Jonathan has good thoughts on this very odd phenomenon of people thinking that you can't have property without the state.
The point he makes is that as a social construction all property rights really require is an enforcement mechanism. This could be anything. There's no reason it needs to be the state. Mutual benefit from recognition of property rights may even require very thin institutions. I think most people probably think some kind of institutional enforcement is required (otherwise we'd all be an-caps), but there's no reason to think it has to be a state.
I am particularly happy to see Jonathan adopting language around coercion that I've pushed for: "No, I’m not saying the free market is free of coercion (i.e. that property rights don’t need a protective, coercive institution). But, markets tend to minimize coercion (embodied in the general cooperative relationships aggregated as the division of labor)". I think it's wrong to talk about non-coercion as a goal. Everything in life is coercive. Property rights are coercive: property rights are just you being able to say "this is mine and if you try to make it yours 300 million other people have my back and will contribute resources to forcefully prevent you from doing that". The goal is to minimize how coercive human life is, and as Jonathan suggests markets tend to work very well at minimizing coercion because market action occurs precisely when action is mutually beneficial and voluntary.
I do have more problems with this paragraph on redistribution:
"The market, though, is characterized by a growing volume of voluntary exchanges. Certainly, incomes today — save those decided by government redistribution (to all income groups and institutions) — are voluntary. Government redistribution is characterized by the use of force. Suppose, for an instance, the existence of a completely unperturbed market. It’s true that institutions change over time, and so does income distribution, even in this setting. So, the idea of redistribution doesn’t presuppose a “default” distribution, rather it distinguishes a coercive stream of income from the voluntary one of the market. To make the point clearer, person A’s income is redistributed by the State to person B, because person A didn’t voluntarily surrender (usually in exchange for something else) her income."
Income distribution today is really not voluntary. It depends critically on the circumstances and the brain and body you were born into and the choices that were made for you when you were young. It's impossible to look at income distribution by something like gender and race and seriously conclude that the size of the pie that different groups get is something that is "voluntary". That's nonsense.
So we're at a bit of an impasse.
We know the market has important coercion-minimizing properties, but we also know that a lot of the resources that people bring to the market and that they live off of are anything but voluntary.
For me, that opens the door to egalitarian policy that constantly has an eye toward ensuring this slippery concept of "equality of opportunity" while trying to avoid this equally slippery concept of "equality of outcomes". It's not an easy distinction to make at all, because one child's "equality of opportunity" is some parent's "equality of outcome".
This is the trade-off of coercions that we as a society have to deal with.
States governed by the principles of liberalism seem to me to strike a decent and workable balance - and that's where the state comes in. But Jonathan is certainly right that there is no necessary connection between states and property rights.