Search for where arguments begin.

People who disagree with each other can collaborate to understand the real source of their conflict by determining their “lowest common assumption” — or if none exists, their utter lack of common ground.

Mathematical analogy.  In mathematics, the “lowest common denominator” of two fractions is the lowest common multiple of the denominators of each of the two fractions. For example, if we want to add 1/4 and 1/6, we have to find the lowest common multiple of 4 and 6. The first several multiples of 4 are 4, 8, 12, 16, 20, and 24; the first several multiples of 6 are 6, 12, 18, 24, and 30. The lowest multiple shared by 4 and 6 is 12, so twelve is the least common denominator of 1/4 and 1/6. To add them together, we convert 1/4 to 3/12, convert 1/6 to 2/12, and then add 3/12 and 2/12, to give us the sum of 5/12. By converting the two original fractions to twelfths, they can interact with each other (for addition and subtraction) on common ground.

Finding the lowest common assumption. When two people disagree, they often talk past each other, and their debate sometimes devolves into overgeneralization, hyperbole, and even ad hominem attack. Moreover, these debates typically end up focusing on points and arguments that flow from certain premises, rather than the underlying assumptions themselves. By drilling down through layers of reasoning and assumptions, debaters are likely to find either (a) an underlying assumption they share, or (b) a fundamental assumption that keeps them apart. In the first case, they may be able to build upon a shared assumption to reach a compromise. In the second case, they may find it more useful to debate their fundamental disagreements rather than debating other points that logically follow from their incompatible starting points; or perhaps they could explore how to work around their conflicting premises.

So when you find yourself in an unproductive debate, try to unpack your own assumptions and those of your opponent, and try to find your lowest common assumption. Then try to build from there.

For example, Republicans and Democrats in Congress may disagree about the role of the federal government, spending priorities, and deficit spending. They could debate these points endlessly without focusing on where their disagreements originate. But if they drill down to their underlying assumptions during a debate on the annual budget, they may discover some smaller, shared assumptions. For example, they might agree that federal spending is appropriate for long-term investments that will eventually produce greater economic growth. From that starting point, both sides could support certain kinds of infrastructure spending that meet this test.

Sometimes debates reveal no lowest common assumption. For example, in the abortion debate, some pro-life advocates believe that life begins at the moment of conception and that every abortion is thus a form of murder, even if the mother is a victim of rape or the fetus is known to have a life-threatening deformity. On the other side, some pro-choice advocates believe that human life doesn’t begin until viability, so the government has no legitimate role regulating a woman’s decision to end a pregnancy in the early months. People on opposite sides of this debate have no lowest common assumption about the status of a one-day-old embryo. As a result, it’s likely pointless for them to debate when viability occurs, because the timing of viability is irrelevant here to someone who believes that human life fully begins at conception. The debaters might therefore find it more useful to discuss what constitutes “murder” and “human life” — and the sources of those ideas — rather than viability. Or perhaps they should instead search for common ground on how best to prevent unwarranted pregnancies in the first place.