causality and determinism

The necessity of the causal bond which is commonly postulated, and which is taken over from the idea of fate, is, according to Hume, not capable of a clear-cut empirical interpretation. He therefore replaces necessity by repetition and permanence; that is, whenever the same circumstances recur, the same effect will follow the same cause. But even with this nothing is gained, as an event happens in its full concretion only once. It is thus necessary that certain demands of continuity be added, stipulating that causes differing sufficiently little from one another have effects also differing but little; that sufficiently remote bodies or events have a negligible effect, and so on. The phenomena must be brought under the heading of concepts; they must be united into classes determined by typical characteristics. Thus the causal judgement, "When I put my hand in the fire I burn myself," concerns a typical performance described by the words "to put one's hand in the fire," not an individual act in which the motion of the hand and that of the flames is determined in the minutest detail. The causal relation therefore does not exist between events but between types of events. First of all -and this point does not seem to have been sufficiently emphasized by Hume- generally valid relations must be isolated by decomposing the one existing world into simple, always recurring elements. The formula "dissecare naturam [to dissect nature]" was already set up by Bacon.

- Weyl's "The Open World" lecture as published in Mind and Nature

Indeterminism is engrained in the notion of causality since the latter requires the separation of all possible world states into equivalence classes.

- If an equivalence class A is always followed by an equivalence class B, then we say "A deterministically causes B".

- If A is followed by a set of equivalence classes that includes B, then we say "B is probabilistically caused by A".

Note that there is indeterminism involved in both cases. In the first case, we don't actually know which element of A is followed by which element of B. Perhaps every instance of a fixed a∈A is followed by a different b∈B, and our causal scheme is too crude to detect this situation.

Since we have no hope of understanding reality without dissecting it, we should shelve away all discussions about determinism for good.