Here’s an example of a lawlike claim: ‘all emeralds are green’. This claim is much like a scientific law, because the predicate ‘is an emerald’ and the predicate ‘is green’ are practically “made for each other”. They’re ideally suited to their linguistic “marriage”, because what makes a beryl count as an emerald is the very thing that makes it green. So you can’t have an emerald that isn’t green.
Although most scientific laws are written using mathematical symbols – such as Newton’s ‘F = ma’ – those symbols capture intimate connections between the real things they stand for, much as words do in the emerald example above. Those connections are generally simple, and consist of such facts as the containment of one set by another (as above), or direct cause-effect links (as in ‘what goes up must come down’), or suchlike. Speculating, we might well wonder whether our very sense of simplicity itself is shaped by our innate ability to sniff out lawlike connections. In any case, these intimate connections give laws a distinct “flavour of necessity” – laws can seem almost empty like tautologies, or almost trivial like definitions.
An important feature of laws is that they support “counterfactual conditionals”: although I’m not actually holding anything in my hand, if I were holding an emerald in my hand, then it would be green. This is why laws are useful in prediction: you can predict that something will be green, just from knowing it’s an emerald.
Now here’s an example of a claim that is not lawlike (in fact it’s not even true): ‘all swans are white’. There is practically no correlation between an animal’s colour and the genus it belongs to, or even the species it belongs to. Many groups have subgroups whose most noticeable distinguishing feature is their colour – so the predicates ‘is a swan’ and ‘is white’ are not at all suited to “marriage” in a law.
Although ‘all swans are white’ may be superficially (grammatically, etc.) similar to ‘all emeralds are green’, it cannot be used to make reliable predictions. If I were to keep a swan in my own private lake, you wouldn’t be able to reliably guess whether it would be black or white.
Sometimes, people talk about “black swans” as if they were occasional anomalies whose possibility everyone should be forewarned and forearmed about. But really, that is not nearly deep enough or sceptical enough. The real problem is not that exceptions occasionally turn up, but that not enough thought is given to whether laws are involved at all when we try to predict things.
Such laws might be statistical – as long as they’re genuine laws which describe real linkages, and which therefore support counterfactual conditionals. Prediction cannot be based on a mere “statistical snapshot” of the way things accidentally happen to be. For example, in the long run, repeated throws of a pair of dice will result in doubles about one sixth of the time. Even if we don’t actually throw the dice repeatedly, we know that if we were to do so, that proportion would be approached with increasing proximity. Or again, in a large enough sample of mammals, the sexes will be represented roughly equally. Even if we don’t actually take a head count, we know that if were to take a big enough head count, we would find roughly equal numbers of male and female. These proportions are not accidental: they’re the products of careful manufacture (shaping, balancing, etc.) of dice, and of evolutionary biology, respectively. Either of these statistical proportions could take part in a statistical law.
But with many statistical phenomena, the numerical proportions we measure are no better than merely accidental. If we extrapolate from the latter for purposes of prediction, our predictions will be unreliable. For example, suppose about one sixth of Australians drive Ford cars. There is nothing to suggest that that proportion is anything but an uninteresting coincidence. In a decade’s time, they may drive entirely different brands of cars, in entirely different proportions. Or again, the human population has been rising because food is getting cheaper, but the wealthier people become, the fewer children they tend to have. So although there has been an overall upward trend, there is no reason to think any sort of law is involved in the rise of the human population. The current rate of population rise is no basis for any reliable predictions about how big the human population will be at any time in the future.
Now for my main complaint: many people don’t bother to ask whether any sort of law is involved in apparent trends such as population rise. They just extrapolate from the current “data”, and expect nature to “continue uniformly the same” (as Hume put it) in the relevant respects, as if a law could describe the process. Often, we have very good reasons to think the process isn’t remotely lawlike – in other words, we have good reasons to think that no law could describe it. Laws are bits of human language, and human language can describe some things but not others.
The reliability of any prediction depends on an essential linkage between what we know already and what we’re predicting. There might be a simple “constant conjunction” between them (to use Hume’s terminology again). Or there might be some other non-causal connection that underwrites a lawlike connection, such as exist in quantum entanglement. But these lawlike connections are not optional – they’re a requirement of prediction. The ever-present question in our minds should therefore be: Is there or isn’t there a lawlike connection between what we’ve observed already, and what we’re trying to predict?
I think that question isn’t asked often enough. And when questions aren’t asked, answers tend to be merely assumed. The assumed answer to the present question is in effect that there is always a lawlike connection of the required sort, because the physical world is assumed to be mechanical and regular simply by virtue of being physical. The naïve Newtonian intuition is that it’s “like clockwork”. Without even asking the question above, we tend to assume that all we have to do is follow the standard pattern of extrapolation from already-observed cases, and the physical world will oblige. Its unfolding patterns may not be obvious at first, the idea goes, but they must be there, waiting to be revealed beneath the apparent confusion.
I think that assumption is profoundly mistaken – so badly mistaken that it’s worth a brief look at the philosophical ideas behind it.
We belong to a tradition that takes the mind to be “spiritual” rather than “material” – it doesn’t interact with material things in the usual way in which matter interacts with other matter. So we think of the mind instead as a centre of consciousness or an engine of experience, in a sense “cut off” from the physical world outside the mind, because it “deals in experience” rather than with material objects. According to this view, whatever the mind knows about matter is made possible because its experiential inputs from the outside world provide “justification” for its beliefs, and if the beliefs are actually true, they count as items of knowledge. This standard analysis of knowledge takes “justification” to be “internal” to the mind. The vague idea is that I cannot accept anything except “what is available to me” within the confines of the “theatre of my own experience”, because otherwise I would have to “step outside of my own skin”. In the supposedly isolated state “inside my own skin”, with only internal cues available to me as “justification”, the best any mind can do is follow the standard pattern of extrapolation from observed cases – in other words, treat white swans in the same way as green emeralds.
Of course most people who belong to this tradition dropped the idea that the mind is “spiritual” long ago. The trouble is, most of us retain its associated epistemological baggage – such as that knowledge consists of true beliefs suitably “justified” by simple “basic beliefs” about experience, as just described. This idea is still so all-pervading, it even finds its way into popular ideas about science: our theories or computer models are analogous to beliefs, so it is widely supposed that they require an analogous “justification” of being supported by “data” – the public counterpart of “basic beliefs” about experience.
Like many philosophical errors, this one is so deep-seated that any alternative can seem unthinkable to those in its grip. How could it possibly be otherwise than that theory is supported by “data”? – Happily, the answer is given in mainstream philosophy of science: observations test theory rather than imply theory. Hypotheses yield predictions which observations either confirm or do not confirm. If a prediction is confirmed, the hypothesis is corroborated by the observation – a very different matter from its being implied by the observation.
But scientists pay little attention to philosophers nowadays. Many imagine that they don’t have to study any philosophy. The tragic result is that they do their own, newly cobbled-together, half-baked sort of philosophy. In a few branches of science (pseudo-science, if we’re honest) internalism of the sort described above has become a will-o’-the-wisp that guides methodology.
For example, consider the application of computer modelling to irregular natural phenomena that look confusingly “ravelled” to the human eye. The hope is that the magic powers of computer modelling can summon forth order from chaos and “unravel” them.
I think that hope is forlorn. Take something as simple as a compound pendulum. A compound pendulum’s individual parts – of which there are only two – behave in a lawlike way, but the whole does not. There is no ideal “marriage” of predicates (of the sort I began with) that link its earlier and later positions. Like so many things, the whole does not have a crucial feature that its parts do have. The mistake of thinking it does is called the fallacy of composition, and it is a common error. (For example, many suppose that if genes are “selfish”, the entire organism must be too.)
A compound pendulum is chaotic in the sense that its position depends in a critical way on initial conditions. Predicting its future position or behaviour from its past position or behaviour is a practical impossibility.
Now of course, it’s easy to simulate a compound pendulum in a computer, because it’s such a simple system. But it’s impossible to get such a simulation to model an actual compound pendulum, because both are chaotic. Their respective behaviours are bound to diverge. Far from “unravelling” the chaos, the simulation multiplies it by simply adding chaos of its own, if anything increasing the inevitability of a mismatch between it and any actual compound pendulum. The simulation may exemplify or illustrate by mimicry the chaotic behaviour of compound pendulums in general, but it’s incapable of modelling any individual pendulum.
In my opinion, the attempt to model the Earth’s climate using computer simulations is many orders of magnitude more misguided than the attempt to model a warehouse full of compound pendulums. That attempt is inspired by the “traditional” hope that the climate is made of physical stuff, and so “there must be predictable order hidden beneath the apparent disorder”. Well, there may be order in the form of lawlike behaviour on the part of individual molecules, but we have no reason to expect lawlike behaviour on the part of the inconceivably many component “parts” (including causal influences) that together constitute the climate.
I’m not a crank: I think we have good reasons to accept the greenhouse effect. In other words, we have good reasons to think that there is a lawlike connection between the concentration of greenhouse gases in the atmosphere and global temperatures. But a quick inspection of the best graphs we have reveal that at every temporal scale, from one year to several millenia, global temperatures go up and go down in a non-monotonic way. Any graph is confusingly “ravelled” to the human eye in pretty much the same way as a compound pendulum “flies around the place like a madman”. So any lawlike connection even with this simplest of causal connections must be extremely tenuous, or buried beneath mountains of extraneous noise. There is no obvious pattern to see here, nor any reason to think there is a “deeper” pattern that computer models could salvage from the disorder.