A 6th grade maths and science teacher emailed me about whether theories could become laws. Below the fold is his request and my reply. The short answer is that when laws grow up, they become theories, not the other way around.
Cameron Peters wrote:
I was hoping you might be able to provide some insight on a question that is circulating amongst the NSTA email list serve concerning laws and theories. Specifically, there is some disagreement ( I would say confusion) of the difference between the two and, in particular, why a theory cannot become a law. Also, the question has arisen as to what a law is before if becomes a law. I’ve used some previous posts of yours to guide my thinking, but if you have any comments that I might pass along to help achieve some clarity, I would greatly appreciate it.
6th Grade Math & Science
Poulsbo Middle School
There are in my view two questions:
1. What is a theory and what is a law, and
2. What is the relation between them?
In what follows I’m going to use the term “domain” a lot – this means the scope of things that a scientific model, theory or law is supposed to cover. It’s not entirely clear how that is specified, but like pornography, everyone seems to know what they mean by it. It’s the area of phenomena that call for an explanation in the eyes of the disciplines that address it – like “ecosystems” or “inheritance” and so on.
Until around the turn of the 20th century, a law was any generalisation in a science that was held to universally hold true for every relevant instance of the domain it covered: e.g., a chemical law covered all cases of chemical systems. Of course this was not ideal – many cases of chemical laws, for example, fail in extreme circumstances. Consider the Ideal Gas Law – it fails when things get too cold, too pressurised or too hot, but in the “ordinary” conditions of gases, it holds fairly well.
In the 20th century, however, people stopped talking so much about laws and started talking instead about models and hypotheses. A model is a mathematical description of a domain (say, atomic physics), or at least something that could one day be made mathematical. A hypothesis is a proposed statement that covers a domain, like “all objects attract each other as the square of the distance”.
In either case, hypotheses and models are able to be shown to either agree with the observations, or not. If not they are said to be falsified (a term due to Karl Popper) or anomalous. Anomalies are not fatal to models and hypotheses, although some vague number of anomalous problems can eventually kill it.
A theory used to be thought to be something like a mathematical or logical deduction from a set of axiomatic statements [Technically this is called the "Syntactical view of theories", because the logic is a formal syntax, and meaning is supposed to come out of the formal structure]. This idea has been abandoned, mostly. For a start, many theories do not lend themselves to axiomatisation, and moreover, science seems to proceed perfectly well without axiomatising theories. The view I favour is that a theory is a family of related, but not deductively related, models. That is, a series of mathematical descriptions that cover roughly the same domain [Technically this is called the "semantic view" of theories].
Why doesn’t a theory become a law? Well in the first instance, it’s the wrong direction. Laws come from theories, and theories are the senior rank in science. The best thing that a hypothesis can do is grow up to become a full fledged theory (something folk seem not to get, and treat “theory” as if it were shakier than a guess or law).
Secondly, we don’t seem to make laws as much as we used to. In part this is because we have become so much more mathematical, and frankly there’s no end to the number of mathematical statements we can make based on our models. In part also it’s because the idea of a scientific law rests on an older notion of natural law that science and philosophy is not so universally agreed upon.
I also do not think, contrary to popular opinion, that there is a set progression that ideas in science go through. Some can burst forth from the forehead of the scientist as a full-fledged theory. Some can hang around for decades or even centuries before becoming firmly established. Some remain hypotheses, others are taken to be good explanations (law-like things), and some just stay as possibilities, without people becoming firmly convinced one way or the other. But if I had to make a generalisation, I’d say that hypotheses, once tested and found to be firm empirically, become explanations (laws, if you like), and these tend to build up theories.
Again I say, the best thing that can happen to a scientific idea is that it becomes a theory. Natural selection, for example, began as a hypothesis, and ended up a law (or rather an explanation when the right conditions apply) in a theory of evolutionary biology (many models of various kinds).
I hope this helps you.