necessary

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Slide 1

§1. Necessary conditions

To say that X is a necessary condition for Y is to say that it is impossible to have Y without X. In other words, the absence of X guarantees the absence of Y. A necessary condition is sometimes also called "an essential condition". Some examples :

Having four sides is necessary for being a square.
Being brave is a necessary condition for being a good soldier.
Not being divisible by four is essential for being a prime number.

To show that X is not a necessary condition for Y, we simply find a situation where Y is present but X is not. Examples :

Being rich is not necessary for being happy, since a poor person can be happy too.
Being Chinese is not necessary for being a Hong Kong permanent resident, since a non-Chinese can becoming a permanent resident if he or she has lived in Hong Kong for seven years.

Additional remarks about necessary conditions :

We invoke the notion of a necessary condition very often in our daily life, even though we might be using different terms. For example, when we say things like "life requires oxygen", this is equivalent to saying that the presence of oxygen is a necessary condition for the existence of life.
A certain state of affairs might have more than one necessary condition. For example, to be a good concert pianist, having good finger techniques is a necessary condition. But this is not enough. Another necessary condition is being good at interpreting piano pieces.