Explaining Behavior 3: The Deductive Model
The logic of explanation and prediction.
Previous in this series: Part 1, What is Theory? Part 2, Styles of Explanation.
What exactly are we doing when we use a general theory to explain something? And what does it mean for a theory to make a prediction? In this entry we delve into what is called the deductive model of explanation. Like anything else, philosophers of science debate it until they’re blue in the face. But I think its a useful model for a deep understanding of what a good theory actually does.
Explanation as Deduction
Let’s start with a stupid simple example. I’ve drawn a sample of 1,000 people who smoke cigarettes, and of another 1,000 people who don’t smoke cigarettes. The sample of smokers has a higher rate of lung cancer. My explanation for this finding is that there’s a causal relationship between the smoking and the cancer. I propose the theory that, in general, smoking cigarettes makes one more likely to develop lung cancer.
We can flip this explanation around into the form of a logical syllogism, in which we deduce a conclusion from two or more premises.
A. Smoking cigarettes makes one more likely to develop cancer.
B. People in Sample 1 smoke, people in Sample 2 don’t.
C. Therefore, people in Sample 1 are more likely to develop cancer.
(I suppose a stickler might add in some steps to go from differing likelihoods to different rates, but you get the idea.)
Stated thus, we have an example of a logical deduction. In a valid deduction, if the premises are true, then the conclusion must also be true. The conclusion is thus a logical implication of the premises, something that logically follows from them.
In the deductive model of explanation, at least one of our premises is a general proposition, the core of a general explanatory theory. In the example above, this is statement A (smoking —> cancer). Since we’re applying this general idea to a specific case, at least one premise must be some relevant fact about this case. This is often called the initial conditions. In the example above, this is statement B (sample 1 smokes, sample 2 doesn’t). The conclusion of our reasoning, statement C, is the thing being explained. Explaining it means making it a logical implication of that general theory applied to those conditions: If the theory is true, then that outcome is exactly what we would expect under those conditions.
Consider a sociological example, also stupid simple for the purposes of illustration. It’s based on sociologist Emile Durkheim’s theory of suicide. In this example, “social integration” refers to the degree of one’s social ties and involvements.
A. Suicide varies inversely with social integration.
B. Married people have greater social integration.
C. Therefore, married people have lower suicide rates.
The general proposition explains the difference in suicide rates because that difference is a logical implication of the proposition, at least given the condition that marriage increases integration.
One cool thing about a general theory is that one can apply it to a range of conditions, and so get it to explain a variety of facts. Consider how we can get some more mileage out of that theory of suicide by adding one more condition:
A. Suicide varies inversely with social integration.
B. Married people have greater social integration.
C. More people are married in Town A than in Town B.
D. Therefore, Town A has a lower suicide rate than Town B.
We thus go from explaining differences between individuals to differences between towns. Or maybe we turn away from marriage to other things that can be a source of social integration, like membership in a religious congregation.
A. Suicide varies inversely with social integration.
B. People who participate in church have greater integration.
C. Therefore, people who go to church have lower rates of suicide.
In this way the same general proposition – the same theory – can explain a variety of facts. When we are able to deduce many facts from one or a few propositions we have, as sociologist George Homans put it, “achieved a great economy of thought” for we “no longer face just one damned finding after another. It has acquired an organization, a structure.” Rather than unrelated things to be remembered separately, we instead have a general pattern, and can reason to its implications in various circumstances.
Theoretical Prediction
This same deductive logic – if these premises are true, then this conclusion is true -- also lets us use a theory to predict new facts. Let’s say I don’t know jack about how belonging to a fraternity or sorority affects a university student’s risk of suicide. But I do know that belonging provides a source of social ties and involvements, and I have Durkheim’s social integration theory to work with, so:
A. Suicide varies inversely with social integration.
B. Fraternity and sorority members have greater social integration.
C. Therefore, fraternity and sorority members will have a lower rate of suicide.
In this case we would call the conclusion a prediction. If I made it in the context of a particular study I was about to conduct – say, I’m about to test this prediction in a sample of N college students – we’d call it a hypothesis. Either way, the deductive logic of a prediction is exactly the same as that for explanation.
The difference between explanation and prediction is pragmatic: We call it a prediction if its something we haven’t yet looked into, a conclusion we don’t already take for granted as a fact. But at the end of the day a theory’s predictions are the same as the things it explains: logical implications of the theory. What a theory explains, it predicts, and what it predicts, it explains.
Implicit Propositions
Normally people don’t cast their explanations in the form of a logical syllogism. In fact, often they’re just single statements, something like “Older Americans commit suicide more because they’re more isolated.” If you want to understand this statement as a general theory, though, you can break it apart into the same components as the examples above.
A. Suicide increases with isolation.
B. Older Americans are more isolated.
C. Therefore, old people commit suicide more often.
Doing this sort of exercise can help clarify the assumptions made in the explanation. For this explanation to be right, we need to be right about the effect of isolation on suicide, and also about the fact that old Americans are more isolated.
Complementary Explanations
Often there are multiple theories that try to explain the same thing. This is especially so in the social sciences. Take a criminology course, for example, and you’ll learn a dozen different theories meant to explain crime. A closer look at the logic of explanation can help us clarify the relationship between them.
For starters, sometimes they’re not actually trying to explain the same fact. They might each deal with facts that can be put in the same broad category, like “crime,” but they’re actually deducing different conclusions. Consider an example:
Explanation 1: Economic strain leads to armed robbery. The poor and unemployed experience greater economic strain. Therefore, they are more likely to commit armed robbery.
Explanation 2: Armed robbery is more likely when there are more suitable targets to rob. People who carry lots of cash, like bartenders and waiters at the end of their shift, are suitable targets. Therefore, these people are more likely to suffer armed robbery.
These two theories might both be called theories of “crime,” but one is explaining variation in who perpetrates robbery, while the other is explaining variation in who is a victim. Not only are these theories not competing to explain the exact same thing, you might even say they complement one another. Since an armed robbery requires both a perpetrator and a victim, you need both theories to provide a more complete explanation of armed robbery. Because of this, sometimes propositions generated independently can be combined into a more complete theory.
Competing Explanations
Theories are competing explanations when they try to explain the exact same facts. Let’s take it as fact that churchgoers have lower suicide rates than those who don’t attend services. Now suppose two competing explanations for this fact:
A. Suicide varies inversely with social integration.
B. Churchgoers have greater social integration.
C. Therefore, churchgoers are less likely to commit suicide.
Versus:
A. Aging reduces the risk of suicide.
B. Churchgoers are, on average, older than the general population.
C. Therefore, churchgoers are less likely to commit suicide.
Each of these explanation tries to deduce the same fact, but with a different set of assumptions. It could be that one is right and the other is wrong, and that is the case here (as a matter of fact, age generally does not reduce the risk of suicide, it increases it).
But competing explanations don’t necessarily contradict one another. It’s always possible that two or more factors contribute to an outcome. For example, I might propose that my neighbor’s tomato plants are taller than mine because his get more light. And he might propose that his are taller because they get more water. And we might both be right: Tomatoes that get more water grow taller than those that get less, and those that get more sunlight grow taller than those that get less, and his tomatoes get more of both, explaining why they’re so much taller than mine.
This point is worth emphasizing: Even if two theories explain the same facts, they are not necessarily mutually exclusive.
Contradictory Explanations
Two explanations are only mutually exclusive if some of their premises or conclusions cannot be true at the same time. Here’s an example where both the propositions and their predictions are contradictory:
A. Punishment makes a domestic abuser less likely to reoffend (via deterrence).
B. This group of domestic abusers were arrested, these others were not.
C. Therefore, there should be less reoffending in the arrested group.
Versus:
A. Punishment makes a domestic abuser more likely to reoffend (via retaliation).
B. This group of domestic abusers were arrested, these others were not.
C. Therefore, therefore, there should be more reoffending in the arrested group.
Both theories are trying to explain reoffending among domestic abusers, but they clearly have opposite ideas about what makes it more likely. And in this case, it leads them to make opposite predictions as well.
One could also conceivably have two theories that arrive at the same prediction but based on contradictory assumptions. Take something like:
“People won’t appreciate your theory because it is obvious and commonsensical”
Versus:
“People won’t appreciate your theory because it is whacky and wrong.”
We have here agreement about the prediction — my theory won’t be appreciated — but contradictory reasons for giving it. A theory can’t be simultaneously obvious and wrong, commonsensical and whacky. If no one appreciates my theory, it means both are right in their prediction — but at least one must be right for the wrong reasons.
That a theoretical prediction can turn out to be right for the wrong reasons is an important lesson, and one that we’ll consider in more detail in the next installment.
Next in Series: Part 4: Testability
Sources:
Braithwaite, Richard Bevan. 1953. Scientific Explanation: A Study of the Function of Theory, Probability and Law in Science. New York: Harper and Row
Hempel, Carl G. 1965. "Aspects of Scientific Explanation." Pages 331–496 in Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: Free Press.
Hempel, Carl G. 1966. Philosophy of Natural Science. Englewood Cliffs: Prentice Hall.
Homans, George Casper. 1967. The Nature of Social Science. New York: Harcourt, Brace, and World.