 Holkot responded in a passage for which he is perhaps best known, that there must be two systems of logic, a logic appropriate to the natural order, exemplified in Aristotle’s works, and a logic appropriate to the supernatural order, a logic of faith, whose rules are supplementary to those of Aristotle (Slotemaker and Witt 2015, 74–81, esp. 78). He concluded that Aristotelian logic did not hold universally, but only for the natural order unless additions were made to take into account theological cases. This did not mean that he abandoned the principle of non-contradiction in matters of faith. Rather the nature of the divine being meant that syllogisms involving Trinitarian terms functioned like expository syllogisms about particulars when unquantified universal terms are substituted for particular ones: