 The above, widely known “paradoxes” then suggest that Hempel’s analysis of confirmation is too liberal: it sanctions the existence of confirmation relations that are intuitively very unsound (see Earman and Salmon 1992, 54, and Sprenger 2011a, 243, for more on this). Yet the Hempelian notion of confirmation turns out to be very restrictive, too, on other accounts. For suppose that hypothesis \(h\) and evidence \(e\) do not share any piece of non-logical vocabulary. \(h\) might be, say, Newton’s law of universal gravitation (connecting force, distances and masses), while \(e\) could be the description of certain spots on a telescopic image. Throughout modern physics, significant relations of confirmation and disconfirmation were taken to obtain between statements like these. Indeed, telescopic sightings have been crucial evidence for Newton’s law as applied to celestial bodies. However, as their non-logical vocabularies are disjoint, \(e\) and \(h\) must simply be logically independent, and so must be \(e\) and \(dev_{e}(h)\) (with very minor caveats, this follows from Craig’s so-called interpolation theorem, see Craig 1957). In such circumstances, there can be nothing but Hempel-neutrality between evidence and hypothesis. So Hempel’s original theory seems to lack the resources to capture a key feature of inductive inference in science as well as in several other domains, i.e., the kind of “vertical” relationships of confirmation (and disconfirmation) between the description of observed phenomena and hypotheses concerning underlying structures, causes, and processes.