Ott 2009: 239) This way of dismissing the nonequivalence of the two definitions becomes more problematic, however, when we realize that Hume does not make the distinction between natural and philosophical relations in the Enquiry, yet provides approximately the same two definitions. As Hume says, the definitions are "presenting a different view of the same object." (T 1.3.14.31; SBN 170) Supporting this, Harold Noonan holds that D1 is "what is going on in the world" and that D2 is "what goes on in the mind of the observer" and therefore, "the problem of nonequivalent definitions poses no real problem for understanding Hume." (Noonan 1999: 150-151) Simon Blackburn provides a similar interpretation that the definitions are doing two different things, externally and internally. J.A. Robinson is perhaps the staunchest proponent of the position that the two are nonequivalent, arguing that there is a nonequivalence in meaning and that they fail to capture the same extension. There are several interpretations that allow us to meaningfully maintain the distinction (and therefore the nonequivalence) between the two definitions unproblematically. However, Blackburn has the first as giving the "contribution of the world" and the latter giving the "functional difference in the mind that apprehends the regularity." (Blackburn 2007: 107) However, this is not the only way to grant a nonequivalence without establishing the primacy of one over the other.

There are reams of literature addressing whether these two definitions are the same and, if not, to which of them Hume gives primacy. Scaling up the picture from the previous example by a factor of 3 then gives us this picture. Walter Ott argues that, if this is right, then the lack of equivalence is not a problem, as philosophical and natural relations would not be expected to capture the same extension. Therefore, whether or not the projectivism of D2 actually is relevant to the metaphysics of causation, a strong case can be made that Hume thinks it is so, and therefore an accurate historical interpretation needs to include D2 in order to capture Hume’s intentions. If it is true that constant conjunction (with or without the added component of mental determination) represents the totality of the content we can assign to our concept of causation, then we lose any claim to robust metaphysical necessity. In this way, the distinction may blunt the passages where Hume seems pessimistic about the content of our idea of causation. If the definitions were meant to separately track the philosophical and natural relations, we might expect Hume to have explained that distinction in the Enquiry rather than dropping it while still maintaining two definitions.

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. The second of Hume’s influential causal arguments is known as the problem of induction, a skeptical argument that utilizes Hume’s insights about experience limiting our causal knowledge to constant conjunction. Again, the key differentia distinguishing the two categories of knowledge is that asserting the negation of a true relation of ideas is to assert a contradiction, but this is not the case with genuine matters of fact. This is because, as Hume maintains in Part VII of the Enquiry, a definiens is nothing but an enumeration of the constituent simple ideas in the definiendum. Recall that proper reasoning involves only relations of ideas and matters of fact.

One way to interpret the reasoning behind assigning Hume the position of causal skepticism is by assigning similar import to the passages emphasized by the reductionists, but interpreting the claims epistemically rather than ontologically. We cannot help but think that the event will unfurl in this way. 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. Some scholars have argued for ways of squaring the two definitions (Don Garrett, for instance, argues that the two are equivalent if they are both read objectively or both read subjectively), while others have given reason to think that seeking to fit or eliminate definitions may be a misguided project. Some scholars have emphasized that, according to Hume’s claim in the Treatise, D1 is defining the philosophical relation of cause and effect while D2 defines the natural relation. In fact, later in the Treatise, Hume states that necessity is defined by both, either as the constant conjunction or as the mental inference, that they are two different senses of necessity, and Hume, at various points, identifies both as the essence of connection or power.

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