At exactly what point has a man grown a beard? Is it when the stubble reaches 2 millimeters long, or 7 millimeters? At what precise minimum length does one call it a beard?

This is a tricky question. Hair grows continuously, so there are no major milestones between having no beard and having a beard. Yet our language forces a binary categorization: beard or no beard.

There is no justification for setting an arbitrary measurement. If someone says 5 millimeters of facial hair is a beard and someone else says 4.9 millimeters, no evidence could possibly resolve the controversy.

Does one tenth of a millimeter have some magical significance?

Most people probably answer no to that question, and step into a trap. If each tenth of a millimeter is inconsequential, isn’t a whole millimeter (ten tenths) also inconsequential? Why not any number of millimeters? Taken to extremes, having no beard becomes indistinguishable from having a beard.

This is the Continuum Fallacy. For situations when there is no definable point between two extremes (e.g. beard or no beard), the person committing the fallacy claims there is no difference between the two extremes.

Examples:

• When does “dark gray” become “light gray”?
• How many wrongs change someone from being a “good person” to an “evil person”?
• How many grains of sand can I add to a bucket before it becomes “heavy”?

Our most contentious political issues are about attempting to fit binary categories like these onto continua. Laws define one thing as “legal” and something else as “illegal.”

Suppose beards are outlawed. A man is arrested. The beard police measure his stubble at 3.65 millimeters. Did he break the law?

This example sounds ridiculous until you replace “beards” with “guns,” or “abortions” and replace the measurement with “magazine capacity” or “trimester”. Let’s explore two of our society’s major political issues in detail.

Guns

People declare themselves as either for or against gun control, as if the debate were between total abolition versus zero weapons regulation. Actually, the term “gun,” or “arms” as the Second Amendment to the U.S. Constitution describes them, must be applied to some portion of a continuum of technologies developed over the centuries.

Flintlock firearms, which existed when the Constitution was written, were improved by the invention of the percussion cap in the early 1800’s, and then the integrated cartridge a few decades later. The integrated cartridge, in turn, enabled the invention of the Gatling Gun during the American Civil War – the first semi-automatic firearm.

Each of these inventions increased the rate of fire. A flintlock musketeer might fire four bullets per minute, whereas various Gatling Guns could fire between 200 and 1,000 bullets per minute. Later innovations made firearms smaller and more effective. For example, the Soviet AK-47 (developed in 1947) brought the firepower of a Gatling gun to a cheap, handheld format.

Which of these technological innovations exceeds the wording “bear arms?”

If you answered “none of the above,” how do you feel about private ownership of vehicle-mounted anti-aircraft guns, heavy artillery, explosive rounds, or depleted-uranium ammunition? How would you feel about unregulated sales of the Mk 19 belt-fed automatic grenade launcher, capable of killing hundreds of people within seconds? Each of these is a point along a continuum of firearm technology.

The gun control debate is a question about where on a technological continuum we draw the line. Which of the thousands of technological advances do we place in the “legal” category, and which in the “illegal” category?

Abortion

The abortion debate is interesting because it’s not actually a debate about when life starts; it’s a debate about when human rights start.

Sperm and eggs are living cells, as are fertilized eggs, as are the cells of a zygote, blastocyst, fetus, and so on. At no point in the process does a living cell spontaneously appear. Rather, all cells alive today came from the division or combination of earlier cells: an unbroken chain of living cells going back billions of years.

There’s a continuum between living things that almost everyone agrees have no moral value: sperm and eggs, to living things that almost everyone agrees have enormous moral value: delivered human babies.

The developmental process offers few, if any, major milestones. Fertilization is cited by abortion foes as the instant when previously worthless gametes become a person.

However, fertilization has many steps, such as the sperm making physical contact with the egg’s cell wall, the sperm’s penetration of the egg’s cell wall, the ejection of DNA from the sperm, the migration of the DNA to the egg’s nucleus, the combination of the two DNA sets, and the first protein production from this new DNA combination.

Which step differentiates person from tissue? Should we impute such enormous moral worth to tiny molecular events? If not, how does something significant happen during the entire process, if not in any part of the process? No wonder it’s a dilemma!

Perils of Continua

Courts need distinct, measurable criteria to determine who is guilty or innocent.

This need for binary determination drives us right into the continuum fallacy. Police must subjectively enforce laws against reckless driving and disturbing the peace. Meanwhile, the wealthy can escape justice with help from lawyers skilled at exploiting the contradictions that arise when applying binary laws to continua.

Should we see hot-button issues, and morality itself, as shades of gray, rather than binaries? If so, we’ll need better ways to select who goes to prison or where to draw the line on topics like censorship, privacy, or animal rights.

Our culture currently lacks a capacity to define a continuum of moral or practical rules that could correspond to the spectrum of reality. With our current linguistic and intellectual toolkit, we cannot define “beard,” much less resolve our hot-button controversies.

At least we can cool our passions with the knowledge that our deepest disagreements are really about points on a line.