If, as Galileo believed, nature works according to mathematical laws and observations of nature are explained when we find the mathematical law relating observable quantities, then we must be quite specific in what we mean by a scientific law, so as to distinguish it from a physical concept or a scientific theory.
The Role of Scientific Laws
In 1687, Isaac Newton (1642-1727) published a treatise entitled The Mathematical Principles of Natural Philosophy, commonly known as the Principia. This monument in intellectual thought contains a remarkable passage on the rules of reasoning. There are four rules, which collectively reflect his profound faith in the unity of nature, and they were intended by Newton to guide scientists in the scientific process.
The first rule is called the principle of parsimony, and it says that scientists should make no more assumptions or assume no more causes than are absolutely necessary to explain their observations. The principle of parsimony is also known as Occum's razor, after William of Occum (1285?-?1349), who stated his principle of economy of thought in the phrase, "a plurality must not be asserted without necessity."
The second rule is the principle of cause and effect, or the belief that what occurs in nature is the result of cause-and-effect relationships, and where similar effects are seen then the same cause must be operating.
The third rule is the principle of universal qualities or the belief that those qualities, such as mass or length, that describe bodies exposed to our immediate experience also describe bodies removed from our immediate experience, such as stars and galaxies.
The final rule is the principle of induction. Induction is the process of deriving conclusions about a class of objects by examining a few of them-reasoning from the particular to the more general (deduction is the process of reasoning from the general to the more specific). The rule states that concepts, hypotheses, laws, and theories arrived at by induction should be assumed as universal both in time and place until new evidence proves the contrary to be true, as Kepler did in developing his laws of planetary motion.
These rules for reasoning are fundamental to the process of discovery of natural or scientific laws. To be more concrete in what we mean by a scientific law, let us adopt the following definition:
Scientific Laws: As formulate by human beings, natural or scientific laws are rules, preferably mathematical rules, by which we believe nature operates, and such laws can be classified as being either empirical, definitional, or derived laws.
In their observations and experiments, scientists often synthesize their observations of phenomena by developing empirical laws, a general statement which identifies a regularity in many observations without offering a theoretical explanation for it. A good example of empirical laws are Kepler's laws.
Definitional laws are a second level of physical law, so named because these laws usually involve the definition of fundamentally important concepts. Examples of such laws are Newton's second law and the law of conservation of energy.
Finally, there are the derived laws which are derived from some underlying theory, such as Newton's law of universal gravitation, which is derived from Kepler's laws, Newton's three laws of motion, and the concept of "action-at-a-distance."
The scientific laws of nature are usually thought of as inexorable and inescapable, in part because the word "law" suggests an erroneous analogy with divine law. Scientific laws, being built on concepts, hypotheses, and experiments, are only as trustworthy as those concepts are complete and as those experiments are accurate. Since humans formulate scientific laws, they are neither eternally true nor unchangeable. In fact with the advance of knowledge and experience, many laws of science prove, sooner or later, to be too limited or too inaccurate. An example is the law of conservation of mass, which today we recognize as having only limited applicability.
How Scientific Laws "Explain"
Since its origin in Greek thought, the larger goal of science has been to explain the intricacies of nature as rationally and coherently as possible. Such an explanation does not necessarily mean attributing a motivating agent, such as God, to events, but it does mean discovering, if possible, mathematical laws between observable quantities. But how do scientists find explanation by discovering mathematical laws? Such laws may aid utilization, control, and direction, but how is anything explained thereby?
For human beings the only tools for understanding physical phenomena are the pictures, allusions, and analogies involving the primitive mechanical events of everyday life that dwell in our imaginations. Over the course of history as physical science has moved toward problems more removed from the realm of common experience, it has been necessary to supplement those mental tools with which we grasp and comprehend phenomena with mathematical concepts and laws.
Let us suggest that, "to explain" means to reduce to the familiar, to establish a relationship between what is to be explained and any (correctly or incorrectly) unquestioned preconceptions. Modern scientists, like their ancient and medieval counterparts, do bring preconceptions to the scientific process; for example, just what we have been discussing, that nature works according to simple models or mathematical schemes. To modern science, scientific laws are an explanation of nature in that they allow scientists to incorporate mathematically the unfamiliar into the body of familiar experience. Collective experience among scientists shows that it requires training and repeated personal success in solving physical problems to be satisfied with and to believe that a mathematical answer explains nature.