Let us begin with the relation of cause and effect. A cause and effect relation can be spoken of as being general or as being a particular instance. For example:
Easterly wind causes ships to sail East. (General)
The easterly wind causes the ship to sail East. (Particular)
As the above would imply, easterly wind is a cause of the effect of ships sailing East. However, perhaps sometimes easterly wind is no cause at all, such as in the case that it hits against no ships or anything else at all, and is moving so uniformly that it even doesn’t effect its surrounding molecules. Perhaps it does so in outer space (if things can be said to move East in outer space). In such a case, there is an easterly wind, but no effect. By this, the easterly wind is not a cause. However, the above example claims are not contradicted in any way. The former is still true since it is a general claim, perhaps restricted to easterly wind near the surface of the Earth. The claim there is that in general or for the most part, easterly wind causes ships to sail east. This won’t be made false by a particular instance of a sailing ship failing to go East, or of the easterly wind being no cause at all in a particular instance. For the latter claim, which is of a particular case, it is also not made false by what is actually the case of some other particular easterly wind and some other particular ship from the one it references.
Obviously, when a wind is not a cause, there will also be no effect or causal relation, so I won’t need to concern myself with whether there is a particular kind of causal relation involved (viz. one of necessary connections). In seeking necessary connections, I will concern myself with a cause only under the assumption that it indeed factors as a cause (i.e. has an effect). What is a necessary connection in a causal relation?
A necessary connection between a cause and its effect says that given the cause, the effect must result.
I want to highlight first of all that this claim is not a general claim. Note: ‘the cause’ and ‘the effect’. But let me defend for a moment that this is not just my taking a claim that is allowed to be general and forcing it to be particular. Actually, making it a general claim makes it incompatible with general causal claims from the start. What we mean by ‘general’ is here something like ‘for the most part’, or ‘more than half the time’. If we allow that necessary connections between a cause and an effect be that given some general cause, then its general effect must follow, a contradiction would follow. That is, if we think that necessary connections involve the claim that given a cause that results in its effect more than half the time, then the effect must result, this would be a logical absurdity in any causal relation that has as a result another effect from the one it has generally.
Not only is it possible for there to be claims of a general sort of causation if necessity is true, but we can also use necessity to make sense in the first place for why a different effect resulted than the one that generally results: it’s because the cause was different (i.e. in a different context, or of a different type), and this difference, not captured by the general claim, necessarily results in an effect of a different sort. (For more details about how a causal context can answer how necessary connections is compatible with general causation (particularly with a struck match that sometimes fails to light), see my previous post: Necessary Connections in Causal Relations.)
I’m of course not interested in further defending necessary connections against cases where some expected effect is prevented from occurring, since I think I sufficiently covered this in my previous posts on necessary connections (the first linked above and the one after that found here). This post is after all about the hallmark of necessary connections, and subsequently how by that hallmark it turns out that all forms and instances of causation exhibit necessary connections after all.
In particular instances of causation, a cause will restrict what can result or occur. So wind hits up against some sails, and this wind hitting against the sails restricts what results. Deterministically speaking, the wind hitting against the sails will alter the ship’s course along one trajectory. In this case, what can occur given the cause is indeed very narrow. However, it is not required that we speak only deterministically. Indeterministically speaking, the wind hitting against the sails makes the ship most likely to travel along trajectory A, more likely (to varying probabilities) to travel along trajectories B, C, or D, less likely (to varying probabilities) to head along E and F, and least likely to head along G. This is an appropriate way of such a wind restricting what can occur, since the wind is what is altering the probabilities that it heads one way rather than another, and the probabilities are themselves restrictive on what can occur. That is, they will be one probabilistic distribution, as opposed to some other.
Such a restriction on what can occur is the hallmark of a necessary connection. Causation, both deterministic and indeterministic, is restrictive on what can occur given the cause. In terms of must, the restriction is that given a cause, there must be one result that is either itself identical with one event or occurrence (in cases of deterministic causation), or else is identical with an event or occurrence that reflects or embodies a probabilistic distribution among other events or occurrences (in cases of indeterministic causation). The latter is not without necessary connections, since the result is probabilistically constrained and, regardless of how many other events can occur similarly probabilistically constrained, one of them must occur, and to the exclusion of the rest. There is perhaps more to get clear about the details for how this works, but what’s clear is that necessary connections are involved. This is true just in virtue of the cause restricting what can occur.
Perhaps it is wondered whether or not there is some other causal relation that neither leads to one event or occurrence, nor is probabilistically constrained. Imagine if you will some cause that results in something so arbitrary that it should not even be considered random. What would such a scenario look like? Take the easterly wind. When it hits the sail, the boat disappears. If the easterly wind is truly the cause here, then we may ask whether or not this result of the boat disappearing was its only possible result. If it is, then this would seem to be an instance of deterministic causation. That is, the easterly wind in this place and time hitting the boat resulted in one possible event, the boat’s disappearing. If not, then we may ask about how many other possible results there were given the cause. If the other results are more or less the wind behaving as usual by directing a trajectory, then we might ask how often it is that the boat should disappear, given the wind. Perhaps it’s exceedingly rare: the first and last time this will happen in our universe. However, it is hard to deny that this is a probabilistic constraint nonetheless–the key language here being ‘exceedingly rare’. To go more extreme and possibly forgo all probabilistic language, suppose we claim further that the boat disappeared for no reason at all. The boat just disappeared, and there is nothing to point to and give any account for when such things occur or how often they occur. However, saying that some event occurred for no reason at all would be identical with saying (or at least imply) that there was no cause for its happening. The wind would thus be no cause. With this discussion in hand, I think it’s obvious that all forms of causation restrict what can occur.
Since all causes restrict what can occur, and this is a hallmark of necessary connections, the conclusion is that all instances of causation have necessary connections.