The Language of Argument

2 1 8

C H A P T E R 1 0 ■ C a u s a l R e a s o n i n g

These diagrams, along with the preceding definitions, should make it

clear that something can be a sufficient condition for a feature without being

a necessary condition for that feature, and vice versa. For example, being the

element mercury is a sufficient condition for being a metal, but it is not a nec-

essary condition for being a metal, since there are other metals. Similarly, be-

ing a metal is a necessary condition for being mercury, but it is not a sufficient

condition for being mercury. Of course, some necessary conditions are also

sufficient conditions. Being mercury is both necessary and sufficient for be-

ing a metallic element that is liquid at twenty degrees Centigrade. Nonethe-

less, many necessary conditions are not sufficient conditions, and vice versa,

so we need to be careful not to confuse the two kinds of conditions.

This distinction becomes complicated when conditions get complex. Our

definitions and tests hold for all features, whether positive or negative (such

as not having hair) and whether simple or conjunctive (such as having both

a beard and a mustache) or disjunctive (such as having either a beard or

a mustache). Thus, not having any hair (anywhere) on your head is a suf-

ficient condition of not having a beard, so not having a beard is a necessary

condition of not having any hair on your head. But not having any hair on

your head is not necessary for not having a beard, because you can have

some hair on the top of your head without having a beard. Negation can cre-

ate confusion, so we need to think carefully about what is being claimed to

be necessary or sufficient for what.

Even in simple cases without negation, conjunction, or disjunction, there

is a widespread tendency to confuse necessary conditions with sufficient

conditions. It is important to keep these concepts straight, for, as we will see,

the tests concerning them are fundamentally different.

Which of the following claims are true? Which are false?

1. Being a car is a sufficient condition for being a vehicle.


2. Being a car is a necessary condition for being a vehicle.


3. Being a vehicle is a sufficient condition for being a car.


4. Being a vehicle is a necessary condition for being a car.


5. Being an integer is a sufficient condition for being an even number.


6. Being an integer is a necessary condition for being an even number.


7. Being an integer is a sufficient condition for being either an even number
   or an odd number.


8. Being an integer is a necessary condition for being either an even number
   or an odd number.


9. Not being an integer is a sufficient condition for not being an odd
   number.

Exercise I

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