# 2.3 Words: dimensions

## Differences and similarities

We would like to be able to say more precisely how categories and in particular the meanings of words differ from one another. This would be a first step in coming up with a theory of meaning. The similarities and differences are ultimately based on facts about the world, but again it is the minds of people that focus in on some of them to create the categories that we think and talk about.

To begin to understand this, we need to start with individual objects rather than with categories. How can objects differ or resemble one another? You may already have discovered part of the answer to this question as you were doing Exercise 2.2. The easiest way to begin is to consider two objects that are very similar to one another and to try to describe their difference. For example, take two apples that are almost identical, except that one is a little larger than the other. These apples difference in size, or more precisely, in volume and probably also in weight. Between these two apples we can imagine many others that are again similar except for their size.

## Dimensions and values

Size is an example of an object dimension, and each object has a particular value on this dimension. Most of the time when we are comparing or contrasting objects on a dimension, we don't actually label specific values. For example, when we understand that two apples differ in size, we do not need to assign a number to the size of one or the other. We say that objects can differ "along" this dimension, which emphasizes how we can think of a dimension as a line, with each value on the line corresponding to a particular value on the dimension.

Size is an example of a dimension with many possible values. In fact, for any two sizes, we can always imagine a size that's in between them. The only limit on the number of possibilities is what we can distinguish. Note also that there isn't an obvious endpoint to size. No matter how small something is, it is possible to imagine something smaller (we don't normally think or speak about a size of 0), and the same is true for large sizes. Size is an example of what we'll call a continuous dimension. Finally, a dimension like size has another property; it has an ordering associated with it. For any two values, we can say which is "more" and which "less". We'll call a dimension like this an ordinal dimension. All of the continuous dimensions we'll be considering will also be ordinal.

Now consider another dimension, one that does not have a convenient name in English. I'll call it "livingness". This dimension has only two values: living and non-living. Things with the first value include plants and animals that are alive; things with the second value include things that have never lived like rocks and things that are no longer alive like potato chips. This dimension is clearly not continuous; we'll call a dimension like this that has a fixed set of values a discrete dimension.

Consider another discrete dimension, one that's more abstract than the ones we've been considering, a university student's major. The values on this dimension are the different majors that are possible: psychology, English, physics, history, etc. Obviously this is a discrete dimension since there is a fixed number of possible values (at least for a given university). But note also that unlike size, this dimension is not ordinal. There is no obvious way to arrange the different majors in an order: psychology is not "more" or "less" than history. (Of course we could use another dimension, like relative popularity, to assign an order to the values on the major dimension, but they are not built into the dimension itself.)

## Dimensions and categories

We started this section with the goal of being able to better describe the differences between categories, in particular, the categories that are the meanings of words. Now that we have the notion of dimension to help us describe differences in individual objects, we can use this to help us describe categories.

Returning to fruits again, let's consider what dimensions can help us distinguish different categories of fruit from one another. Size is clearly relevant: grapes are smaller than apples, which are smaller than cantaloupes. But what can we say about size for the category apple as opposed to the an individual apple. Obviously we can't assign a specific value on the size dimension to the category because apples vary in size. Instead we can think of a range of values for each dimension: the set of values on the dimension that are between that of the smallest possible and the largest possible apple.

Two points need to made about this idea of having a range of values associated with a category. First, remember that we are talking about categories as mental things. This means that it's not the possible sizes of real apples in the world that's at issue; it's what somebody thinks these values are. Second, we're not claiming that people have precise minimum and maximum values for each category they know. For convenience, we'll be treating these ranges as though they are precise, but it is probably true that the boundaries of these ranges for human categories are somewhat vague.

So size (and taste and smell color and various other dimensions) are clearly relevant to what makes an apple an apple. But many other dimensions are not. For one, academic major can't be relevant because apples don't have majors. But major is also irrelevant for some categories whose instances do have majors. Consider the category (university) sophomore. Obviously sophomores normally have majors, that is, in our terms, there is a value on the major dimension for each sophomore, but this major dimension has nothing to do with what makes a person an instance of this category. Sophomores can have any major. In other words, a dimension can be irrelevant for a category for two reasons, because instances of that category have no value at all for the dimension (apples and major) or because instances of that category can have any value for the dimension (sophomores and major).

We'll be encountering dimensions all throughout this course. They are fundamental to the description of both linguistic form and linguistic meaning. So it's important to get this concept under your belt before you go on.

## Exercise 2.3

If you haven't downloaded the version of the program for this unit, do that now:

### Instructions

Start up the program by double-clicking on its icon. Then click on "Show a random object" to get a new instance of the meaning of one of the words in the language. Now click on the button that says "Show meaning dimensions" to bring up a new window. (You should move this window out of the way if it's blocking the main window where you see the object.) In this window you'll see five rows of graphical icons and numbers. Each of these represents one of the five dimensions that distinguish objects and object categories in the MiniWorld world for this unit.

Click on "Show a random object" more times to figure out what the dimensions mean. For each dimension,

1. provide an English name or description for it
2. say whether it is continuous or discrete
3. say whether it is ordinal or not

Now click on "Show all word forms" to open the word forms window. Select different word forms to bring up a number of examples of each so that you can get an idea of what each of the meaning categories is. Then for each word,

1. say which dimensions are relevant for the category and which irrelevant
2. for relevant dimensions say what the range of values (for continuous dimensions) or what particular value defines the category