I’ve spent a lot of time on this blog debunking economists’ claims about productivity. Usually, I come at the problem from a fairly technical angle, meaning I break down the contradictions involved in economists’ methods. Today, I want to try a more philosophical approach. I’m going to talk about dualism — the idea that something can be two things at once.

Dualism in science

Science is filled with dualist statements — claims that a substance is two things at once. Of course, scientists don’t use this terminology. They call their dualist statements ‘mathematical equations’. Here’s a famous one from Albert Einstein:

In this equation, Einstein claims that matter and energy are two sides of the same coin. In other words, there is some mysterious force that can convert matter into energy and vice versa.

Because mass-energy equivalence sounds pretty wild, Einstein’s equation gets a lot of attention. But science is rife with conceptually identical statements. For example, Newton claimed that there is something called a ‘force’ that can be converted into ‘acceleration’:

When you reflect on these equations, you realize that they are making rather profound metaphysical claims about the world — much like claiming that the Father, the Son and the Holy Ghost are the same thing. So were Einstein and Newton just doing theology?

No. They were doing science.

Unfortunately, most introductory science textbooks don’t explain the distinction. Instead, they take a rather theological approach to pedagogy. Textbooks often present formulae as received wisdom, and then tell students to explore the consequences. Similarly, many science popularizers know that the public is hungry for metaphysics, and so they discuss the ‘profound’ implications of various theories. But what popularizers rarely do is explain why scientists trust the formulas they use.

Part of the problem comes down to mathematical notation itself. On its own, a mathematical equation is not science. It is a definition. For example, I can define a quantity F that is the product of mass times acceleration:

Until I test this equivalence, however, I haven’t done science. To do science, we must treat our mathematical definition as a mathematical question. Unfortunately, there is no accepted notation for this way of thinking. But perhaps it might look like this:

To test this equation/question, we devise ways of independently measuring both sides of it. Now, by ‘independently’, I don’t mean measurement that is ‘theory free’, since that’s impossible. All measurement depends on preconceptions about the world. (To measure the length of different objects, for example, you assume that the length of your ruler remains constant.) In science, ‘independent’ measurement simply means we use methods that don’t depend on the theory we are testing.

So if we are testing Newton’s equation, we can’t measure force in terms of acceleration. Instead, an independent measurement might be something like this:

1. measure force with a spring gauge,
2. measure mass with a balance scale
3. measure acceleration using the change in velocity over time.

These measurements all depend on preconceptions about the world. But they do not logically imply Newton’s equation. And so if we find that force is the product of mass times acceleration, we’ve shown that Newton’s equation is not merely a human definition. It is a truth statement about the natural world.

We can do the same thing with Einstein’s equation — albeit using tools that are more complicated. For example, in 2005, Simon Rainville and colleagues used atomic-mass differences to test the equivalence of matter and energy. They found that Einstein’s equation was accurate to seven decimal places.¹

Again, it is the experimental confirmation that renders an equation meaningful. Without the observational component, we are left with nothing but a human definition. And that brings us to theology.

Dualism in theology

If science is the combination of logical definitions with empirical observations, theology is science without the observation. It is a web of human definitions, and nothing more.

As an example, take the Catholic concept of the Trinity, which is notorious for its bizarre logic. According to church dogma, God exists simultaneously as ‘The Father’, ‘The Son’ and ‘The Holy Spirit’. But while these three entities are all God, they are somehow distinct from each other. Thus the Holy Spirit is God. And the Son is God. But the Holy Spirit is not the Son. Confused? That’s because the Trinity is logically incoherent. But don’t worry, the church says it’s be true.

The Trinity is a prime example of theological dualism. We have a set of definitions, and nothing else. Sure, you can argue about the definitions. But there’s no objective way to settle the score. Quarrels over the Trinity are the medieval equivalent of debates in modern fandom. It’s like when Star Wars fans argue about whether Anakin Skywalker ‘died’ when he became Darth Vader. The correct answer is that there is no correct answer. The ‘truth’ is however you define it.

Although it makes for abysmal science, the theological stance is a great way to sound authoritative while you spout bullshit. The self-styled libertarian ‘philosopher’ Ayn Rand was a master of this technique. Here she is laying out her philosophy of objectivism:

The formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of [this] statement. I am here to complete it: Existence is Identity, Consciousness is Identification.

Rand’s writing is a tour-de-force in theological nonsense. Start with a tautology (A = A). Follow it up with some weighty definitions (existence = identity). Claim you have a ‘rule for all knowledge’. Marvelous bullshit.

Dualism in economics

Perhaps the best definition of economics is that it is ‘secular theology’. Economics adopts the veneer of science, but, like theology, is based on untestable definitions.

In economics, the most pervasive dualism is the equivalence between income and productivity:

Unlike Ayn Rand’s poetic bullshit, the dualism between income and productivity is meant to be quantitative and literal. In neoclassical economics, a person’s income indicates their contribution to society.

Like all good theology, the theory starts with a definition. If Alice has some output Q that is sold at some price P, her gross income is defined as:

For example, if Alice grows 10 apples and sells them for $1 each, her gross income would be $10:

If Alice grew half as many apples, her income would be cut in half:

From this angle, it seems like the duality between income and productivity is sound. The problem is that it is actually unnecessary. If we can count what Alice produces (apples), we can measure her productivity directly. So we don’t need income.

Worse still, if the price of apples changes, not only is the income-productivity duality unnecessary, it is also false. For example, if Alice grows the same number of apples each year, the reality is that her productivity is constant. And yet if the price of apples changes, we infer from her income that her productivity has changed. That’s just wrong.

So right off the bat, we have a logical problem with the productivity-income duality. Either it is correct but unnecessary, or it is both unnecessary and incorrect. Either way, the duality is unsound.

Of course, there is nothing wrong with having a hypothesis that is logically unsound. It just means that when you notice the problem, you should abandon the hypothesis. But that’s not what happened in economics. Instead, the income-productivity duality became the basis for the entire system of national accounts.

Along the way, economists invented various fairy tales to justify their theology. For example, in the late 19th century, the economist John Bates Clark tried to ‘prove’ that in a competitive market, each agent earned what they produced. To his credit, Clark realized that the only way this proof worked is if everyone produced the same commodity. The problem is that this assumption renders Clark’s hypothesis moot. If everyone produces the same commodity, we can measure their productivity directly, meaning we don’t need income.

It gets worse. In the real world, where people produce many different commodities, we cannot measure productivity directly. (We cannot compare apples and oranges.) And so economists infer productivity by measuring income. But in this situation, Clark’s proof breaks down.

To address this logical problem, economists have invented more theology. Prices, they claim, are themselves a duality. Prices are both a monetary quantity and a measure of utility:

So yes, prices may change, but that’s because the underlying utility of a commodity has changed. Or maybe it hasn’t. The problem is that economists never measure utility. They infer it from prices. And so the whole operation becomes circular — a theological definition, and nothing more. Joan Robinson nicely summarized the situation:

Utility is a metaphysical concept of impregnable circularity; utility is the quality in commodities that makes individuals want to buy them, and the fact that individuals want to buy commodities shows that they have utility.

In other words, economists propose a definition, and these use this definition to justify itself. That’s theology, folks.

The dualism smell test

Since both science and theology appeal to dualism, it can be difficult to distinguish the two forms of thought. With that in mind, here’s a dualism smell test.

Dualism always starts with a definition. Force is mass times acceleration. The Son is God. Income is productivity. To distinguish between science and theology, you should look at what follows the definition. In the case of science, the definition should be followed by an empirical test. Thus, scientists didn’t just take Newton at his word. They tested his laws of motion and found them to be correct (at non-relativistic speeds).

Now, the wonder of mathematics is that by manipulating algebraic definitions, you can derive predictions that follow from the starting assumptions. It’s important to test these predictions. But if they hold, that doesn’t mean that the assumptions are correct. That’s why scientists always test both the predictions of a theory and its assumptions. The classic example is Newton’s theory of gravity. When combined with his theory of dynamics, you get a rich set of predictions — enough to send people to the moon.

These correct predictions, however, didn’t stop scientists from testing the core assumption — the claim that inertial mass is equivalent to gravitational mass (a dualist statement). Indeed, this ‘weak equivalence principle’ has been tested continuously for more than four centuries. No one has found a violation.

When people like Milton Friedman spout theological nonsense, they’ll try to convince you that assumptions don’t matter. Friedman notoriously claimed that if a theory gives ‘correct predictions’, that’s good enough. Don’t believe him. Assumptions are the most basic part of science. If they are wrong, the whole theory is garbage.

Speaking of Uncle Milton, that brings me to theological dualism. When you do theology, the goal is to use a definition to (seemingly) prove your point and to avoid the fact that you are not testing your definition. One of the more amusing applications of this technique is in supposed logical ‘proofs’ of God’s existence. My favorite proof comes from Rene Descartes and goes something like this:

1. God is perfect.
2. It is more perfect to exist than to not exist.
3. Therefore, God exists.

Do you see what Descartes did here? He used two definitions to make his point. He defined God as perfect. He defined existence as more perfect than non-existence. Presto, God exists.

Sorry, Rene, that’s not how it works. You’ve got to test your assumptions.

Is God ‘perfect’? Hard to say, since God is unobservable and ‘perfection’ is a subjective aesthetic. And is it ‘more perfect’ to exist than to not exist? Again, there’s not much to test here since we’re talking about aesthetics. But mathematicians might disagree. Only imperfect circles exist (in the real world). Yet mathematicians can imagine perfect ones. So maybe it is ‘more perfect’ to not exist.

In short, dualism fails the smell test if it is not followed by an empirical test. If there is no such test, what you have is not science … it is theological rot — a web of interlocking definitions that tell us nothing about the natural world.²

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[Cover image: Wikimedia Commons]

Want to know more about how economists equate income with productivity? Here are five pieces on the topic:

1. No, Productivity Does Not Explain Income
2. Productivity Does Not Explain Wages
3. Productivity and Income … Again
4. Debunking the ‘Productivity-Pay Gap’
5. Real GDP: The Flawed Metric at the Heart of Macroeconomics

Notes