Libertarians, as a general rule, want to argue from a conception of individual liberty and autonomys as self-ownership to a fairly robust right to property. Let's start with two predicates, Person(x) and Owns(x,y). Person(x) means that x is a person -- as opposed to just a thing, like a hammer or a pizza -- while Owns(x,y) means that x owns y. The full depth of the property right involved is not so important here. But to get a feel of what libertarians want to show, here are two quotations that start to cash out the Owns relation:
`x is A's property' means `A has the right to determine the disposition of x'
Narveson suggests the following set as giving some sort of full ownership: (1) exclusive use, which includes the right to permit or refuse the right [sic; I think this is supposed to be `use'] by others; and (2) transfer in the form of sale, exchange, gift or bequeathal.
What's important is that, if x owns y, then no-one besides x (or another owner of y) can use y (presumably, in any way) without x's consent. We will also need a predicate for the relation of x gives y to z; Gives(x,y,z) will work nicely.
Of course, capitalism isn't just a system of free exchanges. It's also a system in which people make things. As part of the property system, libertarians want to say that, if something is made in the right way (with resources that are either unowned or acquired through fair exchange, and a few other so-called Lockean provisos that aren't important quite yet), then it is owned by the maker. So our last predicate is Makes(x,y), meaning x makes y in the right way.
The ultimate, fundamental principle on which libertarians attempt to ground their justification of private property is a right of maximal liberty:
(L) people have a non-overridable right to such liberties as do not interfere with those of others
This, they claim, can be read as a principle of self-ownership:
(S) one owns oneself
Formalise this as
(SO) (x)(y)(Person(x) -> (Owns(x,y) <-> x=y))
Moller Okin's argument focuses on the purported inference from this to a principle of original acquisition. And so shall we. Narveson states original acquisition in this way:
things acquired in ways that meet the initial (Lockean) conditions are indeed the property of those who acquire them, for precisely the same reasons that we have the general right of liberty, and as a straight implication thereof
Formalise the first clause of this as
(OA) (x)(y) ((Person(x) ^ Makes(x,y) ^ -(Ez)Gives(x,y,z)) -> Owns(x,y))
The final clause of the quotation from Narveson is the claim that SO implies OA. Formally, this is false -- Makes and Owns don't show up in SO, so it can't imply OA. However, presumably there is some set of definitions and/or axioms D that, Narveson thinks, will, when combined with S, imply OA. That is, Narveson's claim is
(1) SO + D |- OA
Moller Okin's argument is an attempt to show that 1 is false. Her counterexample is based on the fact that mothers make their children -- literally. She carefully works through Nozick's version of original acquisition, and describes a scenario in which all of the Lockean provisos have been satisfied: the mother was freely given the sperm, say, and procured all the resources necessary to maintain herself and (this bit varies from version to version) give birth to a healthy infant/raise a healthy child to adulthood according to free exchange and the principles of original acquisition. But then she doesn't give her child away -- either to another person or to himself. Instead, she keeps him as a slave. Hence the subtitle of Moller Okin's chapter: `Matriarchy, slavery, and dystopia'.
Let's formalise this counterexample as follows: there is a person, x, who makes another person, y, in the right way, and does not give y to any z.
(MOC) (Ex)(Ey) Person(x) ^ Person(y) ^ Makes(x,y) ^ -(Ez)Gives(x,y,z)
Moller Okin's criticism is that MOC, with OA, implies the negation of SO.
(2) MOC + OA |- -SO
Hence, either SO is inconsistent, or SO implies the negation of at least one of MOC and OA.
(3) SO is inconsistent
(4) SO |- -(MOC ^ OA)
Cashing out (4) gives two possibilities (which are not exclusive): either SO implies the negation of MOC, or SO implies the negation of OA.
(5) SO |- -MOC
(6) SO |- -OA
Of course, if SO implies the negation of OA, and is consistent, then it can't imply OA. And throwing in D won't help things, either.
(7) SO+D |/- OA
So, to sum up, the libertarian wants to claim that self-ownership implies an account of property that includes original acquisition (1). Moller Okin's counterexample shows that at least one of three things must be true: (a) self-ownership is inconsistent (3); (b) self-ownership implies that mothers do not make their children in the right way (5, roughly); or (c) self-ownership does not imply an account of property that includes original acquisition (7). Clearly option a is a disaster for libertarianism. I don't think b is all that promising, either -- at the very least, a libertarian who chooses to take this route would have to work through Moller Okin's discussion of how mothers make their children in exactly the right way just as carefully as she worked her way through Nozick's account of original acquisition. A libertarian cannot, as Narveson does, simply dismiss Moller Okin's counterexample by asserting that `What parents do is initiate a process that eventuates in human organisms, which grow up' and concluding immediately that `We should ... deny that children are `made' by their parents'.
Note that libertarians also cannot simply dismiss Moller Okin's argument as `absurd' -- again, as Narveson does. Anyone who knows a little about formal validity will agree with the analysis I gave in two paragraphs ago. The only option for a libertarian, then, is c.
Denying 1 might seem like a serious blow to libertarians. But is it? What if libertarians don't want OA, but instead want some more sophisticated principle of original acquisition? Recall that OA, the property right, wasn't the original principle. Rather, S, a basic right of self-determination, was. And Nozick is quite clear that, when property conflicts with self-determination, property must yield. Hence he introduces `side constraints', that limit property rights. These can be nicely incorporated into my formalism. For example, suppose we want to replace OA with a qualified version: so long as the made thing y isn't a person, x owns anything she makes in the right way.
(OA') (x)(y) ((Person(x) ^ -Person(y) ^ Makes(x,y) ^ -(Ez)Gives(x,y,z)) -> Owns(x,y))
This can be generalised: if C(x,y) is a predicate formalising a side constraint (or conjunction thereof, etc.), then let
(OA/C) (x)(y) ((Person(x) ^ -C(x,y) ^ Makes(x,y) ^ -(Ez)Gives(x,y,z)) -> Owns(x,y))
We include the side constraint in the antecedent, and so it blocks an inference to ownership in bad cases. Indeed, it does so in Moller Okin's case: MOC and OA' do not imply the negation of SO.
MOC + OA' |/- -SO
Hence Moller Okin's counterexample does not cause problems with this argument.
But there are, I think, at least three problems with this side constraint strategy. First, Nozick (I'm not sure about Narveson) believes that there's nothing wrong with selling oneself into slavery. That is, a side constraint concerning personhood does not show up in the principle governing free exchange. But why should it show up in the principle governing original acquisition, but not in the principle governing free exchange? That seems ad hoc. But, since the idea that there's nothing wrong with selling oneself into slavery is kind of weird, perhaps this isn't a serious objection.
Second, adding qualifications to OA makes it trickier, in general, to derive from SO. We haven't looked at the set of definitions D that libertarians will use to bridge the formal gap, so perhaps SO does indeed imply OA'. But showing this will require more care than I have seen libertarians giving.
Third, and most importantly, adding side constraints seriously compromises the robust property rights that were supposed to be implied by self-ownership. Consider the following side constraint: there should not be a person z such that x's ownership of y interferes with z's self-determination (self-ownership). This seems to be a good way of capturing the non-interference on which libertarians want to base side constraints. We'll call it C*(x,y), and formalise it as
C*(x,y) =df (Ez)(Person(z) ^ (Owns(x,y) -> -Owns(z,z)))
Now we plug this into OA/C.
(OA*) (x)(y) ((Person(x) ^ -(Ez)(Person(z) ^ (Owns(x,y) -> -Owns(z,z))) ^ Makes(x,y) ^ -(Ez)Gives(x,y,z)) -> Owns(x,y))
Note that OA* does just as nice a job of avoiding Moller Okin's counterexample as OA'. It also applies more generally -- it blocks ownership in any case where this would interfere with the self-determination of anyone, not just the purported `owned thing'.
But what does it mean to interfere with someone's self-determination? Suppose Maria has just baked a loaf of bread, using ingredients and an oven that she procured using free exchanges, and Jorge, just outside the door to her bakery, is starving to death. Without Maria's bread, Jorge will surely die in the near future. It seems clear to me that her ownership of the bread -- in particular, her right to refuse to give it to Jorge -- would interfere with Jorge's self-determination, as he certainly cannot determine the course of his life if he is dead. If this seeming is right, then OA* does not imply that Maria owns the bread. (Note that it does not imply that Jorge owns the bread, either, as he did not make it and has not been given it.)
This thought experiment can be generalised. First, let's formalise. If there is a person x such that x owning (or, more generally, using or having) y is necessary for x's self-determination, then no-one but x can own y.
(N) (x)(y)((Person(x) ^ (-Owns(x,y) -> -Owns(x,x))) -> (z)(z=/=x -> -Owns(z,y)))
Now, N is not implied by OA*. However, with the additional assumption that original acquisition and free trade are the only ways anyone can own anything, which libertarians all seem to endorse, N does follow.
Now consider Jamal, who is homeless. It is a bitterly cold night, and without the use of a small house nominally owned by Tasha, Jamal will surely die. It follows from N that Tasha does not own the house -- indeed, no-one except possibly Jamal owns the house. If Jaime nominally owns a course of treatment of a drug, and Lorenzo will surely die without taking it, then Jaime does not own the course of treatment of the drug.
Services are more difficult, because it does not seem like there is a thing that is owned or transferred in the case of, for example, a teacher teaching a student. It is also difficult to generalise to cases in which a suffering person needs any one of a variety of things. For example, Jorge will surely die if he doesn't get some food in the near future, but he would survive for at least a while if he had Maria's bread, or Michael's pizza, or Dana's apples, and so on. But, with the examples above, it is clear that OA* seriously compromises the libertarian's property rights: she does not own anything which is materially necessary to sustain the life of anyone nearby.