If one has a certain ontology -- that is, if one entertains certain basic beliefs about the underlying structure of the world -- there is something irresistible about the idea of a necessary link between causality and inference. However, the demand for a link between inference and causality can also have a paralyzing effect -- because more often than not the knowledge that human beings have of causes is imperfect and often that sort of knowledge seems destined to remain imperfect.
Yet, it seems hard to resist the conclusion that without some tenable theory of the way one or more things are connected to another thing or things, no probative or inferential weight can be given to any observed associations of events in the world (and that this is so whether or not statistical language and concepts are used to describe those associations).
So how are we (theorists of evidence and inference) to wrestle our way out of this conundrum? I am not sure. But my strong guess is that we have to focus on the notion of what used to be called tacit knowledge, on subconscious perceptual and cognitive processes. The general idea is this: Our brains know more than we do. That is to say: Human knowledge does not consist only of conscious knowledge, or knowledge that human beings have been able to express explicitly.
It must or might be the case, I think, that the brain (i.e., the human neurobiological system) somehow comes to have embedded within it some pretty good working hypotheses about the causal structure of (some parts of) the world and that when the human organism observes certain patterns of events, these embedded tacit hypotheses are brought into play and channel (or influence) the conscious judgments that human beings make about whether some pattern of events or association of events does or does not "validly" matter to the inferences human beings should draw, or can "validly" ("logically") draw, on the basis of their observations of events in the world.
That's the general direction in which my thinking is moving. However, if that's the way inference generally works, numerous puzzles remain. One of the biggest ones is what role conscious reasoning can play if much or most of human knowledge is "tacit," literally subconscious. Another problem (related to the first) is to explain how some human beings have managed to make darned good predictions in some domains by deploying complex conceptual constructs and operations (e.g., quantum theory, calculus, and the like), explicit constructs and operations that did not come into those human beings' brains with their mothers' milk (or milk bottles).
Coming soon: the law of evidence on Spindle Law