The Language of Argument

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Sufficient Conditions and Necessary Conditions

by Mill’s methods, the procedures introduced here involve some fundamen-

tal simplifications; whereas Mill introduced five methods, we will introduce

only three primary rules.

The first two rules are the sufficient condition test (SCT) and the neces-

sary condition test (NCT). We will introduce these tests first at an abstract

level. One advantage of formulating these tests abstractly is so that they

can be applied to other kinds of sufficient and necessary conditions, for

example, those that arise in legal and moral reasoning. Once it is clear

how these tests work in general, we will apply them specifically to causal

reasoning.

SUffICIENT CONdITIONS ANd NECESSARy

CONdITIONS

To keep our discussion as general as possible, we will adopt the following

definitions of sufficient conditions and necessary conditions:

Feature F is a sufficient condition for feature G if and only if anything that

has feature F also has feature G.

Feature F is a necessary condition for feature G if and only if anything that

lacks feature F also lacks feature G.

These definitions are equivalent to those in the previous section, because, if

anything that lacks feature F also lacks feature G, then anything that has fea-

ture G must also have feature F; and if anything that has feature G must also

have feature F, then anything that lacks feature F also lacks feature G. It fol-

lows that feature F is a sufficient condition for feature G if and only if feature

G is a necessary condition for feature F.

When F is sufficient for G, the relation between these features can be dia-

grammed like this:

The inside circle represents the sufficient condition, because anything inside

that inside circle must also be inside the outside circle. The outside circle rep-

resents the necessary condition, for anything outside the outside circle must

also be outside the inside circle.

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