 The irrelevant conjunction paradox. Suppose that \(e\) confirms \(h\) relative to (possibly empty) \(k\). Let statement \(q\) be logically consistent with \(e\wedge h\wedge k\), but otherwise entirely irrelevant for all of those conjuncts (perhaps belonging to a completely separate domain of inquiry). Does \(e\) confirm \(h\wedge q\) (relative to \(k\)) as it does with \(h\)? One would want to say no, and this implication can be suitably reconstructed in Hempel’s theory. HD-confirmation, on the contrary, can not draw this distinction: it is easy to show that, on the conditions specified, if the HD clause for confirmation is satisfied for \(e\) and \(h\) (given \(k\)), so it is for \(e\) and \(h\wedge q\) (given \(k\)). (This is simply because, if \(h\wedge k \vDash e\), then \(h\wedge q\wedge k \vDash e\), too, by the monotonicity of classical logical entailment.)