Statistical Regularities and Explanation

Exactness, explanatory power, causality, and meaning in science.

May 12, 2016Filed under theology#m. div.#philosophy#science#sebtsMarkdown source

The following was written in partial fulfillment of the requirements of Dr. Greg Welty's Philosophy: Science and Religion class at Southeastern Baptist Theological Seminary.


The following was prepared as a one-page, single-spaced short response to a question from the readings for this class.

It is easy to mistake exactness for explanatory power in the realm of explanation. Thus, it might be tempting to suppose that precise and consistent statistical regularities have greater explanatory power than inexact laws which have an attendant set of constraints and conditions specifying when and how they apply. However, the inverse is true.

Statistical regularity has no explanatory power. It has enormous utility, in that it allows effective prediction. However, it provides no insight into the reason why the regularity is captures occurs. Explanation is at core a matter of determining the reasons why something occurs, not simply observing that it occurs. If on every first, second, and third Tuesday of the month for three hours early in the afternoon small black marks are rendered onto a mostly white LED display, and the range of marks is tightly bounded, and the marks are known to form meaningful words and sentences and even stories, and there can therefore be strong statistical confidence that next Tuesday the same pattern will occur again, this does nothing to explain the marks. What suffices as an explanation is a person using a typewriter to compose the draft of a novel on those Tuesdays when she has a babysitter for her children. This is certainly not even a ceteris paribus law, and yet it has substantially greater explanatory power than does the statistical observation, regardless of the degree of statistical precision available.

By contrast, even inexact laws subject to restrictions and limitations are capable of offering meaningful explanations, because they can offer insight into the causal mechanisms which drive the processes. Though such statements of causality are inherently circumscribed to a certain degree—the ceteris paribus clauses are necessary—they retain the explanatory power that inheres in causal reasoning. It is both legitimate and explanatory to reason that “all other things being equal, Superman will win in a fistfight with Batman because he has superhuman strength and is functionally invincible to human weaponry.” Granted that all other things may not be equal (as in the famous 1980s story from which recent cinema drew more or less inspiration) and that Batman may, if he has access to Kryptonite, bring about a different outcome, in no way diminishes the explanatory power of the original statement. In fact, it may strengthen it by suggesting what kinds of things must be equal for the statement to hold, and suggesting other kinds of causal factors in the system. Since the system that is the universe—even Batman and Superman’s universe—is very large, it is unsurprising that causal relations can only be described with these kinds of constraints. After all, only God could know the total set of forces acting on a system and therefore could deliver a non-ceteris paribus statement of causal factors exhaustively.

This does not mean that statistical regularity is useless for explanation. In fact, it is a powerful tool for reasoning about the state of the world as part of deriving ceteris paribus-constrained causal statements. To derive such causal statements, one must (usually) first derive sufficient data on which to base an analysis at all. Thus, knowing that Superman has been completely invulnerable to all human weapons of whatever magnitude in the past, and that Batman is an ordinary human, is important in being able to state that Superman will win in an ordinary fistfight between the two. The statistical data drives an inference to the best explanation that he is in fact invulnerable to ordinary human weapons (an explanation which we as outside readers know in fact to be true), and grounds the “all other things being equal” statement. If other factors are introduced, so that other things are not equal, the inference from that statistical data set will still hold; but now other causal elements are in play and new statistical data would need to be gathered, for the sake of further reasoning to explanation. The two go hand in hand, in other words.