How Near Can a Cause Get to its Effect?

Abstract

Are causes continuous with their effects, and, if so, how are they distinguished? Or are they discontinuous, and, if so, how are they connected? I think there are problems over this which have been obscured by traditional ways of talking about causation. It has been generally accepted, at least since Hume, that whatever else may need to be said about causation it involves succession and regularity (Hume spoke of 'constant conjunction'). In this paper I shall not be concerned with regularity, not because there are no problems over this, but because some problems over succession and conjunction will be sufficient for the day. Moreover, I shall only be concerned with what is sometimes called 'transeunt', and was traditionally called 'efficient', causation, where there is a before and after relation in which the cause is said to be the antecedent, sometimes the 'immediate antecedent', of the effect. 'Before and after' is a relation in a time series any time series with an accepted frame of reference. It is not necessary to assume a unique time series; all that I am wanting to exclude is backward causation, where causes would follow their effects.1 If, then, cause and effect are in a time series, will their continuity, if they are continuous, be that of the time series, i.e. dense? Density is continuity in a linear ordering, where, in the case of time, between any two instants there will always be another. Mathematically the time series is also continuous in the sense that it is represented not only by rational but also by irrational numbers. For the purpose of this paper this important distinction can be ignored. It would seem that cause and effect need to be continuous in some sense, and also that they need to be distinguishable units. In the recent literature it has been usual to speak of the units as 'events'. In ordinary speech we also tend to speak of causes and effects as events, and indeed as