We can now formulate tests to determine when something meets our defini- tions of sufficient conditions and necessary conditions. It will simplify mat- ters if we first state these tests formally using letters. We will also begin with a simple 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:
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 ab- sent. 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.