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It stresses Hume’s position that philosophy should conform to and explain common beliefs rather than conflict with them. Armstrong 1983: 4) J. L. Mackie similarly stresses that, "It is about causation so far as we know about it in objects that Hume has the firmest and most fully argued views," (Mackie 1980: 21) and it is for this reason that he focuses on D1. Garrett 1997: 92, 94) Similarly, David Owen holds that Hume’s Problem of induction is not an argument against the reasonableness of inductive inference, but, "Rather Hume is arguing that reason cannot explain how we come to have beliefs in the unobserved on the basis of past experience." (Owen 1999: 6) We see that there are a variety of interpretations of Hume’s Problem of induction and, as we will see below, how we interpret the Problem will inform how we interpret his ultimate causal position. What lets us reason from (A) to (B)?

Even considering Hume’s alternate account of definitions, where a definition is an enumeration of the constituent ideas of the definiendum, this does not change the two definitions’ reductive nature. However, this practice may not be as uncharitable as it appears, as many scholars see the first definition as the only component of his account relevant to metaphysics. 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. 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. 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.

By limiting causation to constant conjunction, we are incapable of grounding causal inference; hence Humean inductive skepticism. The attempted justification of causal inference would lead to the vicious regress explained above in lieu of finding a proper grounding. But once this is lost, we also sacrifice our only rational grounding of causal inference. 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). Don't tell me that, Jo, I can't bear it now! I come now to the matter of your inquiry. Therefore, knowledge of the PUN must be a matter of fact. We have no ground that allows us to move from (A) to (B), to move beyond sensation and memory, so any matter of fact knowledge beyond these becomes suspect. You ask me if in my experience as one of a pair of twins I ever observed anything unaccountable by the natural laws with which we have acquaintance. 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.

Ball and mallet games are mentioned as early as the 13th century in French texts. Croquet is a very old game, widely known and practiced in France since the XI century under the name of 'jeu de mail'. But how had I known that this man's name was Margovan? 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. A man who foozles his drive and slices his approach, but who is nevertheless always down in two strokes after he has got on the putting-green, if not in one, is very hard to beat except his opponent is a really good player. He is on a smooth green which looks so fast that it terrifies him, while if it should slope slightly down hill he is more terrified still. Hume illicitly adds that no invalid argument can still be reasonable.

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