> Further, there'd be nothing to stop you from violating the terms of any contract or even murdering anyone--you'd have unlimited rights.

There being nothing to stop you doesn't mean it's not a violation of an inalienable right or that I didn't have that right to begin with. The widely held belief is that freedom from murder is a right regardless of whether or not an institution is established to protect it. I believe it follows directly from our ability for higher order abstract thought, particularly our ability to empathize with others. So in some respects, you might say that our ability to empathize is what creates inalienable rights in the first place.