. We can't give up or transfer those rights because they aren't actually retained by us. The premise that humans own themselves is contradictory to the concept of inalienable rights. Both can't be true. The idea of self-ownership is very popular today and sounds good on the surface, but actually creates a cancerous thinking that destroys the concept of inalienable rights and with it the basis for our entire form of government and many of the protections that we have put in place to guard those inalienable rights.
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For more information on inalienable rights, read my 5-part series:
Part 1: What are Inalienable Rights?
Part 2: The Source of Inalienable Rights
Part 3: Liberty in Society and Government
Part 4: Government by Consent of the Governed
Part 5: Some Common Misconceptions