The Language of Argument

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

The Sufficient Condition Test

We can now formulate tests to determine when something meets our defini-

tions of sufficient conditions and necessary conditions. It will simplify matters

if we first state these tests formally using letters. We will also begin with a sim-

ple case where we consider only four candidates—A, B, C, and D—for sufficient

conditions for a target feature, G. A will indicate that the feature is present; ~A

will indicate that this feature is absent. Using these conventions, suppose that

we are trying to decide whether any of the four features—A, B, C, or D—could

be a sufficient condition for G. To this end, we collect data of the following kind:

Table 1

Case 1: A B C D G

Case 2: ~A B C ~D ~G

Case 3: A ~B ~C ~D ~G

We know by definition that, for something to be a sufficient condition of

something else, when the former is present, the latter must be present as

well. Thus, to test whether a candidate really is a sufficient condition of G,

we only have to examine cases in which the target feature, G, is absent, and

then check to see whether any of the candidate features are present. The suf-

ficient condition test (SCT) can be stated as follows:

SCT: Any candidate that is present when G is absent is eliminated as a

possible sufficient condition of G.

The test applies to Table 1 as follows: Case 1 need not be examined because

G is present, so there can be no violation of SCT in Case 1. Case 2 eliminates

two of the candidates, B and C, for both are present in a situation in which

G is absent. Finally, Case 3 eliminates A for the same reason. We are thus left

with D as our only remaining candidate for a sufficient condition for G.

Now let’s consider feature D. Having survived the application of the SCT,

does it follow that D is a sufficient condition for G? No! On the basis of what

we have been told so far, it remains entirely possible that the discovery of a

further case will reveal an instance where D is present and G absent, thus

showing that D is also not a sufficient condition for G.

Case 4: ~A B C D ~G

In this way, it is always possible for new cases to refute any inference from a

limited group of cases to the conclusion that a certain candidate is a sufficient

condition. In contrast, no further case can change the fact that A, B, and C

are not sufficient conditions, because they fail the SCT.

This observation shows that, when we apply the SCT to rule out a can-

didate as a sufficient condition, our argument is deductive. We simply find a

counterexample to the universal claim that a certain feature is sufficient. (See

Chapter 17 on counterexamples.) However, when a candidate is not ruled out

and we draw the positive conclusion that that candidate is a sufficient con-

dition, then our argument is inductive. Inductive inferences, however well

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