Primary and Secondary Law. I have called the laws controlling the behaviour of single individuals “primary laws”, implying that the second law of thermodynamics, although a recognised law of Nature, is in some sense a secondary law. This distinction can now be placed on a regular footing. Some things never happen in the physical world because they are impossible; others because they are too improbable. The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws. It has been the conviction of nearly all physicists[7] that at the root of [Pg 76] everything there is a complete scheme of primary law governing the career of every particle or constituent of the world with an iron determinism. This primary scheme is all-sufficing, for, since it fixes the history of every constituent of the world, it fixes the whole world-history. But for all its completeness primary law does not answer every question about Nature which we might reasonably wish to put. Can a universe evolve backwards, i.e. develop in the opposite way to our own system? Primary law, being indifferent to a time-direction, replies, “Yes, it is not impossible”. Secondary law replies, “No, it is too improbable”. The answers are not really in conflict; but the first, though true, rather misses the point. This is typical of some much more commonplace queries. If I put this saucepan of water on this fire, will the water boil? Primary law can answer definitely if it is given the chance; but it must be understood that “this” translated into mathematics means a specification of the positions, motions, etc., of some quadrillions of particles and elements of energy. So in practice the question answered is not quite the one that is asked: If I put a saucepan resembling this one in a few major respects on a fire, will the water boil? Primary law replies, “It may boil; it may freeze; it may do pretty well anything. The details given are insufficient to exclude any result as impossible.” Secondary law replies plainly, “It will boil because it is too improbable that it should do anything else.” Secondary law is not in conflict with primary law, nor can we regard it as essential to complete a scheme of law already complete in itself. It results from a different (and rather [Pg 77] more practical) conception of the aim of our traffic with the secrets of Nature. The question whether the second law of thermodynamics and other statistical laws are mathematical deductions from the primary laws, presenting their results in a conveniently usable form, is difficult to answer; but I think it is generally considered that there is an unbridgeable hiatus. At the bottom of all the questions settled by secondary law there is an elusive conception of “a priori probability of states of the world” which involves an essentially different attitude to knowledge from that presupposed in the construction of the scheme of primary law.