An analysis of the presuppositions of quantitative research

Necessary and sufficient conditions, determinism and indeterminism

The philosopher David Hume presented his insights on causation by way of the famous example of billiard balls (Hume, 1969: §VII). Since deductive logic cannot explain why one ball is set in motion after being hit by another, Hume turns to a more empirical kind of investigation. On the basis of his observations he concludes that in situations where we believe that there is a causal relation, there is a temporal priority of the cause to the effect. There is furthermore a spatio-temporal contiguity of the cause to the effect and, finally, on every occasion on which the cause occurs, the effect follows – there is constant conjunction. As there is, in his opinion, no physical connection between the cause and the effect (the connection does not exist outside of our own minds), the relation between cause and effect is to be found in custom and habit. Since Hume could not find a necessary connection between cause and effect, either in formal reasoning or in the physical world, his analysis answers the question whether and how we can explicate the concept of causality in terms that do not surreptitiously introduce any occult concepts of power or necessary connection, which is exactly what he wanted to do.

The form philosophical discussions of causality take is usually as follows: there are two facts (or types of) C and E or two events (or types of) C and E between which there is a relation R. Questions are raised whether C and E should be taken to refer to facts or events, and, further, whether to individual facts or to events or classes of them. Sometimes the logical structure of the relation is discussed in terms of necessary or sufficient conditions or a combination of both. Given the interaction of several conditions, this leads to complex schemes to enable us to understand particular occurrences. Consider, for instance, the following example in which a cause is defined as a condition. If a barn burns down this might have been caused by a careless smoker, by embers from a nearby forest fire falling on it, by a stroke of lightning or even from spontaneous combustion engendered by fermentation of fresh hay. None of these is a necessary condition, but any one of them might be sufficient. Moreover, no fire will occur unless some additional factors are present (for instance, in the case of the incident of the cigarette, that it falls on some flammable material and that it goes unnoticed). These other conditions, however, would not suffice to start a fire. Each of them is a condition that is an Insufficient but Non-redundant (necessary) part of a condition that is Unnecessary but Sufficient (an INUS condition). The dropping of the burning cigarette is an example thereof. Such a clear example is helpful in order to make particular points concerning causality. As matters of meaning are always involved where examples from social sciences are concerned, an analogous case from that context cannot easily be given. We will therefore continue a bit longer in the area of natural phenomena. After this brief sketch of causality and some of the (philosophical) problems that go with it, a move to the general level will take the argument forward to the relevance of causality in scientific explanations.