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Necessary and sufficient conditions
The concepts of necessary and sufficient conditions help us
understand and explain the different kinds of connections
between concepts, and how different states of affairs are related
to each other.
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 :
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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 :
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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 :
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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.
Sufficient conditions
To say that X is a sufficient condition for Y is to say that the presence of X
guarantees the presence of Y. In other words, it is impossible to have X without Y. If X
is present, then Y must also be present. Again, some examples :
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Being a square is sufficient for having four sides.
Being divisible by 4 is sufficient for being an even number.
To show that X is not sufficient for Y, we come up with cases where X is present but Y
is not. Examples :
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Loving someone is not sufficient for being loved. A person who loves someone
might not be loved by anyone perhaps because she is a very nasty person.
Loyalty is not sufficient for honesty because one might have to lie in order to
protect the person one is loyal to.
Additional remarks about sufficient conditions :
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Expressions such as "If X then Y", or "X is enough for Y", can also be understood
as saying that X is a sufficient condition for Y.
Some state of affairs can have more than one sufficient condition. Being blue is
sufficient for being colored, but of course being green, being red are also
sufficient for being coloured.
Four possibilities
Given two conditions X and Y, there are four ways in which they might be related to
each other:
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X is necessary but not sufficient for Y.
X is sufficient but not necessary for Y.
X is both necessary and sufficient for Y. (or "jointly necessary and sufficient")
X is neither necessary nor sufficient for Y.
This classification is very useful in when we want to clarify how two concepts are related
to each other. Here are some examples :
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Having four sides is necessary but not sufficient for being a square (since a
rectangle has four sides but it is not a square).
Having a son is sufficient but not necessary for being a parent (a parent can have
only one daughter).
Being an unmarried man is both necessary and sufficient for being a bachelor.
Being a tall person is neither necessary nor sufficient for being a successful
person.
1. Rewrite these claims in terms of necessary and / or sufficient conditions :
(a) You must pay if you want to enter.
(b) A cloud chamber is needed to observe subatomic particles.
(c) If something is an electron it is a charged particle.
.
(d) I will pay for lunch if and only if you pay for dinner.
2. Suppose Tom is a tall but unsuccessful person. Does it show that (a) being tall is
not sufficient for being successful, or (b) being tall is not necessary for being
successful?
3. Discuss how these conditions are related to each other and explain your answers
(a) not being poor, being rich
(b) being an even number, being divisible by 2
(c) being an intelligent student, being the most intelligent student
(d) having ten dollars, having more than five dollars
(e) the presence of the rule of law, being a just society
(f) giving money to another person in exchange for a favor, corruption
(g) taking place on a weekday, not being held on Saturday
Different types of necessity and sufficiency
Corresponding to these different notions of possibility we have different concepts of
necessary and sufficient conditions. For example :
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Having four sides is logically necessary for being a square.
Being a father is logically sufficient for being a parent.
The presence of oxygen is causally necessary for the proper functioning of the
brain.
Passing current through a resistor is causally sufficient for the generation of heat.
Being an adult of over 18 years old is legally sufficient for having the right to vote.
The presence of a witness is legally necessary for a valid marriage.
Note that there might be other types of necessity and possibility as well. For example, a
father might advice his son that he must treat his sister well. The sense of "must" here is
not legal necessity, as the law does not require us to treat our siblings well. Rather, the
sense of necessity might have to do with moral conduct. On the other hand, if the son is
told that he must treat his boss well, what is meant might be that being nice to one's
boss is required not so much by morality but by rules of prudence.
http://philosophy.hku.hk/think/meaning/nsc.php