The nature of which natural law theorists speak is first the kind-essence or species such as “humanity.” Natural laws describe the proper functioning, as well as pathologies, of human nature. Secondly, it is individual-essence and habits, that is, “personality,” in particular. Thirdly, it is about the fulfillment of habits in acts. Thus, kind-nature is for the sake of its powers; habits direct powers into various avenues and are, in turn, for the sake of acts springing from them. For example, it is within human power to operate complex machinery. The actual ability to fly a plane or write a computer program is a habit. And flying is an act. Now the chief act of any living creature is happiness. The fundamental property of human nature is the search for happiness. So, natural law tells human beings how best to achieve happiness. The problem is that pleasures or expected utilities resulting from divers habits conflict with each other. Studying natural law is useful if the goal is to discover how best to maximize pleasure, considered formally or in Mises’s words, “rightly understood.” It turns out, for example, that structuring society according to the teachings of economics results in a world which, far from being red in tooth and claw, is on the contrary civilized and peaceful. Thus, natural law is a set of technologies. It is all the causal regularities put in service to human ends. And insofar as every end is itself a means to the desideratum of happiness, it includes information of which ends are destructive of happiness, of which ends are best left unsatisfied or, better, driven out of the soul.
Natural rights are those human rights respecting which promotes social cooperation, general welfare, and human flourishing and happiness; and results in the fastest improvement in the standard of living of the immense majority of the population. In other words, natural rights emerge from the body of natural law as elucidated by natural and social sciences, especially as it pertains to human happiness.
Obeying natural law makes human actions as successful as they possibly can be relative to the society’s level of economic and technological development. Natural rights are the rights which, if respected, are most conducive to such success. In this sense natural rights can be likened, perhaps surprisingly, to rule utilitarianism.
Here's an excellent read for your excellent question: Why Does Justice Have Good Consequences? by Dr. Roderick Long
The whole thing should be read, but I think "5. First Digression: Counterfactuals and Moral Knowledge" will be more direct interest to you.
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