The phrase “necessary and sufficient
conditions” is one of those pieces of jargon that are 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.
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