A conjunction of two propositions may be incompatible with the positum even when each conjunct is separately compatible with or required by the positum.

As Swyneshed recognizes, his rules may lead the respondent into granting triads or larger sets of propositions containing contradictions. In his formulation, “the conclusion must be granted that three incompatible propositions must be granted, and four, and so on” (Spade 1977, 274). The sequence of propositions in D1 above is an example of this. The respondent cannot according to Swyneshed rely on Burley’s rule 5 to grant Proposition 2. Instead, the respondent should grant a disjunction but deny