Non-Causal Explanation

In this essay, I challenged the claim that “To explain an event is to provide information about its causal history”.

I. Introduction

Following Hempel’s D-N model of explanation, theories equating the explanation of an event to providing its causes sprang up. Among these theories, the idea that “to explain an event is to provide information about its causal history” is initiated by Lewis in his paper Causal Explanation. Admittedly, providing causal histories of a certain event is a very prominent characteristic most explanations share under many circumstances. However, interpreting all explanations of events as the provision of information about their causal histories can be far-fetched, and is prone to meet with potent counterexamples which are difficult, or even impossible, to resolve.

In this essay, I will elaborate on two types of situations where Lewisian causal explanation theory fails—namely, dispositional explanation and distinctively mathematical explanation. I will illustrate how Lewis is aware of the potential risks his theory is confronted with and how he attempted to defend himself in the following section. Then I will focus on dispositional and distinctively mathematical explanations respectively to show why Lewis’s defense is not successful.

II. Explanation as Information about an Event’s Causal History

According to Lewis, any event that needs explanation stands somewhere in the complex causal net. It has a complex causal history. The causal history of an event has a tree-like structure, and in the branches of the tree reside various other events. My tripping over might be caused by the threshold in front of me, and my friends’ giving me a call, and the surrounding crowd’s blocking my sight of the threshold. The existence of the threshold may be caused by the architect’s design and the craftsman’s work. For the causal history of my tripping over, I can incorporate everything mentioned above: the threshold, the call, the crowd, the architect’s design, the craftsman’s work, my going to the place, my birth… Or even the Big Bang!

But it is ridiculous to say that my tripping over can be explained by the Big Bang. Neither would Lewis say the Big Bang is explanatory. To be counted as an explanation, the information provided should be sufficient, correct, and up-to-date, promoting the overall understanding of an event’s causal history for the person informed. And explanations can be evaluated by standards such as whether they contribute to clarifying the causal history of the event, whether they are able to identify falsehood, or whether the causal process they involve is familiar, etc.

At first glance, this causal interpretation of explanation seems to work very well. After all, when we are asking why-questions, a satisfactory answer we get normally starts with “because”, and ends up with some strong, clear, and correct statements about the causes of the event in question. Yet Lewis admits that there are obstacles in the application of such theory, which are represented by three typical cases. The first case is that when we try to explain the traveling path of light, we appeal to Fermat’s law, which says that light travels in the path which takes up the least time. However, Fermat’s law appears to stand nowhere in the causal history of the path that the light takes. The second case noticed by Lewis is that we explain the stopping of the collapse of a star as “a more collapsed state would violate Pauli’s Exclusion Principle”. In this case, the explanation seems to provide no causes at all. The third case is that when we are explaining one’s immunity to smallpox, we may say that he has been vaccinated, and the possession of the antibody makes him immune. Yet there seems to be no causal link between the possession of the antibody and the immunity.

Briefly, Lewis tried to defend his theory from these counterexamples in two directions: to the first and second cases, he replies that information about causal history is indeed provided, and to the third case he replied that dispositions such as being immune to smallpox cannot be regarded as events. From Lewis’ perspective, Fermat’s principle itself is rejected as an explanation. It is explanatory because it implies explanatory information such as the speed of light, and how waves propagate in different media, which are causes of the light’s path. Secondly, explanatory information is also provided in the collapsing star case, just in a negative way; yet negative information about causal history, argues Lewis, is still explanatory information. In reply to the third case, it is said that being immune is a dispositional property, yet not an event to be explained.

III. Dispositional Explanation

But this dispositional objection to causal explanation theory is dismissed too hastily by simply asserting that dispositions are not events to be explained and the causal histories of dispositions are untraceable, because in many contexts, especially in non-physical sciences, we are always including dispositional properties among the causes of a particular event. Under certain circumstances, some dispositional properties are even dominant causes of the event in question. If there is no way to tell the causal history of a dispositional property, then the causal event caused by that property would become obscure, and there cannot be credible causal explanations for the causal event as well.

Consider the following study on marketing conducted by Lambrecht, Tucker, and Wiertz in 2015 and their explanation of the result of their study. In the research, they collected statistics on people who included hot search keywords in their Twitter posts. Some of them included those words in their posts on the very first day when they occurred on the top search list; some used them on the second day; the latest users studied posted the words on the fourth day. What the research group did was investigate how the frequency of clicking on ads on Twitter is related to individuals’ time of including top search keywords in their posts. Surprisingly, they found that the highest frequency of clicking on the ads appeared in the group where people included the words on the fourth day. The explanation of the result is that these people have a disposition to agree with other people’s opinions and believe what others say.

This explanation may not, in a strict sense, be a scientific and rigorous one, but still is convincing and has potent explanatory power. The argument can be reduced to the form as follows:

(a) A and B are strongly positively correlated events.
(b) We can think of a dispositional property d of the subject S, which is causally related to A and B.
(c) Therefore, we may reasonably speculate that A and B can both be explained by d.

In this particular case, A stands for including hot keywords in the Twitter post on the fourth day; B stands for clicking on ads more frequently; and d stands for the property of easily agreeing with others.

But put this explanation in the light of causal explanation theory, it is strange how the explanatory power of d should be granted. For d is a dispositional property, and has no explicit causal history. Consequently, adding d to the causal history of both A and B should yield no extra information about the history of both events.

One possible way out is to replace Lewis’ “causal history” with “causal connection”, as Marc Lange indicated in his paper What Makes a Scientific Explanation Distinctively Mathematical. If we grant that something is explanatory not only because it provides information about its causal history, but also because it provides information about its causal results, and anything causally related to it, then the explanatory power of dispositions can possibly be justified. Nevertheless, I don’t think making such an alteration is prudent. After all, it is even stranger to say that the driver’s drunkenness is because of the car accident.

IV. Distinctive Mathematical Explanation

Lange depicted a very detailed picture of what distinctive mathematical explanation is, and why such explanation is non-causal. Yet it appears that his ambition is far greater than merely rejecting the adequacy of causal explanation theories. He also aspires to show that no explanation is non-causal, except for distinctively mathematical ones. On this point I can hardly agree, though Lange’s project on the whole is indeed a very compelling one.

There is a uniform recipe for Lange’s versions of non-causal explanations. In the traditional philosophical debates between empiricists and rationalists, there is a long-lasting headache for the former: to explain the acquisition of knowledge in logic and pure mathematics like algebra and geometry. Logic and mathematics are very peculiar because they can be true without any reference to the empirical world. The so-called distinctive mathematical explanation can be regarded as an empirical event which has a mathematical counterpart, to be explained by a pure mathematical theorem. To name some, the mother cannot equally distribute 13 strawberries to her 3 children without cutting them because 13 is not divisible by 3. And if I cut the three angles of a triangular cardboard and put them together, two of the edges can form a line, because the sum of the three angles of a triangle is 180 degrees. The “pure reason” world of mathematics has no direct causal relation with the empirical world, which is the realm of causation. Consequently, explanations appealing to mathematics manage to escape the discussion of causation with ease.

In the same manner, I argue that explanations appealing to logic have this sort of advantage as well. For example, I can explain that when I am in Mansfield College, and Mansfield College is in Oxford, it can be concluded that I am in Oxford, because if A⊂B, and B⊂C, we can conclude that A⊂C. An explanation like this is also a non-causal one.

V. Conclusion

Now, I have examined the theory which interprets explanation as providing information about an event’s causal history and tried to attack it from certain aspects. I think the theory fails to deal with explanations which have a dispositional element in them, and cannot account for distinctively mathematical and logical explanations. Presumably, there are other corners of explanation where the theory in question fails to reach. Yet I think these two groups of counterexamples already have the power to prove that the causal history account of explanation can turn out to be unsatisfactory.

Bibliography

[1] Lewis, D. K. “Causal Explanation.” 1986.
[2] Lange, M. Because without Cause. Oxford University Press, 2016.
[3] Sober, E. “Equilibrium Explanation.” Philosophical Studies, 1983, 43(2): 201–210.
[4] Hempel, C. G., and Oppenheim, P. “Studies in the Logic of Explanation.” Philosophy of Science, 1948, 15(2): 135–175.