Chapter 5 Classification Systems

Clarity and precision are important for critical thinking. Using words or concepts in a fast and loose manner is an invitation to errors of many kinds. It is now time to talk about the importance of precision and clarity in our use of words and symbols for critical thinking. First, we will discuss how words classify and what they refer to, and after that, we will turn to the discussion of the importance of definition.

If we reflect on maps, it is clear that different maps or parts of maps may classify what they represent in different ways. Consider a road map of Ontario. Cities and towns may be represented by circles of different sizes, where the size of a circle represents population, but they could also be represented by squares representing the physical size of the urban area. Different ways of representing Ontario might be good for different purposes, and one can imagine specialized maps that identify cities and towns by economic activity, treaties, religion, quality of drinking water, or even the number of claimed UFO sightings.

Maps are just one sort of system of representing the relationships of objects classified in different ways. Our theories and hypotheses similarly vary in the ways in which they classify the things that they represent. The concepts we use do not simply list the things in the world but organize them into patterns; in fact, there is no way to list things without classifying them in some way. Here is an example. Suppose Karen, who lives in North Bay, has a brown long-haired dachshund named Mabel that likes cornflakes, naps in the sun, and has once bitten the postal worker. Mabel may be known in the neighbourhood as “that sleepy wiener dog,” “Karen’s pet,” or “lil’ bitey,” and each of these terms will function like a name picking Mabel out from the other things in the neighbourhood. In this case, those names pick out a unique individual. But what if terms are used to pick out a number of things with common properties, such as “dachshunds”?

This is where we start to make classes, or build a classification system. We can refer to Mabel as a brown dog, in which case we are saying Mabel is a member of the class of all things that are brown dogs. We are saying Mabel belongs in this group because she and the other members are similar in some respect. Mabel is also part of the class of all things who are “animals that have bitten a postal worker,” of which a quick google search reveals cats are also a member. In fact, there are indefinitely many terms that have Mabel as a referent (“weighs less than one million kilograms,” “is wingless,” “cost more than four hundred dollars,” “lives in North Bay,” “is not a mountain lion,” “is not immortal,” and so on).

5.1 Building a Classification System

We classify things for many different purposes, and so there are many possible classification schemes.

By definition, classification is a kind of division according to a rule: a group of individuals is divided into subgroups by a rule that sorts them by a set of common properties.

Imagine that you have a pile of toys and you want to sort them into groups so that you can put them away on a set of shelves. You might put all the Legos on one shelf and all the stuffies on another and all the dolls on a third. You could label each shelf (“the Lego shelf,” “the stuffy shelf,” and so on) so you know what to put there. A good classification scheme would divide the toys into a coherent set of groups, where each group went on a different shelf, and each and every toy was assigned to only one group, such that every toy had a place on one shelf or another.

Imagine that you decided to put stuffies on one shelf and red things on another shelf and Legos on a third. If none of the Legos or stuffies were red, this system might work well enough, but suppose one of the stuffies was red (not to mention all the tiny red Lego pieces). Now you have a problem: Your rules of classification would tell you to put the red stuffy on two different shelves—the shelf for stuffies and the shelf for red things. Of course, you can’t put it on both shelves at the same time. So your classification system would fail to tell you where to put stuffies (or Legos) that are red. A good classification scheme won’t do that. Here are the rules we will use to build a good classification system:

The first two rules of classification, that a scheme should be exhaustive and exclusive, have the consequence that everything in the group being classified is put into a group and only one group; the other two rules are aimed at usefulness.

We can all understand that the rotten potatoes don’t have to be divided by size (yuck). So we have three categories then: big keepers, small keepers, and rotten non-keepers. How do you know which potatoes are big and which are small? That is another classificatory distinction that requires a rule. In this case, the circumstances will determine which are big and which are small. If this particular kind of potato only ever grows really big or very small, this task is easy. Or maybe only the middle-size ones rot, making it easy to differentiate big from small. But it seems like potatoes usually have varying sizes and rot somewhat randomly. This means you will need a clear-cut boundary for how to divide the potatoes by size. This exercise in thinking about potatoes is to show how what potatoes are like and what we want to do with them will in part determine the kind of classification scheme. There are a number of assumptions about potatoes and our purposes that make the classification scheme adequate or inadequate.

Many things, particularly natural kinds and manufactured objects, come already classified in certain ways. Paper money, for example, comes only in certain denominations. New cars come in a finite number of models and colours, and metals are either iron or gold or tin, and so on.

Key Takeaways

• Objects get classified together in groups because they are similar in some respects.
• Classification systems help us organize the world by dividing individuals into subgroups using a rule that sorts them by a set of common properties (e.g., brown dogs).
• Classification systems must be exhaustive: nothing is left out.
• Classification systems must be exclusive: groups don’t overlap.
• Classification systems must be clear: rules need to be understandable.
• Classification systems must be adequate: it needs to do its job.
• The first two rules of classification systems (i.e., exhaustive and exclusive) ensure that everything being classified is put into only one group; the latter two (i.e., clear and adequate) ensure that the classification system is useful.
• The kind of a thing being classified determines, in part, the kind of classification scheme that is accurate.

Exercises for Classification

Part I. Classification Practice

Evaluate these classification schemes. Are they exhaustive, exclusive, clear, and adequate to the task? If so, say why. If not, explain why.

1. (Toys) Very small things go on the top shelf. Large stuffed animals go in the box. The books go on the middle shelf and everything else goes in the closet.
2. (Marble collection) multi-coloured solids, the clear coloured, the clear colourless with swirls inside, and the clear colourless without swirls inside.
3. Big animals, scary animals, smelly animals, animals named George.
4. Friends (be nice to them), people who can hurt you (be nice to them), everyone else (who cares?).
5. My mom, my brothers and sisters, my parents, my friends, the people I hate, everyone else.
6. (Kinds of animals) Pets, vermin, game, work animals, food animals.
7. (Pre-season list for the coach) Last year’s returning players, kids with attitudes, losers, kids who are promising but need more skills, kids I can’t tell about yet.

Part II. Create a Classification System

Think of a number of different things that are small enough to put on a shelf. List ten of these things picked at random. Now make a classification system that will sort and organize them onto three shelves that puts like items on like shelves. (Don’t cheat by picking things that will clearly fit the classification system; pick the things first.)

Chapter 6. Definitions