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 concept sometimes lead to unnecessary scientific debates. For example, the proponent of a causal hypothesis may not expect it to apply universally, whereas a scientist who finds exceptions to the hypothesis may announce that it is disproved.

The logician’s concept of causality avoids the ambiguity of the scientist’s concept. Logicians distinguish three very different types of causality: sufficient condition, necessary condition, and a condition that is both necessary and sufficient.

If several factors are required for a given effect, then each is a necessary condition. For the example of Archimedes’ death, both successful Roman invasion and his refusal to abandon his math problem were necessary conditions, or necessary causal factors. Many necessary conditions are so obvious that they are assumed implicitly. If only one factor is required for a given effect, then that factor is a sufficient condition. If only one factor is capable of producing a given effect, then that factor is a necessary and sufficient condition. Rarely is nature simple enough for a single necessary and sufficient cause; one example is that a force is a necessary and sufficient condition for acceleration of a mass.

Hurley [1985] succinctly describes the type of causality with which the scientist often deals: “Whenever an event occurs, at least one sufficient condition is present and all the necessary conditions are present. The conjunction of the necessary conditions is the sufficient condition that actually produces the event.” For the most satisfactory causal explanation of a phenomenon, we usually seek to identify the necessary and sufficient conditions, not a single necessary and sufficient condition. Often the researcher’s task is to test a hypothesis that N attributes are needed (i.e., both necessary and sufficient) to cause an effect. The scientist then needs to design an experiment that demonstrates both the presence of the effect when the N attributes are present, and the absence of the effect whenever any of these attributes is removed.

Sometimes we cannot test a hypothesis of causality with such a straightforward approach, but the test is nevertheless possible using a logically equivalent statement of the problem. The following statements are logically equivalent [Hurley, 1985], regardless of whether A is the cause and B is the effect or vice versa (with -A meaning ‘not-A’ and ≡ meaning ‘is equivalent to’): A is a necessary condition for B ≡ B is a sufficient condition for A ≡ If B, then A (i.e., B, ∴A) ≡ If A is absent, then B is absent (i.e., -A, ∴-B) ≡ Absence of A is a sufficient condition for the absence of B ≡ Absence of B is a necessary condition for absence of A.

Mill’s Canons: Five Inductive Methods
John Stuart Mill [1930], in his influential book System of Logic, systematized inductive techniques. The results, known as ‘Mill's Canons’, are five methods for examining variables in order to identify causal relationships. These techniques are extremely valuable and they are routinely used in modern scientific experiments. They are not, however, magic bullets that invariably hit the target.