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Note that these two other balls are already on the table, and remember that white and yellow are the cue balls. We are therefore left in a position of inductive skepticism which denies knowledge beyond memory and what is present to the senses. 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, that the inferences are never valid). How much do balls expand when they get hot? This is to disregard the discussion through which Hume accounts for the necessity of causation, a component which he describes as "of much greater importance" than the contiguity and succession of D1. 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. Having described these two important components of his account of causation, let us consider how Hume’s position on causation is variously interpreted, starting with causal reductionism.

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. 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. However, not everyone agrees that D2 can or should be dropped so easily from Hume’s system. It should be noted, however, that not everyone agrees about what exactly the Problem consists in. Generally, the appeal is to Hume’s texts suggesting he embraces some sort of non-rational mechanism by which such beliefs are formed and/or justified, such as his purported solution to the Problem of Induction. However, Hume has just given us reason to think that we have no such satisfactory constituent ideas, hence the "inconvenience" requiring us to appeal to the "extraneous." This is not to say that the definitions are incorrect. It is an inconvenience that they appeal to something foreign, something we should like to remedy.

But though both these definitions be drawn from circumstances foreign to cause, we cannot remedy this inconvenience, or attain any more perfect definition… Unfortunately, such a remedy is impossible, so the definitions, while as precise as they can be, still leave us wanting something further. We cannot claim direct experience of predictions or of general laws, but knowledge of them must still be classified as matters of fact, since both they and their negations remain conceivable. That will do him good, and he'll come home in such a tender, penitent state of mind, that I shan't dare to see him." she said, adding, as she went slowly home, feeling as if she had murdered some innocent thing, and buried it under the leaves. "Now I must go and prepare Mr. Laurence to be very kind to my poor boy. A gloriously beautiful heroine of a discreditable adventure I must in justice admit that she was; but that fact has only this importance: her beauty was such a surprise to me that it cast a doubt upon her identity with the young woman I had seen before; how could the marvelous fascination of her face have failed to strike me at that time?

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. Given that Hume’s discussions of causation culminate in these two definitions, combined with the fact that the conception of causation they provide is used in Hume’s later philosophical arguments of the Treatise, the definitions play a crucial role in understanding his account of causation. This is an important but technical explication and defense of the Humean causal reductionist position, both as a historical reading and as a contemporary approach to 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.

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