If you clear land for farming, don't you think you have a natural right to the use of that land? If a neighbor dumps toxic waste there, haven't they violated your property rights?
Consider a more complex situation. In the early part of this century, companies heavily polluted the New Jersey waterfront. They saved some money by dumping chemicals into landfills instead of disposing of them properly. Now, half a century later, the current generation is spending tremendous sums of money to clean up that land. Even after partial rehabilitation, the value of that land is depressed considering its proximity to highly-desirable Manhattan.
Entertaining the notion that "natural rights" exit,[1] did those companies, through their purchase of that waterfront land which was not very valuable at the time, acquire a natural right to not just use that land for their immediate purposes, but to extract the value of that land for themselves, arbitrarily far into the future? That's exactly what our system of private property allows people to do, and it's almost certainly not economically efficient in the intergenerational sense.
The other complex cases are things like land in the west. None of that land would be inhabited without the tremendous efforts of the Army Corps of Engineers in the 1800's to irrigate that land. Nobody who owns land in say Arizona can claim that they have a "natural right" to all of the proceeds of that land. Their activity on that land is a vast inter-generational joint-venture. A private company in the government's position at the time could have taken a huge equity stake in any activity in the west, one that would thanks to the law of property inure to this day. Though anybody who originally bought that land would be long-dead today, all his or her successors would have taken subject to that equity stake.
[1] Of course there is no such thing as "natural right" at least not to anyone who doesn't believe in a deity.
001sky is not making a frivolous point. If all land were private, most of population of the planet wouldn't even have a place to stand, much less to cross. Most populist libertarians are for privatizing almost all public land.
Putting things another way, some people seem to be under the odd misapprehension that "privately owning a piece of land" is tantamount to sovereignty over it. When in actual, complicated reality what one really buys when one "buys land" is a more limited set of rights to possession, use, development, etc. of the land that have been wrapped up in a title. And thus there exist limitations to what one can do with "private property" as exemplified by the fact that other people can get an easement to use one's land for access to their own or might own the minerals under your house.
