This is based on comments I made in the Critical Cafe in November 2001 and at other times.
This is work in progress and is rather condensed in form, which may lead to misunderstandings. I welcome comment on content and presentation.
The notion of a 'scientific law' is often misunderstood. (This is probably partly due to the legal baggage associated with the word 'law', and it would probably have been better if a completely new word had been coined for the idea.) For example, one article I saw referred to science as 'law-driven', as if 'scientific laws' somehow determine what happens. This is to put the cart entirely before the horse. The universe is as it is, and scientific laws are part of the tools we use to try to understand why it is as it is.
'Laws' are not even, as the word misleadingly suggests, the most important part of science. Science is built around theories, and a good theory has two key characteristics: it attempts to generalise (so that it applies to a much wider range of possible experiences than the observations or experiments in immediate question), and it attempts to explain. (A full discussion of explanation will have to wait till another time.)
There are no laws in physics that are not parts of theories, and it is not possible to know for certain that a 'law' is true for all places and all times. Physicists today sometimes consider the possibility that the 'laws' of physics may have changed over time, or could be different if the boundary conditions of the universe had been different.
What we label as 'laws' in physics and chemistry is actually a ragbag collection that owes as much to the history of the subjects and to the exigencies of teaching and engineering as to anything more fundamental. They tend to be the quantitative aspects of theories, the bits that you can set well-structured questions on in exams, the bits that are used in practical work as 'rules of thumb'. Some are effectively definitions - the 'ideal gas laws' define an ideal gas and help to define a scale of temperature; no-one expects any real gas to 'obey' them exactly. Even the nomenclature of 'law' is haphazard: Lenz's 'law' and Le Chatelier's 'principle' express the same aspect (the First Law) of the same thermodynamic theory, but in different domains.
'Laws' in science, as excerpts from theories, always relate independent variables, or serve as the definition of the dependent variable. For example, Boyle's law (PV=constant) relates the two variables P and V, which can be independently defined and measured. Newton's second law, f=ma, serves in practice as a definition of force, f.
'Laws' can only be applied to reduced, linear parts of systems, for example, we can apply Newton's first to real-life bodies only insofar as we can treat those bodies as isolated masses in the absence of other factors like friction. This means that most scientific 'laws' are laws of physics. People often think of physics as being the model of what a science should be because it contains a high degree of reduction. But this is also to put things backwards. Physics (or physics-with-chemistry) is the name we give to those parts of experience that are most amenable to reduction. It is wrong to suppose that all branches of science should be reduced in this way, and therefore it is wrong to suppose they can be reduced to 'laws'.
We cannot expect to find 'laws' of complex systems, and I think that the attempt to do so can lead to serious error. (Much more on this to come later.) It's common in other fields to find statements labelled 'laws': for example, the 'laws of supply and demand' and the 'law of diminishing returns', but these have only the vaguest resemblance to the 'laws' of physics, and to use them as if they were like Newton's laws of motion (for example) is a fallacy with the direst implications for clarity of thought. (Example to come.)
It follows from the above that nothing can be 'proved' from a 'law'. You can, of course, make deductions from a 'law', as you can from any statement in a theory, but that deduction is in itself theoretical, and subject to testing against experience. This point is not specifically popperian, but Popper would regard falsifiability as the criterion for testing.
It also follows that something that is trivially true cannot be a 'law' in the physical sense. A 'law' is part of a theory, and a theory gives real information: it attempts to describe and explain and therefore can be tested against experience. (I was prompted to add this by Lawrence Boland's comment that 'Say's law' in economics is trivially true.)
Copyright © 2003 Richard Burnham