The Natural Law argument states that the observation of governing laws and existing order in the universe indicates the existence of a superior being who enacted these laws.
Russell's criticism to this argument begins by noting that ``... a great many things we thought were natural laws are really human conventions''. He next mentions that if one examines the world closely, one finds that there are no real laws, all phenomena ``... are statistical averages of just the sort that would emerge from chance.'' He gives the example of getting two sixes upon rolling dice and notes that the frequency of this happening about once in every thirty-six throws is not an evidence of design, but rather of the lack of one. He concludes from this that
The laws of nature are of that sort as regards a great many of them. They are statistical averages such as would emerge from the laws of chance; and that makes this whole business of natural law much less impressive than it formerly was.
He agrees that a statistical interpretation of the the laws of the universe might represent a momentary state of science. However, he asserts that ``the whole idea that natural laws imply a law giver is due to a confusion between natural and human laws''. He considers human laws to be those that command people to behave in a certain way, and the natural laws to be a description of how things behave in reality. He reasons that from natural laws
... you cannot argue that there must be somebody who told them to do that, because even supposing that there were you are faced with the question, 'Why did God issue just those natural laws and no others?' If you say that He did it simply from his own good pleasure, and without any reason, you then find that there is something which is not subject to law, and so your train of natural law is interrupted. If you say, as more orthodox theologians do, that in all the laws which God issues He had a reason for giving those laws rather than others - the reason, of course being to create the best universe, although you would never think it to look at it - if there was a reason for the laws which God gave, then God Himself was subject to law, and therefore you do not get any advantage by introducing God as an intermediary. You have really a law outside and anterior to the divine edicts, and God does not serve your purpose, because He is not the ultimate law-giver.
The first criticism concerning ``human conventions'' is invalid because it concerns a specious definition of law. If someone defines three feet to a yard as a natural law, then the definition is incorrect and therefore does not fall within the domain of our argument concerning natural laws.
The crux of Russell's argument, i.e the statistical dependence of natural phenomena as they are understood today can be attacked by considering the statistical nature of the universe to be a law itself. Such a change in the point of view would be tantamount to the Kuhnian paradigm-shift that heralded the transition from Classical to Quantum Physics. The disciplines of Statistical and Quantum Mechanics, and all their derivatives rest upon the pillars of precise dynamics of probabilistic systems. An important implication of Russell's argument is the invalidity of the entire edifice of science, since science rests on the assumption that the world is inherently simple and understandable. Simplicity implies the existence of descriptive relations (laws) and understandibility implies the predictive power of those laws.
Russell's use of a dichotomy between the human and natural laws is a surmise. Empirical evidence would indicate, contrary to his assumption, that the separation of human and natural laws follows from insufficient knowledge. For example, the earth and the heavens were supposed to follow different laws, but then with the progress of knowledge, people came to the conclusion that both obey the same laws. Induction on this trend implies a union of the domains of human and natural laws.
His argument about the relation of God to the laws is fallacious. First of all he asks the question, ``Why did God issue just those natural laws and no others?'' He assumes, of course, that this question can be answered and gives no reason for his assumption. Next, from the argument that God enacted certain natural laws through fiat, he concludes that this is impossible since it represents a break in the natural law argument. He is again assuming, without any reason, that natural laws should apply to God. There is no basis for his making this statement. His next argument which ``shows'' that God is Himself controlled by a higher law is again erroneous. An important exception to his conclusion is when a certain law is an inseparable attribute of God, and does not exist without Him. He is assuming that the law can be separated from God, but his assumption is without any basis.
His criticism of the Natural Law argument is less plausible than his criticism of the First Cause Argument.