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.
Abelard himself might have eventually backed away from this view (Martin 1998), but there are reports that suggest some of Abelard's followers, the so-called Nominales, wholeheartedly embraced the extreme interpretation of the maximal proposition.
At least at one point in his career, Peter Abelard appears to seriously entertain the radical reading of the maximal proposition (Henry 1991, 92 139).
Moreover, one can consider non-empty subsets of the maximal proposition as intermediate truth values.
Despite the appeal of commonsense, there were some medieval philosophers who took the maximal proposition to imply that if Socrates loses a finger, Socrates ceases to exist.
As described above, William holds that such maximal propositions contain the sense of those propositions that fall under them.
The student of medieval mereology will be extremely interested in the maximal propositions presented in treatments of the Topic from the whole and the Topic from the part.
An extrinsic middle, by contrast, is a sentence not containing the terms that form the antecedent and the consequent of the putative consequence, but which is a general rule describing the 'fact' that warrants the passage from the antecedent to the consequent (reminiscent of Boethius' maximal propositions), and which concerns the form of sentences.
According to William, maximal propositions contain or signify all the propositions under them.
So for maximal propositions to serve as grounds for the relation of consequence, a transformation on the status of topical arguments (from probable to necessary) had to occur at a later stage (Stump 1982, 290).
