Propositions that express a sufficient condition

4.2.2 Propositions that express a necessary condition

Propositions that express that concept A is a necessary condition for concept B can be formulated as: B exists only if A is present. Alternative ways to express that A is necessary for B are: ■ “B does not exist without A”; ■ “If there is B then there is A”; ■ “A is needed for B”; ■ “There must be A to have B”; ■ “Without A there cannot be B”; ■ “If there is no A there cannot be B”. In our example this would mean: “In a successful innovation project there is management commitment” or “Management commitment is required for success”. Again, there are four possible combinations of A and B. If A is a necessary condition for B for all instances of the domain, then an instance can only occur in three of the four cells. There can be no instances of the object of study in the cell “A absentB present”. A proposition can also express that A is both sufficient for B and necessary for B. Then both corresponding cells are empty. Such a Present Absent Concept B Absent Present Concept A Figure 4.1 Scatter plot of instances indicating a sufficient condition proposition will not be discussed further in this book, as the propos- ition can be treated as a combination of two single propositions. If a very small number of instances is located in the, presumably, empty cell in comparison to the vast majority that is located in the other ones, we argue that this situation can be considered as a pragmatic deterministic sufficient or necessary condition see Box 8 in 4.3, below.

4.2.3 Propositions that express a deterministic relation

Propositions that express a deterministic relation between concept A and concept B can be formulated as: If A is higher, then B is higher. This type of relation is depicted in Figure 4.3 as a continuous increas- ing relation between A and B: B increases with A. In our example this would mean: “if there is more top management commitment, then the innovation project will be more successful”. The deterministic relation between A and B could also be a continuous decreasing relation, depending on the proposition. A deterministic relation between A and B is not always a continuous increasing or decreasing relation. It can also be a relation that is partly increasing and partly decreasing. For a deterministic relation it only matters that there is one specific value of B for one specific value of A. Present Concept B Absent Absent Present Concept A Figure 4.2 Scatter plot of instances indicating a necessary condition