Property Rights...

...an exercise in informal logic.

Start with Ayn Rand's definition of rights: "Rights are conditions of existence required by man’s nature for his proper survival."

I have rights because they're necessary for my existence. I take the right of my existence as my axiom.

However, having food to eat is not a condition of existence necessary to my survival.

I just made a patently ridiculous statement. I promise you I'm going to back it up. I'll ask you to pause, here, for a moment, before you continue, and try to predict what I'm going to say next.

I don't have food to eat right this second. I could go and get some from my pantry, but even if my pantry were empty, I still wouldn't fail to survive. What is necessary to my survival is the ability to -acquire- food. My survival is dependent not upon my having the materials to satisfy my material requirements, but upon my having the ability to -acquire- those materials. More, because I must adhere to the rights of others, I must do so without infringing upon the ability of others to acquire such materials for themselves.

As a corollary to this, I have a derivative right to acquire and keep those things that enable me to acquire those materials necessary to my survival, so long as that acquisition does not infringe upon that equal right of others.  That is:

A.) I have a right to my existence.
B.) Therefore, necessarily, I have a right to acquire those material things necessary to my existence.
C.) Therefore, necessarily, I have a right to possess those material things necessary for me to acquire those material things necessary to my existence.

You don't know what I need for proper survival, except that which I have clearly marked as unnecessary to my survival, such as the chair I left out on the curb. In the absence of perfect information, we can only signal indirectly. If Ug makes a sharpened wooden stick - a spear - to hunt with, taking that spear impairs his ability to procure resources for his proper survival; a society which permits that spear to be taken likewise impairs that ability, both directly, in that this spear is no longer available to him, and indirectly in that he can no longer evaluate whether or not creating a spear will in fact contribute to his proper survival. His ability to procure resources for his proper survival is dependent upon society respecting that steps he has taken towards ensuring that survival are respected as being part of that survival as well. His spear must be respected.

But more importantly, the flint which he uses to sharpen that spear must be respected as well, even if nobody else in that society knows the purpose of the flint. Anything Ug has produced or acquired must be treated as though it were necessary to his proper survival in the absence of a clear indicator from Ug otherwise; if Ug throws the flint into the scrap heap, he's clearly signaled that it isn't necessary to his proper survival.

To make the latter distinction clear, imagine that Tog, Ug's friend, has already tried hunting with flint, and discovered it useless. He may have clear personal evidence that the flint is unnecessary to Ug's survival - but the flint -is- necessary to Ug's survival. Tog must respect that Ug is a creature with purpose - which gets into the "proper" part of survival - and therefore must respect that anything in Ug's possession is something which Ug may have discovered necessary to his survival. It doesn't matter whether or not Tog can surmise or discover a purpose for the flint.

Thus, you can take the chair I've left out by the curb, but not the one in my house.

This extends to strict trade currencies as well; if Ug trades his spears for shiny rocks, something all of his tribesmen want but which all acknowledge serve no particular purpose, those shiny rocks are imbued, as if by magic, with Ug's purpose. He may store them for the day when hunting is bad, so he can trade them at that point in time for something necessary to his proper survival. And this point is where all property rights become innate, because all property duly produced, traded for, or found in conditions in which purpose can be asserted without violating the others, can later be traded for property in turn. I can pawn my chair, even if it serves no purpose for me whatsoever.

Or:

A.) I have a right to my existence.
B.) Therefore, necessarily, I have a right to acquire those material things necessary to my existence.
C.) Therefore, necessarily, I have a right to possess those material things necessary for me to acquire those material things necessary to my existence.
Da.) You don't know what material things I necessarily need for me to acquire those material things necessary to my existence.
Db.) Therefore, you must, in order to avoid severing any of my rights, it is necessary to assume all material possessions imbued with my purpose are necessary, directly or indirectly, to my existence.
Dc.) Therefore, all material possessions which I have acquired with purpose are to be assumed to be necessary to my existence, directly or indirectly.
Ea.) Trade is merely a mechanism by which I may acquire those goods necessary for my existence.
Eb.) Therefore, even goods which you know I do not directly need, but which I have nonetheless acquired, are similarly protected as necessary to my existence, indirectly.

Thus, property rights, derived from nothing but my right to existence in a universe in which material goods are necessary to that existence.

In order to disprove this notion of property rights one of two things must be denied:
1.) The right to my existence.
2.) The transitive property of this right.  (I/e, if it's transitive, it includes food and trade goods both; if nontransitive, it doesn't.  If it's transitive, it includes those things necessary to my existence in the future; if it's not, only those things I need in the immediate are protected.)

Note that denial of either of these things leads to a situation in which civilization is impossible at the most primitive scale; Ug cannot make spears, neither for his own use, nor to trade, because the labor involved in doing so confers no benefits on Ug, and is therefore detrimental to Ug's survival, taking away from time in which he could be doing things that do guarantee his survival.  Civilization at a more complex scale is no more possible, depending as it does on not merely these rules, but much deeper derivations (such as the right to property which isn't material at all).