 To overcome the latter difficulty, Clark Glymour (1980a) embedded a refined version of Hempelian confirmation by instances in his analysis of scientific reasoning. In Glymour’s revision, hypothesis \(h\) is confirmed by some evidence \(e\) even if appropriate auxiliary hypotheses and assumptions must be involved for \(e\) to entail the relevant instances of \(h\). This important theoretical move turns confirmation into a three-place relation concerning the evidence, the target hypothesis, and (a conjunction of) auxiliaries. Originally, Glymour presented his sophisticated neo-Hempelian approach in stark contrast with the competing traditional view of so-called hypothetico-deductivism (HD). Despite his explicit intentions, however, several commentators have pointed out that, partly because of the due recognition of the role of auxiliary assumptions, Glymour’s proposal and HD end up being plagued by similar difficulties (see, e.g., Horwich 1983, Woodward 1983, and Worrall 1982). In the next section, we will discuss the HD framework for confirmation and also compare it with Hempelian confirmation. It will thus be convenient to have a suitable extended definition of the latter, following the remarks above. Here is one that serves our purposes: