I never really saw the need for the third right -- Pursuit of Happiness. It always seemed to be embodied in the second -- Liberty. If I have Liberty, don't I get the right to pursue happiness anyway? For free, as it were. And then I got wondering about the first too -- Life. Isn't that similarly redundant?
And so in the spirit of a McKinsey-esque MECE, it looks like we can get away with a single right -- Liberty -- plus a Scope on that right. And the name we give to that scope is Property. In this sense, Property is not a Lockean "possessions", but simply the range of a person's liberty. For example, Life is Liberty applied to the most important scope of all - our bodies.
Everything else is then merely an argument about scope; about property. Everything else is about what lies within my scope, or yours, or both, or neither. That's why a theory of property is important -- it is essentially a theory of liberty. This is what Paul's philosophy teacher was on about.
I think this explains the apparently insatiable demand in the USA (witness, for example, the efforts of the RIAA and MPAA in defence of "intellectual" property), for property. It's understandable. The Land of the Free needs to be the Land of the Property. Property is what you get to be Free with.