Wrong-way reductions


Wrong-way reduction is a logical fallacy no one seems to have pointed out before.1 Regular people rarely make this error on their own. It’s common for philosophers, cognitive scientists, and theologians. The wrong-way reductions made by these professionals escape into the general culture, and cause trouble for everyone else.

A wrong-way reduction is emotionally attractive when you have a problem that is nebulous—complicated, messy, and ambiguous. A wrong-way reduction claims to replace that with a simple, tidy, clear-cut problem. What’s wrong is that the new problem is harder than your original one—or even impossible! For a wrong-way reduction to seem useful, you must ignore this, and take the possibility of solving the new problem as a matter of faith.

This is particularly common and obvious in rationalist eternalism..

One problem reduces to another if the second problem is easier, and a solution for the second is most of a solution for the first.2

An informal example: Suppose you want to get from your home in rural California to Athens, Georgia. There are many ways you could do that, some harder than others. Most of this problem can be solved by taking an airplane from San Francisco to Atlanta. This leaves only the easier problems of getting to and from the airports. What’s “reduced” here is the difficulty of the journey.

A more technical example (which you can skip): the best way to find the least common multiple of two numbers is to reduce the problem to finding their greatest common denominator. For two numbers x and y, LCM(x, y) = xy ÷ GCD(x, y). There are efficient ways to find the GCD. There are other ways to find the LCM, but they are less efficient than finding the GCD and multiplying.

Reduction, the wrong way

A wrong-way reduction transforms an easier problem into a harder one.

An example: Suppose you want to predict the outcome of a football game. One approach would be to estimate each team’s likely score. Then you could simply compare the two numbers to see which is greater.

This reduction goes the wrong way, because it is much easier to predict who will win the game than to predict exact scores.

Metaphysically motivated wrong-way reductions

Why would anyone make this sort of mistake?

If you wrongly believe that the second problem is easier than the first, this is not a logical fallacy. It’s an honest error of fact.

However, wrong-way reductions are often motivated errors, driven by wrong metaphysical attitudes. Often wrong-way reductions are advocated by people who know that the second problem is harder—or even impossible!

Wrong-way reductions are usually motivated by eternalism, the denial of nebulosity. Eternalism is unwilling to accept the inherent messiness, ambiguity, and uncertainty of life. In the grip of eternalism, we try to turn messy, ambiguous, and uncertain (but workable) problems into tidy, clear, certain ones—even when those are entirely insoluble.

Here’s an example. Divine command ethics turns the difficult problem of choosing how to act into the impossible problem of knowing God’s will. Ethics gets messy when different ethical considerations point in different directions in a single situation. Then it may appear that God has given contradictory instructions. How then to resolve the ambiguity? Honest theologians admit—when pushed hard enough—that it may be impossible to know what God wants then.

To cope with the cognitive dissonance of relying on the impossible to cope with the merely difficult, eternalists produce evasions, obfuscations, and denials. These boil down to an “if”: if we knew what God wanted, then that would be a simple, infallible guide to correct action. The fact that we don’t know gets passed over quickly, hoping you won’t notice.

This example is slightly contrived, mainly because divine command ethics has so many other defects that knowing God’s will gets barely mentioned in discussions of this ethical approach. I chose it because it’s so simple and so obviously unworkable.

Rationalism frequently advocates wrong-way reduction. Utilitarianism—a rationalist theory of ethics based on quantifying harms and benefits—is an example. Unfortunately, the utilitarian calculations are more difficult than effective moral reasoning, so this is a wrong-way reduction. The analogy with football match prediction is close: it’s usually easier to figure out a morally adequate course of action than to sum and compare utilities.

More generally, in other rationalist eternalisms, the problem of accessing the eternal ordering principle is more difficult than solving the practical problems the eternalism is supposed to address. In fact, in each case, it is outright impossible—and has to be.

  1. 1.This seems odd. Have I missed something?
  2. 2.Here I am using “reduction” as it is used in mathematics, not as it is used in the philosophy of science. The other sense of “reduction” involves explaining a material phenomenon in terms of an understanding about another, “lower level” one. Most scientific reductions are not mathematical ones.