## Does science have a specific method: Explanation

### 0.1 Introduction

Science offers explanations of different phenomena. That is, one of the goals of science seems to be to explain various events, phenomena, regularities and so on. Why do people get cancer? Why do metals expand when heated? Why do I feel dizzy when I spin in circles? Why don’t I feel the speed of the earth’s rotation?

Many explanations are motivated by practical considerations. We care about our health and what to know why we get diseases or why certain people are healthier than others. We care about our environment and want to take the necessary steps to prevent its destruction. Other explanations are motivated by our desire to know. We want to know about other galaxies or astronomical behavior or the activity of building blocks of things.

The explanations that science has provided have been extraordinarily successful. We are capable of explaining more than ever before. But what is the nature of a scientific explanation? What are its key ingredients?

Before two different answers are given to this question, it is worthwhile to introduce two key terms.

Definition 1 (explanandum) The explanandum is the thing (phenomenon experience, observation, event, occurence, law) that is being explained.

Definition 2 (explanans) The explanans is the general laws (e.g. laws of nature) and particular facts that do the explaining.

### 0.2 Hempel’s covering law model of explanation

One answer to these questions is given by the philosopher Carl Hempel (1905–1997). For Hempel, an to given an explanation is to give a certain kind of answer to an explanation-seeking-why question (I’ll call these “why questions” for short):

1. why is x like this?
2. why does x behave like that?
3. why do I not fly off the earth even though it is moving?

For Hempel, the kind of answer that an explanation must take is that of an argument where:

1. the conclusion states that the explanandum) occurs
2. the premises give reasons why the conclusion is true
3. the conclusion is deductively entailed by the premises
4. the premises are true (so the argument is sound)
5. the premises consist of at least one general law (law of nature), e.g. “all water boils at 100 degrees Celsius” or “all metals expand when heated”.

Thus, according to Hempel, to explain $x$ is to show that $x$ follows deductively from (is covered under) at least one or more general law. That is, it explains the explanandum by showing how it is a logical consequence of a general law (and any particular facts).

The general structure then of the covering law is given in the following:

• P1: General law(s) (explanans)
• P2: Particular fact(s) (explanans)
• C: Phenomena to be explained (explanandum)

Example 1 (Why does sugar dissolve in water?)

### 0.3 Criticisms of the covering law model

Objection 1 (symmetry.) Suppose, on a sunny day, you are standing a certain distance from a flagpole that is 15m tall. You notice that the flagpole casts a 20m shadow. You ask yourself “why does the flagpole cast a 20m shadow? The flagpole is only 15m tall, shouldn’t it only cast a 15m shadow?”

An explanation for this phenomena can be given using the covering law model of explanation is given in the argument below (this example is drawn from Okasha, Samir. 2002. Philosophy of Science: A Very Short Introduction. Oxford: Oxford University Press, pp.45-46):

• P1: The flag is 15m tall.
• P2: The angle of sun with respect to the flagpole is 37 degrees.
• P3: All light travels in straight lines
• P4: Laws of trigonometry
• C: Therefore, the shadow of the flagpole is 20m.

One feature of the covering-law model is that, to put it coarsely, if $A$ (the explanans) is used to explain $B$ (the explanandum), then $B$ can be used to explain $A$. That is, there is a symmetry between the explanation and the object being explained. To put this more precisely, the explanandum can be replaced with a component of the explanans to explain that component.

This point is best seen through an example. Consider the flagpole example in the argument below. The explanandum there is the 20m shadow of the flagpole. Now suppose we were to ask “why is the flag 15m tall?” (P1). This could be explained simply by swapping the explanandum (C) with (P1) as is done in the argument below:

• P1: The shadow of the flagpole is 20m.
• P2: The angle of sun with respect to the flagpole is 37 degrees.
• P3: All light travels in straight lines.
• P4: Laws of trignometry
• C: Therefore, the flag is 15m tall.

This explanation meets all of the criteria set forward by the covering law model: all of the premises are true, the conclusion is entailed by the premises, and there is at least one general law. Nevertheless, it is strange to think that this explains why the flagpole is 15m tall. We think instead that the explanation ought to cite considerations having to do with the actual construction of the flagpole itself.

The key point to take away from this is an explanation should involve an asymmetry between the explanandum and the explanans. That is, to put it coarsely, if $A$ (the explanans) is used to explain $B$ (the explanandum), then $B$ should not be an acceptable explanation for $A$.

Objection 2 (irrelevance.) Consider an example found in Okasha Samir’s Philosophy of Science: A Very Short Introduction (2002:47-48) where a child wanders into room full of pregnant women. The child sees a man and asks a nurse why he isn’t pregnant. The nurse responds that the man is on birth-control pills, that individuals on birth control do not usually get pregnant, and that is why he is not pregnant. This explanation meets all of the criteria set forth by the covering-law model. It involves true premises, these premises entail a conclusion, it makes use of a general law, and the explanandum is the conclusion of the argument.

The problem exposed by this example is that the covering law model allows for an explanans that is irrelevant to the conclusion. The fact that the man is on birth control is irrelevant to why he is not pregnant. Whether he takes the birth control or not has no bearing on the truth or likelihood of the conclusion. What is relevant is the fact that he is a human male.

Thus, the covering-law model of explanation overdetermines the types of responses to why-questions that count as explanations.

Note 1 The explanans should involve information that is relevant to the explanandum. The point that the above example illustrates is that in order for a response to a why-question to count as an explanation, the explanation needs to contain information that is relevant to what is being explaned.

### 0.4 The causal model of explanation

An alternative to the covering-law model of explanation is the causal model of explanation. According to this theory, one explains a phenomena when one states what caused it. For example, if asked why my water plant has died, one could give an explanation for this by pointing to what caused the plant to die (e.g. plants needing water and I have not watered it).

In some respects, the causal model and the covering-law model overlap, e.g. in cases where the explanans of a covering-law model is also the cause of the explanandum. However, in other cases, it does not. To see the ways in which they differ, consider the flagpole and male-pregnancy example cited by Okasha Samir’s Philosophy of Science: A Very Short Introduction (2002:45-48).

In the case of the flagpole example, the fact that the shadow of the flagpole is 20m was used to explain why the flagpole itself was 15m. The problem here concerned the symmetry between the explanans and the explanandum. The causal model avoids this problem since causation itself is asymmetrical. While the flagpole’s 15m height causes the 20m shadow, it is not the case that the 20m shadow causes the flagpole’s 15m height.

In the case of the male-pregnancy example, the use of birth control was used to explain why a particular man was not pregnant. This was taken to be irrelevant, and one of the key points taken from this example is that the explanans ought to be relevant to the explanandum. In the case of the causal model, since taking birth control is not the cause of the man not being pregnant, this explanation would not be sufficient. What would be sufficient is something that plays a causal role, e.g. that males cannot become pregnant.

Objection 3 (Causality is an obscure notion) A theory of explanation ought to make explanation more, not less, clear. However, in using the notion of causality to explain explanation, the causal model of explanation may have done just that. Some philosophers contend that there is no intelligible notion of causality.

When we say that $A$ causes $B$, typically we mean (i) on the occurrence of $A$, $B$ follows and (ii) $A$ is responsible for bringing about $B$.

However, consider any case of causation. For instance, consider a billiard ball colliding with another billiard ball. In this example, what do we observe? We observe the first billiard ball moving at speed and moving toward another ball, touching that billiard bill, and then the other billiard ball begin moving. That is, we observe an occurrence where $A$ is followed by $B$. What we don’t observe is the fact that $A$ brought about $B$ (just that $B$ occurred after $A$). In short, we only observe the constant temporal conjunction of $A$ and $B$, not that $A$ causes $B$.

For this reason, and others, many take causality to be a puzzling concept. And, since you should not explain a puzzling concept like explanation with an equally puzzling concept like causality, the causal model for explanation is problematic.