The typology of cumulativity

Sentences containing plural expressions can be true in a number of situations: The sentence Two boys fed two cats, for instance, it true if boy 1 and boy 2 each fed two cats -- but also if boy 1 fed only cat 1 and boy 2 fed only cat 2. The so-called `truth conditions of this sentence thus differ from those of the sentence Every boy fed two cats, which is false in the latter situation (even if there are only two boys). This project wants to find out how the truth-conditions of plural sentences come about. But why would this be an interesting question? Our general aim, after all, is to understand the human `language faculty` (i.e.: Why can we understand sentences of our native languages even if we have never come across them before?) -- and thus we also have to investigate which objects can act as meanings for the expressions of human languages (i.e.: What exactly is the meaning of every or two?) and which mechanism do we use to put together the meanings of smaller parts (e.g. two, cats) to get to the meanings of bigger parts (e.g. two cats). Plural sentences are particularly relevant to this larger enterprise as our theory of meaning does not capture them sufficiently so far. What seems to happen intuitively in our plural sentence above is that we `sum up` boys and cats that were fed by these boys in parallel. Yet, it is unclear how exactly this `summing-up` mechanism works and what exactly we are `summing up` -- for instance, do we merely want to `sum up` cats or also properties of cat-feeding? Is the phenomenon limited to nominal plural expressions like two cats? Or does it extend to other expressions where we intuitively `sum up` different kinds of `objects` (e.g., in the case of dance and sing)? And how do the meanings of expressions that permit such a `summing up` differ from those that -- at least at first sight -- don`t (like every boy)? Semantic theory (which deals with the meaning of natural language) offers different hypotheses in this respect, which, however, cannot easily be distinguished on the basis of an individual language like English -- one of the reasons being that there is always the possibility that a language will contain elements that are not overtly `realized`. Yet the different hypotheses diverge in their predictions concerning cross- linguistic patterns (for instance: If we made the assumption that English contains a `silent` element that makes a meaning contribution in plural sentences, we would expect that at least some languages realized this element overtly). The project will therefore investigate the predictions of the different hypotheses cross-linguistically, using the publicly accessible, recently developed Terraling database: In this database, researchers can pose questions for which other linguists will provide data from their respective native languages.

Sentences containing plural expressions can be true in a number of situations: The sentence `Two boys fed two cats', for instance, it true if boy 1 and boy 2 each fed two cats -- but also if boy 1 fed only cat 1 and boy 2 fed only cat 2. The so-called `truth conditions' of this sentence thus differ from those of the sentence `Every boy fed two cats', which is false in the latter situation (even if there are only two boys). This project intended to find out how the truth-conditions of plural sentences come about. But why would this be an interesting question? Our general aim, after all, is to understand the human `language faculty', thus we must investigate which objects can act as meanings for the expressions of human languages. Plural sentences are particularly relevant to this enterprise as our theory of meaning does not capture them sufficently so far. What seems to happen intuitively in our plural sentence above is that we `sum up' boys and cats that were fed by these boys in parallel. Yet, it is unclear how exactly this `summing-up' mechanism works and what exacly we are `summing up'. In order to target this question, this project focussed on cross-linguistic work, using the open-access, newly developed Terraling database: linguists provided data from their respective native languages, answering queries we formulated. The idea was that if there any special mechansims needed to permit the `summing-up' in plural sentences, these should be visible in at least some languages. What we found, however, was the `summing-up' seems to be a foundational property of human language -- e.g., none of the languages investigated showed any `extra' morphology necessary to yield a `summing-up' reading. This observation contradicts many `classical' semantic theories, which assume that human languages use expressions with `classical logical' meanings as their minimal building blocks. Moreover, we showed that these `classical logical' meanings (in the domain we investigated) always correspond to complex expressions and thus cannot act `primitive' building blocks. Furthermore, showed that even those expressions which at first sight seem to have `classical logical' meanings, often exhibit a plural-like (and thus not a `classical-logical') meaning. This raises the fundamental question whether human languages contain any `classical logical' expressions at all (even if these are complex). The fact that plural meanings are a basic component of natural languages raises the question which kinds of objects we can form pluralities from/ can be targeted by the afore-mentioned `summing up'. Intuitively, we can only `sum up' objects that are different. As our project shows that the `summing-up' can also target abstract object, we can conclude that the notion of difference involved must be abstract as well.