## The nature of scientific law

When I hear other people talk about “laws of nature,” I recognize that their view of science seems to be quite different from mine.  It is not that they call them “laws of nature.”  Rather, it is what people say about scientific laws that leads me to see a difference.  For example many people conclude, on the basis of science, that there is no such thing as free will and that the universe is governed by deterministic laws.  I am unable to find any basis for those views.  So here, I present my own understanding of science.

I see scientific laws as idealizations, not as descriptions.  Idealizations can be quite useful, and that’s why science uses them.  I remember when, as a child, I first heard of Boyle’s law.  It is a very precise law, asserting that pressure and volume of a gas are inversely proportional.  And what I remember from that time, is thinking that Boyle’s law could not possibly be true.  For it expressed a precise and simple mathematical relationship, but experience had already persuaded me that nothing in nature fits a precise mathematical relationship.

It turned out that I was right.  In fact the important gas laws of physics, which include Boyle’s law, are often referred to as the ideal gas laws, because they are true only of idealized gases but not of any actual observed gases.  They provide very good approximations to how actual gases behave, but they are only approximations.

When I later heard of Ohm’s law, I did not have any qualms about accepting it as being exactly true, even though it also expresses a precise and simple mathematical relationship.  The reason I accepted that, was that Ohm’s law was quite clearly a logical truth (or an analytic proposition).  That is to say, Ohm’s law expresses the definition of the quantity resistance, as used in the theory of electricity.  So, as a definition, Ohm’s law is necessarily true, or true by definition, or true by virtue of the meaning of the terms.  Ohm’s law is nevertheless an idealization.  The mathematical relationship is exact, so that is not what is idealized.  Rather, it is the view that electrical resistance is an intrinsic property of an electric circuit that is an idealization.

I have long been puzzled by Wigner’s paper on “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”  And what puzzles me, is that Wigner would think it unreasonable for mathematics to be useful to science.  Mathematics has always been about idealizations, particularly about idealizations that involve pattern or symmetry.  So if scientists want to use idealizations as a way of better understanding the world, then what better place to look for possible ways of idealizing, than in mathematics?

With those two examples, Boyle’s law and Ohm’s law, what can we say about scientific laws?  In neither case, can we say that they are rules governing the universe.  If Boyle’s law is only approximately true, then it is not a governing law, but is better thought of as an observed statistical relation.  And if Ohm’s law is a logical truth or analytic proposition, then it should be seen as having no informative content or no descriptive content.  Because it is a logical truth, nothing could be observed that violates Ohm’s law.  But that is not a constraint on the physical universe.  It is only a constraint on how we properly use the term electrical resistance.  As best I can tell, much the same applies to all scientific laws.  That is, those laws are not rules that govern the universe.

We should see scientific laws a epistemic, rather than as metaphysical.  A scientific law is part of how scientists make better and more accurate observations of reality, and make better predictions.  But it is not some statement that is part of the fundamental structure of the universe.