A necessary connection between a cause and its effect says that given the cause, its effect must occur.
Consider that a match is struck, causing it to light. Now consider that a match is struck, but it fails to light. Necessary connections are thereby disproved, right!?–one cause, the striking of a match, sometimes succeeds and other times fails in its effect, its very own lighting.
But this argument holds no weight whatsoever. It’s a trick.
Generally speaking, a match does not have just one effect, but several depending on the context it finds itself in– in gusty/stable winds, created from poor/superior manufacturing processes, struck too hard/too soft/just right. Indeed for all cases of the match, one and only one effect will result, necessarily so, from the particular context in play. That a match sometimes lights and sometimes fails to light just follows from the differing contexts. The one who denies necessary connections must come up with an effect that fails even when the context is considered.
There is one argument against necessary connections that considers the context. It requires the notion of a causal defeater, something that serves to prevent an effect from coming about. For example, many a gust of wind when striking the match has causally defeated its being lit. Now, those who argue on these lines argue that we should indeed consider the causal context. However, from an entire causal context, a causal defeater is still possible in principle. If so, it just cannot be the case that the effect must occur.
The argument against necessity in considering the context the cause is in goes like this in brief:
A cause C in its context does not cause some effect E necessarily, because:
(1) If C in its context, then E, then whatever is added to C in its context, D say, then E still must be so.
(2) But D might be a causal defeater of E, and E would not occur in that case.
(3) Therefore, E is not necessary given C in its context.
The problem with this argument is that it is a fantasy to think that a fixed causal context C is preserved in adding D in any example I can think of. So for instance, let’s consider the match again. We have a causal context that would include facts surrounding the immediate match head. The wind, for example, would exhibit a range of stability. Thus, when one sort of causal defeater, the cyclone that appears out of nowhere and sucks up the match as it is struck, is instantiated, it also contradicts the causal context we fixed. The wind is no longer stable, but highly gusty. Clearly, any causal context at all can be fixed that would wreck the job of the causal defeater, resulting in the necessity the defeater was brought in to destroy.
And it is not that the context avoids causal defeaters just by stipulating that there can be no causal defeaters. No, for any defeater, a causal context can be fixed such that the defeater clearly contradicts the context. More than this, fixing a causal context results in cutting off an entire class of causal defeaters. In fixing upon the wind immediately surrounding the head of the match, all manner of causal defeaters from cyclones, to heavy breaths, to fans, would be disqualified. Indeed, such causal defeaters would necessitate the match’s remaining unlit. That is, far from spelling doom for necessity, necessity is the right way to understand causal defeaters themselves.
There is more to say about necessary connections (and in arguing for them). Particularly, I am interested in fitting necessary connections into indeterministic causal relations. More to come!