Lex Naturalis presents a unique theory of law. The work is structured as a series of interrelated essays which, taken together, constitute a new theory of law. The work argues: First, that positive law and natural law are complementary, not competing. Second, that normative inference (is-to-ought) can be a logically valid form or reasoning. Thus, the work presents resolutions to the two leading questions of contemporary legal theory. This book also provides a dialectical synthesis of competing ontological, epistemological and axiological theories. Breaking both from Catholic natural law neo-platonic idealism and from international relations theory realism (nominalism), the work argues for a monist (not dualist), materialist (not idealist), cognitivist (not relativist) and wholist (not atomist) view. Thus the work combines the best aspects of both Catholic neoplatonism (moral cognitivism, wholism) and the best of nominalism (materialism) to present a powerful scientific theory of law which sees positive law and natural law as complementary (some laws are natural, such as the prohibition of murder, others are positive such as parking regulations). Finally, the work argues that logic must be understood as consisting of practical reasoning and theoretical rationality, and that a binary logic of either true or false, only is inadequate to explain legal phenomenon and that binary logic generates paradoxes which can be avoided in multivariate logics. The work addresses classical questions of the relationship between positive and natural law, normative inferencing, and social contract theory, as well as providing a friendly critique of contemporary legal theorists, notably Professor Duncan Kennedy at Harvard Law School. Scholars, Judges and even practitioners will find many interesting and useful ideas in these pages.