Tips on Arguing: Necessary and Sufficient Conditions

Brandon T. Bisceglia

The phrase “necessary and sufficient conditions” is one of those pieces of jargon that is used across a wide range of fields. It pops up in papers on science, philosophy, mathematics, and even social issues. Knowing what it means can save you a lot of undue confusion.

Although the terms “necessary and sufficient” are often used together, they are really two separate things: necessary conditions and sufficient conditions. Each has a distinct function. Necessary conditions are required for an effect to take place. However, they do not guarantee that the effect will occur. In logic, they can be phrased as “without x, there can be no y.”

For example, a temperature of 32 degrees Fahrenheit or below is a necessary condition for snow, because anything warmer will result in rain. But a cold day doesn’t always bring snow. It could just as easily be cold and sunny.

Sufficient conditions, on the other hand, do guarantee that an effect will occur. They can be phrased as “if x, then y.” With a sufficient condition, though, the same effect can also occur for some other reason. If, for instance, the president signs a bill given to him by Congress (a sufficient condition), it automatically becomes a law (the effect). However, it doesn’t have to happen that way. The president could veto the bill, and Congress could vote to override his veto. In that case, the bill still becomes a law, even though it wasn’t signed.

The difference between the two types of conditions may seem subtle, but the distinction has profound implications. In the situation of the bill, the president’s signature is not a necessary condition, because it can be overturned by another branch of government. Our entire system of “checks and balances” depends on these careful divisions of necessary conditions and sufficient conditions.

If you are trying to convince someone of your position in an argument, you usually want your conditions to be both necessary and sufficient. It is the strongest indication that two events are causally linked, because this kind of condition always leads to the effect, and the effect cannot happen without it.

The application of heat is both a necessary and a sufficient condition for cooking. You can’t cook without heat, and heating food guarantees that it will cook. Cooking is, in fact, defined as what happens to food when heat is applied to it. They always occur together.

If you take a little time to learn some common academic expressions, you’ll be more prepared when you inevitably encounter the seemingly impenetrable language of many documents.