I will sprinkle clean water upon you to cleanse you from all your impurities, and from all your idols I will cleanse you. I will give you a new heart and place a new spirit within you, taking form your bodies your stony hearts and giving you natural hearts. I will put my spirit within you and make you live by my statutes, careful to observe my decrees. [Ezekiel 36:25-27]
A search of the Web for terms like "natural law axioms" or "axiomatic natural law" yields nothing suggestive of any attempt to bring rigor to the classical subject so ably developed by St. Thomas Aquinas in the Summa Theologica. See "the Natural Law."
Given the disrepute Natural Law has suffered at the hands of skeptical scientists and fideistic clerics, it strikes me that it is high time someone addressed this subject with some care. Although I am quite prepared to admit that my background as a student of Natural Law in all of its variations is less than adequate, I believe I am sufficiently prepared in abstract mathematics (as in the general study of axiomatics), physical science, psychology, sociology, philosophy and theology to take a decent stab at the problem. I have already presented some very preliminary ideas at the Dayton Pro-Life Science and Technology Symposium, but I came away dissatisfied by what I'd accomplished.
After reviewing an interesting article by David Solomon on First Things, I realized it would be helpful to try and sort out the essential areas of study that contribute suitable axioms to the final framework. Solomon's article is a review of a book of essays on Natural Law. (See Natural Law Theory: Contemporary Essays. I have not yet had an opportunity to read this book, nor the other highly recommended book in this field, Common Truths: New Perspectives on Natural Law, though I plan to remedy that situation soon.)
The following comment by Solomon gave me a strong hint as to why contemporary philosophers have floundered in this area:
Modern rationalist thought, however, has attempted to preserve the force and objectivity of traditional moral thought without what it regards as the needless baggage of traditional metaphysics. This goal, pursued most brilliantly and influentially by Kant and his disciples, often involves invoking the notion of natural law. But this modern resort to the concept of natural law does not require that such laws be teleologically grounded. That is, it doesn't require that natural laws link certain actions with certain natural human ends. This goal of "natural law without nature," as one might call it, continues to drive many contemporary research programs in ethics and politics. Even MacIntyre declared in After Virtue that classical ethical thought had to be revived without the aid of Aristotle's "metaphysical biology" (although his more recent writings suggest that he might not insist on that point today).
As usual, it would seem that the bootstrap approach of Immanuel Kant has led many of his students down a blind alley. It should be evident to anyone who cares to consider the matter that an area without substantive observation is an area without substance. Aristotle discovered this over two thousand years ago, and modern science owes him a deep gratitude for his efforts. The deeper criticism of the contemporary approach, however, is that it has jettisoned appeals to teleology. Aquinas' brilliant observation that "The good is prior to the right." however, fails utterly without such an appeal, because "the good" then becomes arbitrary, and without this necessary ordering of goods and rights, there is no theory of natural law.
The key question in any development of a theory of natural law, then, is how to ground teleology. One is forced to this perspective in spite of "the steady erosion of this teleological picture of the world under the pressure of the new science" that Solomon refers to in his essay. It is clear that this general erosion is a consequence of the success of modern science in developing a bottom-up approach to scientific advance, which is what the scientific method very largely is. In particular, one need not appeal to any sense of "purpose" (as the ancients did) when considering the laws of physics, and one can succeed in the study of evolution without any appeal to the idea that features were developed by nature in order to supply needed capabilities.
All of this is, at bottom, irrelevant to the area of natural law for a very simple reason, there is no real natural law theory that does not appeal to God's design in some way, and thus God's purposes for humanity. Any approach that jettisons the appeal to God's design will end up being circular, or what is just as bad, utterly without substance.
In this day and age, of course, the subject of God's design is a highly controversial one. People who dare to approach it can quickly find themselves subject to derision by very intelligent people.
Even the relatively recent attempts to find signs of God's design in the fundamental constants of nature (a rather brilliant argument about the support of life by these highly tuned constants) has suffered an important onslaught by cosmologists who have made important statistical arguments favoring multiverse theories based on the accepted theory of the early inflationary universe.
No one can explain the inflationary period (which seems to be necessitated by the observed large-scale structure of the universe, as seen in the cosmic background signature) without an appeal to multiple universes. And if multiple universes exist, there is a real possibility that the design we see is an artifact of our presence in a viable universe. We would not exist, presumably, in a non-viable universe. Thus, to the argument that the universe was designed to support life breaks down when considering this rather novel application of the anthropic principle. Although it seems plain enough that the arguments in favor of multiple universes with arbitrary sets of physical laws leave much to be desired, the possibility of their existence has led many to back down from appealing to this as an "argument from design."
It seems to me that we have been approaching this topic from the wrong direction. Let us consider the following line of reasoning as an alternative.
So this is what I propose. I will augment these hypotheses by a set of hypotheses that effectively amplify the meaning of basic terms of the discourse, such as "good" "purpose" and their relationship to us and God, in much the same way that David Hilbert's axioms of Euclidean geometry amplify his undefined terms. I will then proceed to a consideration of highly dominant phenomena, with a view to discerning God's intentions for us, as well as phenomena that represent departures from the mainstream. In doing so, I will appeal to the most basic of all appeals, survival, or, viability. Any phenomenon that can be seen to naturally disappear in succeeding generations of a given population will be considered inherently inviable. Thus, I am led to a consideration of yet another heuristic referred to by Christ, "By their fruits you will know them." [Matthew 7:16&20] This heuristic is implicitly used in virtually all standard appeals to Natural Law.
Much work remains, of course, but this is where I propose to start.