Black-Box Fallacies

To deal with complexity, we need to analyze things into components, and hide information inside those components.

The black-box metaphor is common in science and engineering. A black box is a system with a well-defined and well-understood interface. The contents of the system are either hidden or can be ignored. We can think about the system only in terms of its “surface”: the inputs and outputs. Hence the term “black box”. In science and engineering, we call things “black boxes” if either (a) we don’t know how they work, or (b) we choose to ignore how they work, usually to simplify reasoning.

For example, a black-box optimization algorithm has two inputs: a space S and a black-box function U : S → R. The algorithm has no access to the internal details of U. It can only apply U to points in S. From this information, the algorithm tries to find a point in the space that has the highest value of U, within time constraints.

Any black-box optimization algorithm must sample some set of points in S, and return the point with the highest value of U. It could just sample points randomly across S. It could start at a random point, and then “move” from one point to another based on local sampling. Whether one algorithm works better than another depends on the nature of U, which is hidden. There is no correct algorithm for this problem definition.

See No free lunch in search and optimization.

The concept of a black box is useful for defining problems. However, a black box can also hide a problem or reduce it to triviality. Black-box optimization hides the interesting part of optimization, which is the relation between utility functions and optimization algorithms.

Black boxes are also used in argumentation, often fallaciously. There are four fallacies involving black boxes:

• Black-Box Foundation: A black box is used as a fake foundation for beliefs or values.
• Black-Box Solution: A black box is used as a fake solution to a problem.
• Black-Box Problem: A black box is used as a fake problem, to justify a proposed solution.
• Black-Box Reduction: A problem is reduced to a simpler problem by hiding part of it inside a black box. A solution to the simpler problem is then treated as a solution to the original problem.

Let’s consider each fallacy in more detail.

The Black-Box Foundation Fallacy

Consider the argument that the existence of the universe is explained by the existence of God, and is otherwise unexplained. The theist says: “You atheists can’t explain how or why the universe came into existence, but we can. The universe was created by God!”.

Positing the existence of God does not explain the existence of the universe. It just adds another entity, God, which creates new problems of explanation. How do we know that God exists? How did God come into existence? Why did God create the universe? Why did he create this universe?

The claim that God created the universe is not an explanation. It just puts the question “Why does the universe exist?” into a black box called “God”. We have no knowledge of God. He is unfathomable. He can do anything. The notion of God is unconstrained, and thus it has no explanatory power.

Religions use the concept of God as a false foundation. The question “Why does the universe exist?” is permissible, but “Why does God exist?” and “Why did God create the universe?” are taboo. This creates the illusion of a foundation. God is a black box that questions disappear into, and explanations and justifications pop out of.

In general, religions place big questions about life, the universe and everything into a black box, and then declare them to be “solved”, or at least off-limits to thought. This is a fallacy.

Black boxes also show up in scientific theories, where they are used to fill gaps and holes. Dark matter and dark energy are black boxes. Is this fallacious? No, because science does not place these concepts off-limits to inquiry. They are somewhat dubious constructs, but they are not used to terminate thought.

In a sense, all theoretical constructs are black boxes. At the bottom layer of science, we have mysterious things. Every theory has some black boxes. The regress of explanation must terminate at the unexplained.

For example, we could say that gravity is a black box in Newton’s theory of motion. Gravitation is a hidden mechanism that is only observable through its effects. But the concept of gravity is part of a theory that has explanatory power, and that theory is open to thought. For example, in the theory of general relativity, gravity is not a black box: it is explained as due to the curvature of space-time (a black box).

It is not a fallacy to posit black-box entities, such as gravity or space-time curvature, as part of a theory that has explanatory power. It is a fallacy to claim that something is explained simply by positing a black box.

The Black-Box Solution Fallacy

In this fallacy, a problem is claimed to be solved by a black box. The box conveniently protects the solution from criticism.

Technology is often invoked as a black-box solution. Many people dodge or deny real issues by hand-waving at hypothetical future technology. We could call this “the deus-ex-machina fallacy”. The deus ex machina of ancient Greek theater was a (plot and mechanical) device that lifted characters out of a predicament, implying that they had been saved by the gods.

In recent history, technological progress has postponed certain social/global problems. Since the industrial revolution, a steady increase in food production solved (for now) the problem of feeding the growing human population. Food production grew faster than the population, creating a period of relative abundance. This was mostly due to the use of nonrenewable resources, especially fossil fuels. Technology can solve the problem of feeding 4 billion people, 8 billion people, and maybe even 12 billion people, at least for some period of time. But this doesn’t solve the bigger problem of population growth. We can’t have infinite growth on a finite planet.

Rather than grappling with this issue, we have pretended that it isn’t a real problem, mainly by assuming that future technological advances will always bail us out. We have also assumed (fallaciously) that fertility will converge on replacement level. (See Fertility and Destiny for more on that topic.)

To have a stable and prosperous civilization, we need to regulate our population. This is a social problem, and it requires a social solution. No technology, existing or hypothetical, can solve it. But people wave their hands at imaginary technology as a black-box solution.

There are other black boxes that are used in a similar way. Rather than dealing with difficult social and philosophical problems, people hand-wave at progress, human ingenuity, the market or simply the future.

The Black-Box Problem Fallacy

A black-box problem is a hidden problem that is posited or presupposed to justify a proposed solution.

For example, every ideology posits a BIG PROBLEM that must be solved by (a) spreading the ideology and (b) transforming society. The BIG PROBLEM is usually vague and hidden.

Feminism’s BIG PROBLEM is “the patriarchy”, aka “systemic sexism”. Systemic sexism is conveniently hidden from direct observation, and it is defined in vague terms. Supposedly, it permeates society and culture. When challenged to provide evidence of systemic sexism, feminists usually point to sex differences in behavior and outcomes (but only if those differences seem to favor men). Of course, there is a better explanation for those differences: biology. To protect their BIG PROBLEM myth from falsification, feminists reject biological explanations as PART OF THE PROBLEM.

There is more than one fallacy involved here. The dogmatic exclusion of other explanations is fallacious. The cherry-picking of evidence to fit the theory is fallacious. But there is also a black-box fallacy involved. The theory of systemic sexism is a black box. Feminists might suggest some causal mechanisms, such as unconscious bias, but these are also vaguely defined and not directly observable.

As with God, the content of the black box is placed off-limits to thought. Questioning the existence of systemic sexism is considered to be sexism, and thus oppression. Taboo protects the belief from falsification.

Systemic racism is analogous. It is a pseudo-explanation for race differences in behavior and outcomes. It is conveniently hidden from direct observation, and it is defined in vague terms. Biological explanations of race differences are dogmatically rejected.

The pseudo-problems of systemic sexism and racism are used to justify anti-male and anti-white social policies. More importantly, they are used to justify virtue-signaling and promote wokism.

Conspiracy theories are similar to ideologies. Both posit the existence of a BIG PROBLEM that must be solved. The difference is the nature of the problem. An ideology claims that the BIG PROBLEM is due to the structure of society/culture. A conspiracy theory claims that the BIG PROBLEM is due to hidden agency: a group of people working behind the scenes.

Conspiracies can exist, and so can systemic problems. But we should be skeptical toward claims of BIG PROBLEMS that are vague or hidden.

The Black-Box Reduction Fallacy

A black-box reduction is the use of a black box to hide aspects of a problem, thereby reducing it to a simpler problem. This is not a fallacy in itself. But it becomes a fallacy if essential aspects of the problem are hidden, and a solution to the new problem is treated as a solution to the original problem.

We convert problems to math by hiding details. For example, if I am trying to calculate the amount of paint necessary to paint a room, I can reduce the room to the surface area of the walls. This hides an enormous amount of information about the room, but that information is not relevant to the paint-calculation problem. It might be a fallacy if I reduced the room’s shape to a simple cube, ignoring alcoves, closets, doors, etc. However, it could still be a useful approximation.

In some cases, the reduction goes too far. The “spherical cow” metaphor pokes fun at the tendency of mathematical models to be overly simplistic.

Since black-box reduction is necessary for abstract thought, it might not seem fallacious even when the hidden information is essential to the problem. Instead, it might seem clever, sophisticated, mathematical, scientific, etc.

The black-box reduction fallacy is common in science and engineering. It also occurs in philosophy, when people reduce philosophical problems to non-philosophical problems.

For example, some people “solve” Newcomb’s paradox by simply ignoring the details that make it paradoxical. They present the problem as a simple decision between two options with expected outcomes. Option A has a better expected outcome than option B, so you pick A. Simple, right? But this formulation hides the paradox inside the black box of expected-utility maximization. It transforms a philosophical paradox into a trivial math problem.

See How Not to Solve Newcomb’s Paradox.

When a problem has been reduced to math, we should carefully validate that the math captures the essence of the problem.

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Information-hiding is not a fallacy. It is a necessary part of thought. We always reduce the complexity of things. But it is a fallacy when the hidden information is relevant to the question at hand.

Black boxes are often used to do rhetorical tricks. Like the magician’s top hat, things mysteriously pop out of them and disappear into them. But this is just trickery.

Putting a problem into a black box doesn’t solve it. Hand-waving at a black box is not a solution to a problem. Hand-waving at a black box does not establish the existence of a problem. And reducing a complex problem to a simpler black-box version does not solve it.