  According to William, maximal propositions contain or signify all the propositions under them. Thus, the maxim, ‘Of whatever the species is predicated the genus is also predicated’ signifies or contains the sentences ‘If it is a man it is an animal’, ‘If it is a rock it is a substance’, etc. Only the most general form is truly a maximal proposition, but it is the more precise (certior) sentences contained under the maxim that provide the inferential force for particular arguments. William may have developed this view in response to the vocalists. Abelard explains that multiple senses are needed given William's view that things, not words, warrant inference; only the more precise formulations can signify the things themselves (Abelard LI Top: 231.26-238.34). An anonymous author confirms Abelard's understanding of William's view. The argument, ‘Socrates is a man therefore Socrates is an animal’ is warranted by the topical maxim noted above. It is not the maxim itself but the more precise version contained in it, ‘If it is a man it is an animal’, that provides the force for this particular inference. According to this text, William argued that it is not the words (voces) or the sense (intellectus) of the more precise sentence that provides the inferential force, but the fact that the more precise sentence signifies relations (habitudines) between things (Green-Pedersen 1974: Frag 8;10;12).