Laws and causation

We have seen that the crucial issues in the justification of scientific theory have to do with how to justify the generalizations that theo­ries make.

I have been assuming that natural laws say simply that all A's of some kind are B's. But, as Hume realized, scientific laws say more than that. You will remember that when he introduced the problem of induction he talked about the “secret powers” of bread. What he meant by this was that to say that bread is nutritious is not just to say something about what it does, but also to say something about what it can do. To have a power is to have the ability to do something.

Hume is pointing out that the law that bread nourishes us is not simply the generalization that

GENERALIZATION: All people who eat bread are nourished by it.

It also has the consequence

LAW: Anyone who ate bread would be nourished by it.

We can bring out the difference between these propositions by tak­ing up again the idea of a possible world. The generalization says only that all the people who eat bread in the actual world gain nour­ishment from it. But the law says that all the people who eat bread in other possible worlds are nourished as well, so it applies, in some sense, to people who don't exist in this world.

Of course, the law doesn't mean that people who eat bread in every possible world are nourished. There are worlds where the law does not hold; otherwise it would be a necessary truth that bread nourishes. Nevertheless, in all the worlds where the law does hold, all the bread eaters are nourished. The class of worlds where natu­ral laws hold is called the class of “nomically possible worlds.” (“Nomically” means “having to do with laws” and comes, like “nomologically,” from the Greek word for law.)

The key fact, then, is the necessity of laws. Just as metaphysically necessary truths are true in every possible world, so natural laws are true in every nomically possible world. One thing that you cannot explain without a sense of the necessity of laws is the fact that because it is a law of nature that hot air rises, a body of air would have risen if heated, even if, in fact, it wasn’t heated.

This fact has serious epistemological consequences. The problem of induction shows that it is hard to justify going from the fact that some of the A's in the actual world are B's to the belief that all of them are. But, to justify the law that all A's are B's, we have to show not only that all the A's in the actual world are B's, but that all of the A's in the nomically possible worlds are B's also. When Mendel claimed that it was a law of nature that purple alleles dominated white ones, he was committed not just to a view about the outcomes of all actual crosses, but also to a view about what the outcomes would have been of crosses nobody ever made. If there is a problem about justifying the former inference, there must be more of a prob­lem about justifying the latter.

We can consider the problem at its clearest in a simple case.

If I had made that cross, the offspring would all have been purple.

A sentence like this is called a contrary-to-fact conditional or a counterfactual. It says what would have happened if something that didn't happen had happened.

Counterfactuals are extremely important to science, for two rea­sons. First of all, one way of describing the difference between gen­eralizations and laws is to say that generalizations don’t, but laws do, support counterfactuals. The true generalization

All the coins in my pocket are silver

is not a law, which is reflected in the fact that it is not true that this penny would be silver if it were in my pocket. Generalizations, like this, that are not lawlike are called accidental generalizations. They do not support counterfactuals. Laws, on the other hand, do support counterfactuals, as we have seen.

The second reason that counterfactuals are important is that when we say, for example, that having two purple alleles causes a pea to be purple, we are committed, among other things, to the counterfactual

If this pea had had two purple alleles, it would have been purple.

We can understand what this counterfactual means in possible­worlds terms: it says that in all the nomically possible worlds where the pea has two purple alleles, it has purple flowers. All causal sen­tences entail Counterfactuals in this way. And much of natural sci­ence is about causality. Justifying the claim that science gives us knowledge requires that we be justified in having such counterfac- tual beliefs. The issue of how these beliefs are to be understood and justified is also a topic of current concern in logic and the philoso­phy of science.

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