Law of nature: a law-like description of some process or processes in nature. Establishing laws of nature on the basis of observation or experiments is the aim of the natural sciences.

Contrary to widespread belief, laws of nature are not causes of the processes in nature. Rather, they are general (that is, exceptionless) statements such as "All swans are white", conceived by human beings as being true about those processes. Because of their general form — because, that is, they are meant to cover not only all cases that have so far been observed but all cases that ever will (or could) be observed — laws of nature cannot, strictly speaking, be "proven"; they can only be refuted. Thus, the above example would be refuted by a single observed instance of a black swan. In fact, the potential refutability of a law of nature by observations or experiments (falsifiability) is the most important characteristic of a law of nature.

Science or Parascience?

A non-falsifiable law of nature is not, strictly speaking, a law of nature at all, but something belonging to the field of parascience or religion. An example would be the following statement:

"All human actions are egoistically motivated. Even those that do not look egoistic are motivated by the agent's egoistic desire to appear non-egoistic to others."

This statement* does not lend itself to possible refutation by any kind of observation and is therefore unscientific.

Contemporary laws of nature are usually expressed as mathematical formulas stating relations between physical quantities. This has the advantage of replacing our vague and ambiguous everyday language by the precise and (nearly always) unambiguous language of mathematics. An interrelated and consistent system of laws of nature is called a scientific theory, and the representation of a specific state of affairs based on theories is called a model. The use of models in science goes to show that laws of nature can describe only images of reality as perceived by an observer rather than reality itself.

Even if the model predicted by a theory corresponds in every respect to our observations of nature, this does not necessarily mean that the theory behind the model corresponds to reality. Some philosophers and also natural scientists, however, believe that theories and laws of nature are not mere instruments used to describe or predict our observations of nature but that they are, or purport to be, true descriptions of reality as it is in itself. Newton's law of gravity, which described the planets' motions around the sun, would be "real" in this sense even if there were no people around to observe those motions and formulate laws about them.

There is, of course, a problem with this conception if two opposing theories produce exactly the same models of the same phenomena. An example of two such competing theories is the many-world interpretation and the Copenhagen interpretation of quantum mechanics. Presumably, we cannot decide which of the two is correct based on mere observation of nature. Since they contradict one another, however, they cannot both be true — or, at least, not if we regard the truth of a theory as consisting in its correspondence to reality. We simply have no way of distinguishing between truth and falsity in this case. For this reason, most physicists regard the question of whether a theory is true in itself as meaningless, or at least unanswerable and unimportant.

Thus, a scientific theory does not have to be "true" as long as it satisfies the following four conditions:

  • Internal consistency: the theory may not contain any contradictory or self-contradictory statements.
  • External consistency: the theory may not contradict other established scientific theories; it must lend itself to being fully integrated into the whole of science.
  • Falsifiability: the theory must have consequences whose negation can in principle be confirmed by observation. One consequence of evolutionary theory, for instance, is the development of complex species from more primitive species. The occurrence of fossils with reversed chronological sequence would falsify evolutionary theory.
  • Explanatory power: the theory must be able to either fully explain states of affairs hitherto unaccounted-for or serve as an instrument to derive them from more basic states of affairs.

Good and Bad Theories

We can determine the better and the worse one of two competing theories even if they both satisfy the above four criteria and are underdetermined by mere observation as well. The principle that we can apply in this case has become known by the name Ockam's razor: The fewer laws a theory requires and the simpler these laws are, the better is the theory as a whole. Old theories are replaced by new ones if the new theory turns out to be shorter or simpler — although it also happens if the new theory is more powerful, that is, able to explain more processes, or if a law belonging to the old theory has been refuted by observation. Such replacement of an old theory by a new one, at least when those theories are highly comprehensive, is called paradigm change, since the result is an entirely new perspective on a known state of affairs. Often, the old theory can be derived as a special case from the new one, as was the case with Newton's law of gravity, which could be derived from general relativity theory.

The two major current theories of physics are general relativity theory, which describes the behavior of matter within large regions of space, and the so-called standard model, which includes quantum mechanics and describes the behavior of elementary particles within small and medium-sized spatial regions. Relativity theory was developed single-handedly by Albert Einstein in 1916. The standard model, by contrast, developed as a result of the contributions of many physicists in the course of the 20th century. Neither of these theories has yet been refuted by experiments or observation. This is especially remarkable in the case of relativity theory, which is already nearly 100 years old.

Physicists are not as happy about the standard model, though, since it does not present itself as brief and simple but as massive and complex. In addition, it does not explain why there are the elementary particles that it postulates, nor why the natural constants take on the values that they do. Thus, the arrival of a single, simpler theory in the course of this century that could replace both theories at once is eagerly anticipated. At present, string theory seems the most promising candidate for the position of this next (and last?) theory of physics. However, our 20th-century mathematics is still not developed enough to facilitate a formulation of the laws of string theory that would be sufficiently precise and consistent.

Where Do We Go from Here?

Thus, despite all its progress, natural science has still not arrived at the end of the route. Of course, in connection with the theme of this dictionary the question might be raised whether this route is finite or infinite. Are we going to get to the point of developing in the near future a "theory of everything" that would include all laws of nature and be able to fully explain all empirical observations? Whether or not this will occur, we can surely expect some spectacular discoveries that might surpass everything that we have previously discovered. A survey of the current limits of our knowledge is provided in our list of the ten puzzles.

*Karl Popper, The Logic of Discovery.

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