 One can see that in the above definition the auxiliary assumptions in \(k\) are the \(e\)-development of further closed constant-free hypotheses (in fact, equations as applied to specific measured values, in typical examples from Glymour 1980a), where such hypotheses are meant to be conjoined in a single statement (\(\alpha\)) for convenience. This implies that the only terms occurring (non-vacuously) in \(k\) are individual constants already occurring (non-vacuously) in \(e\). For an empty \(\alpha\) (that is, tautologous: \(\alpha = \top\)), \(k\) must be empty too, and the original (restricted) definition of Hempelian confirmation applies. As for the proviso that \(\alpha \not\vDash h\), it rules out undesired cases of circularity—akin to so-called “macho” bootstrap confirmation, as discussed in Earman and Glymour 1988 (for more on Glymour’s theory and its developments, see Douven and Meijs 2006, and references therein).