# Necessary vs. Sufficient: Under the Right Conditions

#### The Problem

In Jermaine’s US Government class, he learns about the controversy surrounding former President Barack Obama’s place of birth. Specifically, his teacher explains the unvalidated allegations that Obama was not born in the United States, and therefore would not have been qualified to be president. “I was born in the United States,” Jermaine reasons, “so I could run for president right now if I wanted to!” Unfortunately for Jermaine, this is not true. What is the flaw in his logic?

Jermaine mistook a necessary condition of the presidency for a sufficient one. Yes, it is necessary for the President of the United States to be a natural born citizen of the country, but this isn’t the only qualification. Another qualification is that a presidential candidate must be at least 35 years old. Alas, Jermaine is still in high school, so his birthplace is not sufficient alone to run for president.

#### Definition: Necessary vs. Sufficient

The logical concepts of necessity and sufficiency apply to conditional relationships between two statements. Conditional statements often take the form of “If ___, then ___”, but the term applies to any scenario in which there is a relationship between two statements. A necessary condition is one that is needed for the other half of the conditional statement to be true. A sufficient condition is one that is enough to guarantee the truth of the other part of the statement, though there may be other conditions that could also affirm the statement to be true.

#### How It Works

Necessity and sufficiency are perhaps best understood by illustrating some examples.

First, let’s look at a necessary condition. A primary qualification for jury duty in Massachusetts is being at least eighteen years old. Therefore, if someone is serving on a jury in a Massachusetts court, you know that they are at least eighteen years old since this age minimum is a necessary condition for serving jury duty in that state. Being eighteen is not sufficient alone to serve on a jury, though, since jurors must also be free of conflicting interests in the attendant case.

Now let’s consider a sufficient condition. Kicking a soccer ball into the net is sufficient for scoring a goal since a goal is defined by the ball crossing the goal line and going into the net via a legal touch. By that definition, the necessary condition for scoring a goal is that the ball crosses the goal line. Kicking the ball into the net is not necessary for scoring a goal, though, because you could also use your head to score.

Some conditions are both necessary and sufficient. For example, pressing a key on a piano is necessary and sufficient for making the intended sound of that instrument. It is sufficient for making the sound because pressing a key is enough to produce the corresponding note. It is also necessary because the piano will not produce that sound unless the key is pressed.

It is also possible for something to be neither necessary nor sufficient. Typing on your smartphone’s keypad is neither necessary nor sufficient for sending a text message to your friend. It is insufficient because you can’t just press random letters - your message will make no sense! You’d have to press them in a deliberate order to form words and then a coherent message. But typing is not a necessary step either. You could use the phone’s voice-to-text feature to transcribe your spoken word into text.

#### Applying It

An understanding of necessity and sufficiency helps us reason through the relationships between and within various statements. It also helps us define difficult concepts and establish conditions for certain positions, like the qualifications for a US president. Necessity and sufficiency are prevalent in the legal system, too, as they help determine the conditions that render someone guilty or innocent of a crime. For most crimes, a person is guilty if it is proven that they had actus reus, the physical action of a crime, and mens rea, a guilty intention. These are the necessary conditions for establishing guilt. Necessity and sufficiency are prevalent in mathematics, as well. For example, a whole number ending in the digit 2 is sufficient for the number to be even. It is not necessary, though, because an even number can also end in 0, 4, 6, or 8. In sum, these concepts play important roles wherever reason is used, so they influence nearly every aspect of everyday life.

## Think Further

1. Why is it important to know the difference between necessary and sufficient? In what fields might it be particularly important?
2. How can you improve your ability to recognize necessary and sufficient conditions?
3. Why do you think necessary and sufficient conditions are confused so often?