# 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:

- Easy to explain
- Do what you want most of the time
- Provide a straightforward way to do non-default assertions
- Work with singletons and masses
- 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. Without a quantifier we don't know exactly how many students have wrapped themselves around the building but whether it be one, two or all the students they all surround it the same. There is no default quantifier. But, for {lo} and {le} the distributivity is. If we quantify to make explicit we want to talk about a specific number of students, a similar result arises:

mu le tadni cu sruri le ckule

Here we are being explicit about how many students each surround the building; In this case five. But it doesn't actually matter specifically how many students there are. When we specifically quantify our descriptions with outer quantifiers we create a plurality. When we predicate plural descriptions we assert the proposition on each thing that makes up the plural. Even if we specifically say there is single student which surrounds the building, if we consider that a 'plurality' of one it still works out. The distributivity doesn't end up mattering with a single referent so the rule is nice and general. All quantified descriptions or plurals are distributive.

le mu tadni cu sruri le ckule

^{TODO: how does inner-quantification change the semantics here? Are we making a mass of a five constituents, which we then ask to be predicated distributively? That would seem odd. It almost seems tautological to simply {mu tadni} or {mu lo tadni}. Xorlo says that its ambiguous to whether it creates a mass or not. I say it shouldn't.}

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).

mu lei tadni cu sruri le ckule

Unlike inner-quantification with groups which specifies how large the group is, outer-quantification tells us how many groups there are. In this case that would be, five groups of students surround the building. But is it distributive over the various groups? It is infact, because outer quantifiers create pluralities just with {lo} and {le}. It doesn't matter what kind of description you're quantifying. As soon as it gains an outer quantifier the description demands being predicated distributively. That means in our example, each group of students surrounds the building independently. If you have a hard time visualizing this, imagine there are 50 students standing around the school. 10 are wearing white shirts, 10 black shirts, 10 red shirts and so on. Each individual group of students is surrounding the building. But no individual constituent student is surrounding the building.

lei mu lei tadni cu sruri le ckule

Here we just get fancy to see what happens. We have a base description of {lei tadni}, a group, which we then quantify on the outside with {mu} giving us five cohesive groups of students. We then throw {lei} around that! So what do we get? We now refer to a super-group comprised of the five smaller groups and we assert that they, the give groups, surround the building. To distinguish this in your mind from the previous example, imagine that each group of varying colored students is compact so that no individual group surrounds the building. But the groups themselves are layed out in a circle, like the points of a pentagram around the circle. Now it can be said that the five groups of students surround the building, but no individual group surrounds the building and further no student surrounds the building. The statement doesn't necessarily exclude the possibility that the students are arranged in the previous example where each group is equally diffused around the building; because of course even in this case, the super group can still be considered to be surrounding the building - but it doesn't necessitate that to be true any longer.