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The regularity theory, associated with Hume, holds that causation consists in nothing more than constant conjunction under a universal law: C causes E if and only if events of type C are invariably followed by events of type E. There is no hidden 'necessary connection' beyond this regularity. This view fits with empiricist scruples about metaphysical excess, but faces the problem of distinguishing genuine causal laws from accidental regularities (all gold spheres are under a mile in diameter — yet this isn't a causal law). Mill's methods and later INUS condition accounts (Mackie) attempted to refine the regularity approach.
Read Hume's Treatise 1.3.14 on the idea of necessary connexion, then Mackie's 'Causes and Conditions' for the INUS refinement. Try to construct a counterexample to the basic regularity view before reading the responses.
From your study of causation and causal relations, you know the core philosophical puzzle: causation seems to be more than mere correlation — when one event causes another, there appears to be a necessary connection between them, not just a temporal sequence. Striking a match in oxygen causes ignition; it doesn't merely precede it. The question is what this "necessary connection" actually is. Hume's revolutionary answer was: nothing. You never observe necessity; you observe only that striking is reliably followed by ignition. The regularity theory builds an account of causation on that austerity.
The basic regularity account states: event C causes event E if and only if events of type C are invariably followed by events of type E, under a universal law. There is no hidden metaphysical glue beyond this regularity — no causal powers, no productive relations, no necessary connections in nature. When we say fire causes heat, all that is objectively in the world is the constant conjunction: fire-type events are universally followed by heat-type events. The subjective feeling that we "see" the necessity is, Hume argued, a projection of our own habituated expectations onto the external world. We observe regularity; we feel necessity. The necessity is in us, not in the world.
The immediate problem is distinguishing genuine causal laws from accidental regularities. Consider: all gold spheres are less than a mile in diameter, and this has been true throughout history — a universal regularity. But being a gold sphere doesn't *cause* smallness; the regularity is merely accidental, not lawlike. Or consider a clock that always runs slightly ahead of another: the earlier reading is always followed by the later reading, but the first clock doesn't cause the second to advance. John Stuart Mill's methods — agreement, difference, joint method, concomitant variation — were attempts to operationalize the distinction: a genuine cause is the factor that is present when the effect is present and absent when the effect is absent, across systematic variation of other factors. But Mill's methods identify correlations, not causation; they don't escape the original problem.
John Mackie's INUS account is a more sophisticated refinement. A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition. That is: the full set of conditions that produces an effect is often far richer than any single factor (it's insufficient on its own), yet the particular cause we identify is a necessary component of that bundle (without it, that particular sufficient condition fails). Multiple different bundles might suffice for the same effect (the condition is unnecessary), but within the bundle that actually obtained, the cause was required. This captures why we say the short circuit caused the fire: the short circuit was a necessary part of the bundle of conditions (dry weather, flammable material, no sprinklers) that was sufficient for ignition — even though other bundles might have caused the fire some other way.
The INUS account is a genuine advance, but the regularity framework as a whole still faces hard cases. Overdetermination (two simultaneous, each sufficient causes), pre-emption (one cause that beats another to the effect), and symmetric overdetermination (two simultaneous, each alone sufficient) all produce cases where regularity analyses give unintuitive verdicts. These difficulties motivate the transition to counterfactual theories of causation — theories that analyze causation in terms of what would have happened if C had not occurred — which you will encounter in the next topic.
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