  William divides the standard A, E, I, and O sentences according to what he calls the matter of the sentence materia propositionis). The matter of the sentence is determined by the relationship between what is signified as the subject and the predicate. Each standard-form sentence is found in one of three matters: natural, contingent, or remotive. In a sentence of natural matter the predicate inheres universally in the subject: ‘All men are animals’. In a sentence of contingent matter the predicate inheres in the subject, but not universally: ‘All men are white’. In sentences of remotive matter the predicate in no way inheres in the subject: ‘All men are stones’. The validity of direct inferences between contraries, subalterns, etc. depends on the matter of the sentences involved. In all matter, contraries cannot both be true. So regardless of the matter, if an A sentence is true the corresponding E sentence is false. In natural and remotive matter, if either the A or E sentence is false the other must be true: if ‘No men are animals’ is false then ‘All men are animals’ must be true. However, in contingent matter both sentences may be false. It is possible for both ‘All men are white’ and ‘No men are white’ to be false. William gives a similar treatment for contradictories, subcontraries, and subalterns (ISW I 3-3.3; II 1.1-1.3; IGP I 5.4-5.6).