 After this extended discussion of alternatives (occupying a quarter of his treatise), Paul sets out to develop his own solution, based firmly on Roger Swyneshed’s proposals from the 1330s. In his second chapter, he systematically lays out his distinctions (divisiones) and assumptions (suppositiones), then draws seven Conclusions and seven Corollaries. The basic idea is Swyneshed’s, namely, to provide a solution which does not depend on postulating tacit or hidden or consequential significates for insoluble propositions beyond what is clearly shown---what they standardly suggest or indicate by the straightforward combination of their parts (in Heytesbury’s phrase, “ sicut termini communiter pretendunt”). Instead, as Swyneshed had proposed, Paul tightens the criterion for truth, to exclude those that falsify themselves, weakening the criterion for falsehood to admit those examples that do falsify themselves even if otherwise impeccable. Roger’s second and third notorious Conclusions reappear as Paul’s fifth and second respectively. Paul will later describe the second Conclusion as a fundamental principle: