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The family of reductionist theories, often read out of Hume’s account of necessity outlined above, maintain that causation, power, necessity, and so forth, as something that exists between external objects rather than in the observer, is constituted entirely by regular succession. Briefly, against the distinction, Kenneth Winkler offers an alternative suggestion that Hume’s talk of secret connections is actually a reference to further regularities that are simply beyond current human observation (such as the microscopic or subatomic), while ultimately interpreting Hume as an agnostic about robust causation. Since the Problem of Induction demands that causal connections cannot be known a priori, and that our access is only to constant conjunction, the Problem seems to require the most crucial components of his account of necessity. It is therefore not entirely clear how Hume views the relationship between his account of necessity and the Problem. Because of the variant opinions of how we should view the relationship between the two definitions proffered by Hume, we find two divergent types of reduction of Humean causation. If, as is often the case, we take definitions to represent the necessary and sufficient conditions of the definiendum, then both the definitions are reductive notions of causation.

In addition to its accounting for the necessity of causation mentioned above, recall that Hume makes frequent reference to both definitions as accurate or just, and at one point even refers to D2 as constituting the essence of causation. Recall that proper reasoning involves only relations of ideas and matters of fact. Whether the Problem of induction is in fact separable from Hume’s account of necessary connection, he himself connects the two by arguing that "…the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other." (EHU 4.6; SBN 27) Here, Hume invokes the account of causation explicated above to show that the necessity supporting (B) is grounded in our observation of constant conjunction. Louis Loeb calls this reconstruction of Hume targeting the justification of causal inference-based reasoning the "traditional interpretation" (Loeb 2008: 108), and Hume’s conclusion that causal inferences have "no just foundation" (T 1.3.6.10; SBN 91) lends support to this interpretation. However, there are philosophers (Max Black, R. B. Braithwaite, Charles Peirce, and Brian Skyrms, for instance) that, while agreeing that Hume targets the justification of inductive inference, insist that this particular justificatory circle is not vicious or that it is unproblematic for various reasons.

But not all are in agreement that Hume’s intended target is the justification of causal or inductive inference. However, not everyone agrees that D2 can or should be dropped so easily from Hume’s system. How can you know, sir? D. C. Stove maintains that, while Hume argues that inductive inference never adds probability to its conclusion, Hume’s premises actually only support "inductive fallibilism", a much weaker position that induction can never attain certainty (that is, what is billiards that the inferences are never valid). Here we should pause to note that the generation of the Problem of Induction seems to essentially involve Hume’s insights about necessary connection (and hence our treating it first). Hume’s discussion of necessary connection presented above. But given the Humean account of causation outlined above, it is not difficult to see how Hume’s writings give rise to such reductionist positions. There could be no harm in what had been done in so many respectable families, and by so many women of the first consideration; and it must be scrupulousness run mad that could see anything to censure in a plan like theirs, comprehending only brothers and sisters and intimate friends, and which would never be heard of beyond themselves.

She started no difficulties that were not talked down in five minutes by her eldest nephew and niece, who were all-powerful with her; and as the whole arrangement was to bring very little expense to anybody, and none at all to herself, as she foresaw in it all the comforts of hurry, bustle, and importance, and derived the immediate advantage of fancying herself obliged to leave her own house, where she had been living a month at her own cost, and take up her abode in theirs, that every hour might be spent in their service, she was, in fact, exceedingly delighted with the project. Wait long enough, and the solar wind blowing the sail outwards will take the Earth outward too, since the two are gravitationally bound together! The only apparent answer is the assumption of some version of the Principle of the Uniformity of Nature (PUN), the doctrine that nature is always uniform, so unobserved instances of phenomena will resemble the observed. However, since this interpretation, as Hume’s own historical position, remains in contention, the appellation will be avoided here. The motivation for this interpretation seems to be an emphasis on Hume’s D1, either by saying that it is the only definition that Hume genuinely endorses, or that D2 somehow collapses into D1 or that D2 does not represent a genuine ontological reduction, and is therefore not relevant to the metaphysics of causation.