Nagel is responding to other views on social justice. To better understand his project, let's first give a summary of social justice so far.
The problem of social justice arises from the conditions of modern society. Because we participate in mutual cooperation with others, goods arise. For example, workers in a factory make a certain product which earns money. Students and faculty in a university work together to further knowledge. A just society is a society that shares the goods fairly. Not only do the benefits of cooperation need to be distributed fairly; we also have to distribute burdens fairly. The problem of social justice is to ask what arrangement in society would be just?
Nozick's view, which Rawls calls Natural Liberty, is the view that justice requires first and foremost individual rights. Everyone should have equal rights and jobs should be earned based on talents. The goal is to have an efficient free market. The consequences of luck, such as where you are born or how beautiful you are born, are not obstacles to justice. If you are born poor, dumb, dirty and ugly, it's not unjust.
Rawls' view is Democratic Equality, which requires that equality is the main requirement for justice. Basic personal liberties are to be maximized. Also, there should be fair equality of opportunities. Everyone who has the talent, intelligence and skill should be able to have the same opportunities, such as going to college, getting work training or having enough food to eat. In addition, any inequalities of power of goods should be such that they benefit the worst off in a society. The results of luck in matters of social class, race, ethnicity, culture, race, beauty, brains, etc., are regulated by society.
Nagel says that both of the above views have a problem of scope. In other words, the views get something wrong about what kinds of interactions and practices fall under the category of things that can rightly be called "just". Nagel thinks that the natural liberty view defines the scope of justice too narrowly. Nagel says that socio-economic status is a clear result of existing social systems and hierarchies. Because socio-economic status is caused by social institutions and practices, it falls within the scope of justice. Justice applies to social institutions and practices and the results of those institutions and practices. Nagel thinks that the view of democratic equality defines the scope of justice too broadly. He thinks Rawls' view does not allow room to consider competing social values or social costs. According to this view, all causes of social inequality that are not caused by an individual are arbitrary. Because the causes of social inequality are abitrary, it is up to a society to fix these inequalities. But Nagel thinks that some inequalities are more unfair than others. Society need not fix all inequalities; it must only fix the most unfair inequalities.
Nagel's proposal for social justice is the following: Because socio-economic inequality is socially created, it falls under the scope of social justice. But some natural differences are not socially created, so it is not clear that they fall under the scope of social justice. Only the things that truly result from social cooperation should call under the heading of social justice.
For example, pretend that 10% of a population has a gene that causes them to die at a young age. There are ways to test for this gene at birth. Certainly it is a great disadvantage to die at a young age. A shortened lifespan is an obstacle to certain kinds of success. Nagel says that justice does not require that society helps these people. There may be a huge social cost or economic cost to the society to help these people. This cost may outweigh the benefits of trying to help these people. Because nature (and not society) is the cause of this inequality, justice does not require that we fix this inequality.
Another example that Nagel considers is natural talents and education. Some valuable pursuits are naturally associated with inequality, such as education, excellence in art, research and exploration. Opportunities to have advanced education or to perform advanced research are not equally afforded to all. Differences in natural talents and prior education determine future opportunities for such things. The question is whether society needs to provide more than simply substantive fair equality of opportunity. Must society make sure that such inequalities are good for the worst off in society? Nagel thinks not. Nagel thinks that these pursuits are valuable whether or not they benefit the people who are lowest and worst off in a society.
The unequal benefits of education are up to nature, not society.
The last example is about sex and life prospects. Sex, or gender, is unlike intelligence or wealth because it is not as if there is a broad spectrum of sex. There are two sexes (male and female) and everyone is either one or the other. This natural division of reproductive labor has far-reaching consequences. Women are subject to inequalities that are not just the result of their ability to reproduce but also result from social systems. For example, women may have less opportunity for power in politics, employment or economic independence. The question is whether justice requires that we eliminate social inequalities that arise out of sex differences. For example, if women make less money at the same jobs as men, does justice require that women are compensated equally? Even if there are social costs to fixing such inequalities, must we fix these inequalities? Nagel thinks that in a modern society, inequalities that result from gender are not a matter of mere luck or nature. All women born into our society are affected by the social structures that disadvantage women regardless of whether women actually are mothers. Because the social inequalities based on gender are socially created, justice requires that we try to compensate for these inequalities. Nagel thinks that women who do not have children should have the same opportunities as men. But women who do have children should not be worse off than men.