Implicatures In sensu composito

Lagerlund writes in the Stanford Encyclopedia, online:

"While the de dicto/de re terminology was used, it was not all that common."

"Medieval logicians preferred to use what they took to be Aristotle's terminology, talking about modal sentences in the composite sense --

in sensu composito --

and divided sense

-- in sensu diviso).

"The structure of a composite modal sentence can be represented as follows:

(quantity/subject/copula, [quality]/predicate)mode

A composite modal sentence corresponds to a de dicto modal sentence.

"The word ‘composite’ is used because the mode is said to qualify the composition of the subject and the predicate."

The structure of a divided modal sentence can be represented as follows:

quantity/subject/copula, mode, [quality]/predicate

"Here, the mode is thought to qualify the copula and thus to divide the sentence into two parts (hence the name, ‘divided modal sentence’). This type of modal sentence was characterized as de re because what is modified is how things (res) are related to each other, rather than the truth of what is said by the sentence (dictum) (see Lagerlund 2000: 35–39, and the entry on medieval theories of modality for further details)."

"Like virtually all medievals, Abelard thought that Aristotle's modal syllogistic was a theory for de re modal sentences. He says very little about it in his logical works, however. In less than five pages in the Dialectica (245–249) he treats modal, oblique, and temporal syllogistic logic. Earlier in the same work, he says a little about conversion rules. He argues in both the Dialectica (195–196) and the Logica (15–16) that the conversion rules can be defended even on a de re reading, but the conversions he discusses are not modal conversions since the mode must be attached to the predicate and follow the term in the conversion, making the conversion into the conversion of an assertoric sentence. The conversions of de re modal sentences, as Abelard has defined them, do not hold, as Paul Thom has convincingly shown. (Thom 2003: 57–58.)"

"There is no modal syllogistic explicitly outlined in any of Abelard's logical works, though in the Dialectica, he exemplifies some of the valid mixed moods: M–M in the first figure, MM– in the second, and M–M in the third (M represents a possibility sentence and ‘–’ an assertoric). He also shows that uniform modal syllogisms are not generally valid, so that MMM is not valid unless the middle term in the major premise is read with the mode attached to it, as in what follows."

Everything which is possibly B is possibly A
Every C is possibly B
Every C is possibly A

"A consequence of this, of course, is that the middle term in the minor premise is ‘possibly B’ and hence no longer a modal sentence. MMM is consequently reduced to M–M."

"Anything more systematic than this has to be drawn out from Abelard's definition of modal sentences and their semantic interpretation. Thom has done this in his book (Thom 2003), where he claims that there is a very specific system developed that is not at all similar to Aristotle's modal system. Abelard was therefore not attempting an interpretation of Aristotle, but must be seen as developing a new system based on his reading of de re sentences. But this project must overcome several problems, particularly since Abelard cannot use the conversion rule."

For a discussion by R. E. Dale of Lewis's apt use of an ascription 'in sensu diviso' for his account of a theory of meaning, vide ch. 5 of Dale's PhD thesis, online, "The theory of meaning" at russelldale.com.