Evolving Thoughts

Laws, theories and models

Posted by John S. Wilkins on February 21, 2009
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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:

Dr. Wilkins,

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.

Best Regards,

Cameron Peters
6th Grade Math & Science
Poulsbo Middle School

Dear Cameron

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.

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Comments

  1. #1 Kate Devitt
    February 22, 2009

    Great post. Thanks. Your point about the folk emphasis on laws over theories is an important one.

  2. #2 MPL
    February 22, 2009

    This is a naive perspective on it, but from my limited experience, laws seem to be ‘the sort of thing a logical positivist would like’, by which I mean they tend to have direct observational meanings and tests.

    I don’t think it’s quite correct to say that “Laws come from theories”. Laws can be discovered by experiment and hang around looking for a theory for a while—Kepler’s laws kicked about for a century before Newton’s theory explained them.

    Theories may rely on laws (Evolution relies on Natural Selection), and they may spit them out as consequences (derive Kepler’s laws from Newtonian mechanics). Theories may also explain laws in terms of things not directly observable—a whole host of chemical and physical laws were explained by the idea of atoms too small to be seen.

    Asking why a theory can’t become a law is a bit like asking why a family can’t become a person.

  3. #3 Lassi Hippeläinen
    February 22, 2009

    Personally, I don’t like “laws” in science. Just as the original questions shows, non-scientific people think that a Law is at the top of the hierarchy. The notion must come from politics, where a law is the highest form of agreement.

    But in science, laws are not negotiable. They cannot be revoked by a political decision. The concept “Law of Nature” tries to separate scientific laws from political laws, but it hasn’t worked. Much of public discussion about science (e.g. evolution or global warming) still treats science as if it were negotiable, and could be voted on.

  4. #4 John S. Wilkins
    February 23, 2009

    MPL is right in one sense – laws are not usually derived from theories in a historical sense, but they are derivable from theories once all is done and dusted – that is to say, you can’t derive a theory from the laws, but you can derive a law from the theory, once the theory is well elaborated and bedded down. I meant it as a logical relation.

  5. #5 AnthonyK
    February 23, 2009

    I note that your views are being commented on adversely by your Linnaean friend. Apparently you’re wrong – and not just on “laws” and “theories”. Just about everything.
    I wonder, could you and he ever form some sort of clade of your own – an intellectual bond producing its own meme? Is this relationship parasitic, or merely symbiotic? At the moment, he’s built himself a nest of his own and is frantically displaying to you, and any other suitors here – me? I’m confused – in an attempt to woo us away from your thoughts.
    I don’t know. Which of you is the one true Claddist?

  6. #6 John S. Wilkins
    February 23, 2009

    We Don’t Mention the Moron.

  7. #7 AnthonyK
    February 23, 2009

    I knew it. Science has a secret agends to supress studity! You, Mr Wilkins are a “brainist”. And I’m telling the internet.

  8. #8 John S. Wilkins
    February 23, 2009

    There Is No Reality Based Cabal. Now, answer the door in a few moments, will you?

  9. #9 Gary
    February 23, 2009

    Well, now you’ve confused me. I’ve always thought laws were mathematical descriptions rather than explanations and models and theories were explanations.

  10. #10 Strider
    February 23, 2009

    Great post. Any citations? Also, as long as we’re being pedantic isn’t it grammatically correct to write “an hypothesis”? Just askin’.

  11. #11 Mike Haubrich, FCD
    February 23, 2009

    Hey, Strider, that bit of pedantry regarding “an hypothesis” or “an historical,” etc. is most irritating when adhered to by Americans who properly pronounce our “h”‘s at the beginning of our fancy words (if we get nothing else right.) It is derived from a cockney tendency to drop their “h”‘s and so, when corrected on the correct version of the “a” article to use, I release an hellish sigh.

  12. #12 Robert E. Harris
    February 23, 2009

    In the case of low-density gases, the kinetic theory of gases produces the ideal gas law as one result. If it did not, the kinetic theory would be wrong and not a theory. Many other consequences follow from the kinetic theory. For example, collision frequency at a wall leads to the Knudsen method of determining vapor pressure: let the saturated vapor leak out a small hole into vacuum and assume the leak rate equals the collision frequency with a piece of wall with the same area as the hole. This works well for low enough vapor pressure and small enough hole area, provided the hole is not a tube of more than infinitesmal length. (There are kinetic theory corrections known for holes of finite length.)

  13. #13 Moderately Unbalanced Squid
    February 23, 2009

    I was under the same impression as Gary. I’ve always thought of laws as a mathematical description of a relationship, regardless of what the mechanism linking that relationship can be. Eventually a theory may come around explaining why the relationship exists, but it doesn’t really have an impact on the law.

  14. #14 Bob O'H
    February 23, 2009

    Nice to see a fellow anachist! The sooner we dump the idea that we can find Laws of Nature the better.

    In the 20th century, however, people stopped talking so much about laws and started talking instead about models and hypotheses.

    Except for some philosophers. My favourite invention in this area is ceteris paribus Laws, which are laws that operate except when they don’t.

  15. #15 AmthonyK
    February 24, 2009

    The difference is, if you break the laws of nature the Reality Police put you somewhere very special….

  16. #16 David Marjanović
    March 6, 2009

    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.

    Well, I’d say the Ideal Gas Law holds perfectly well for the ideal gas — the only complication being that the ideal gas is a mathematical/philosophical abstraction and doesn’t exist in nature.

    It still gets used a lot for calculating the behavior of real gases, because, under not too extreme conditions, most gases happen to be close enough to ideal.

    ————

    Let me jump on the bandwagon of “laws as generalizations across observations that need to be explained by a hypothesis or theory” like Kepler’s laws of planet motion by Newton’s and then Einstein’s theory of gravity. I’d say evolution by natural selection is a theory, not a law: it explains the mechanism rather than simply stating which causes give which results. The only disadvantage is that this requires theories within theories (in this case within the theory of evolution by mutation, natural and sexual selection, and drift).

    ————————

    The question of “an” vs “a hypothesis” has nothing to do with grammar; it’s a question of pronunciation. Two different sounds are used for h by different English speakers (that’s not counting British dialect speakers ‘oo simply drop it altogether!), and, judging from this discussion, it seems that users of this one prefer to use “an”.