Plurality by example

This page attempts to explore an 'easy to explain by default' interpretation of the various gadri and how they affect propositional distributivity in the case of plurality and masses. In other words, what are the different way we can make distributive and non-distributive assertions on different kinds of referents? For our case, we'll start by giving some simple definitions of the gadri and then attempt to use them to determine whether they satisfy the following desired characteristics:

1. Easy to explain
2. Do what you want most of the time
3. Provide a straightforward way to do non-default assertions
4. Work with singletons and masses
5. Work with individual and plural descriptions

To restrain the scope of this page, we can consider the difference between {lo} and {le} (and their various counter-parts) as irrelevant and orthogonal to the discussion.

Introduction

Brief definitions of gadri

• lo/le: Identifies a referent to be predicated distributively. Whatever the description refers to, we assert propositions on the things that make it up.
• loi/lei: Identifies a referent to be predicated non-distributively. Whatever the description refers to, we assert propositions on that as a cohesive unified object.
• lo'i/le'i: not used

Other necessary cmavo

• lu'o: Identifies a referent to be predicated non-distributively. The referent is the cohesive constituency made up by the provided sumti.
• lu'a: Identifies a referent to be predicated distributively. The referents are any constituents making up the provided sumti.

Examples

The students surround the school.

le tadni cu sruri le ckule

When we use {lo}/{le} we are asking that the referent be predicated distributively. In this case, we claim that any students being referred to, each independently surround the school. A frightening notion and probably not the intended message. Here we assume that the description {le tadni} has been made to refer to more than one student. However, if we quantify to make explicit we want to talk about only one student a similar result arises:

pa le tadni cu sruri le ckule

Here we explicitly remark that it is one student which surrounds the school but the non-distributivity is the same.

le pa tadni cu sruri le ckule

^{TODO: how does inner-quantification change the semantics here? Are we making a mass of a single constituent, which we then ask to be predicated distributively? That's my intuition.}

lei tadni cu sruri le ckule

However when {loi}/{lei} is utilized, we ask that the referent be predicated non-distributively. In this case, we are constructing a description which declares that there is some object for which is made up of one or (usually) more constituents that all satisfy {tadni}. A group, a mass, a collective, a cohesive constituency. While the description predicate of the sumti defines the qualifications of the constituents (that each satisfies {tadni}) the resulting referent is an abstract object that represents the whole. It is this collective or mass which becomes the subject of the description.

Therefore, due to the non-distributivity of {loi} and {lei} we are actually remarking or asserting a proposition about that collective, rather than on the individuals. With this, we escape the gruesome fate of the pupils and we achieve communicating what we actually intend. That is to say, there is a group of students which as a whole surround the building.

lei mu tadni cu sruri le ckule

So how does quantification affect non-distributive descriptions? That's an interesting question. The most straight-forward interpretation of this example is probably that there is a mass of 5 students which surround the building. Essentially the same as the unquantified non-distributive example but we're simply being explicit about just how many students the collective mass is comprised of. We still end up with a description whose referent is some abstract constituency and we're still asserting a proposition about that group (in this case, of 5 students).