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. 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. Blackburn 2007: 101-102) P.J.E. 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. Of the common understanding of causality, Hume points out that we never have an impression of efficacy. Strictly speaking, for Hume, our only external impression of causation is a mere constant conjunction of phenomena, that B always follows A, and Hume sometimes seems to imply that this is all that causation amounts to.

Ergo, the idea of necessity that supplements constant conjunction is a psychological projection. It is therefore an oddity that, in the Enquiry, Hume waits until Section VII to explicate an account of necessity already utilized in the Problem of Section IV. 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. 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. For instance, D.M. Armstrong, after describing both components, simply announces his intention to set aside the mental component as irrelevant to the metaphysics of causation. Clearly it is not a logical modality, as there are possible worlds in which the standard laws of causation do not obtain. It seems to be the laws governing cause and effect that provide support for predictions, as human reason tries to reduce particular natural phenomena "…

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. In the Treatise, however, a version of the Problem appears after Hume’s insights about experience limiting causation to constant conjunction but before the explication of the projectivist necessity and his presenting of the two definitions. Note that he still applies the appellation "just" to them despite their appeal to the extraneous, and in the Treatise, he calls them "precise." Rather, they are unsatisfying. Hume illicitly adds that no invalid argument can still be reasonable. In other words, rather than interpreting Hume’s insights about the tenuousness of our idea of causation as representing an ontological reduction of what causation is, Humean causal skepticism can instead be viewed as his clearly demarcating the limits of our knowledge in this area and then tracing out the ramifications of this limiting. First, there are reductionists that insist Hume reduces causation to nothing beyond constant conjunction, that is, the reduction is to a simple naïve regularity theory of causation, and therefore the mental projection of D2 plays no part.

Once more, all we can come up with is an experienced constant conjunction. Updated information from the feed is automatically downloaded to your computer and can be viewed in Internet Explorer and other programs. Updated interface. Tool to allow continuously updated commentaries to be published to a web page. 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. Although this employment of the distinction may proffer a potential reply to the causal reductionist, there is still a difficulty lurking. Hume argues that we cannot conceive of any other connection between cause and effect, because there simply is no other impression to which our idea may be traced.

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