What’s in a Theory?

Exploring the Paradoxes of Theory Confirmation

By Steve Humphrey
Illustration by Andrea Hutchinson

Scientists create theories to describe, explain and make predictions about the physical world. But it is not easy to verify that the theories are true. In fact, it has been generally accepted that it is impossible to verify a theory. The best we can do is confirm it to some degree. Why is this?

I’m sorry, but this will involve logic.

The general structure of testing is this: we use a hypothesis (theory) to generate predictions about future observations. For example, if I am investigating the effectiveness of some new cancer drug, I start with the hypothesis that it will be effective in treating a certain kind of cancer. On the basis of this, I make a prediction that if I give it to a patient with that kind of cancer, the patient will get better. That is, if the hypothesis is true, then the prediction will be true. Now, suppose our prediction comes out true, and this particular patient improves. Can we conclude that the hypothesis is true just because it was used to make a correct prediction? No.

The argument “If the hypothesis is true, then the prediction will be true, the prediction does turn out true, therefore the hypothesis is true” is an invalid argument. It has the same form as “If my pet Olivia is a dog, then Olivia is a mammal. Olivia is a mammal. Therefore, she is a dog.” But my baby is a cat, so the premises are true and the conclusion false, making it invalid. Now, if we make many predictions based upon that hypothesis, and many of them result in positive outcomes, then we say we have confirmed the hypothesis to some degree. This is why drug trials go on so long and involve so many patients. We need enough confirmatory data to raise our confidence in our hypothesis. This is an inductive argument.

But, of course, it is more complicated than this. The famous philosopher of science Karl Popper argued that the test of whether some hypothesis would qualify as a scientific hypothesis is whether it is falsifiable. That is, is there some outcome that would conclusively imply the falsity of the hypothesis? (Think about hypotheses involving astrology. What would count as falsifying the claims of astrology?) And if the argument went as simply as the following, “If the hypothesis is true, then the prediction will turn out true, the prediction is false, therefore the hypothesis is false,” then it would be clearly falsified. It would have the same form as “If my pet Olivia is a dog, then she is loyal and loving, always at my side. She is sweet, but she is not always at my side. Therefore, she is not a dog.” This is a valid deductive argument, called modus tollens.

But predictions are not made simply on the basis of some hypothesis. There are other facts that must be used to generate the prediction. For example, in the case of the drug trial, I have to factor in the doses given, the different stages of the disease the patients are in, the ages and general health of the patients, whether they smoke, etc. So, even if one of the patients fails to improve under treatment, it may not be the fault of the drug. The failure may be attributable to other factors. And there is always a plethora of other factors to take into account. Again, this is why drug trials go on so long and involve so many patients.

Next time, I will be discussing probability. V

Steve Humphrey has a Ph.D in the history and philosophy of science, with a specialty in philosophy of physics. He teaches courses in these subjects at the University of California, Santa Barbara, and has taught them at the University of Louisville.