Philosophers often draw distinctions. They divide up a set of things into two or more categories according to some principle(s) or criteria. In ethics, we might see a philosopher attempt to categorise actions into ‘Moral’ and ‘Immoral’, or into ‘permissible’ and ‘prohibited’. In the philosophy of science, philosophers have tried to categorise theories into ‘scientific’ and ‘pseudoscientific’, and people into ‘scientists’ and ‘non-scientists’. The architecture of distinctions can be very useful.
This means we need a robust way to evaluate distinctions. What makes a good or useful distinction?
To draw a distinction, we need three things:
- A domain. This is the set of things which we want to categorise.
- Categories. Two or more different groups into which the domain is going to be sorted.
- Criteria. The rules or principles according to which we’ll perform the categorisation.
For example, suppose we want to distinguish between different types of animal. Our domain is all the animals. Our categories are, say, “Birds”, “Mammals”, “Reptiles” and “Amphibians”. We put forward a series of taxonomic criteria to decide what makes a creature a mammal, a bird, and so on (e.g. “Mammals are warm-blooded and produce milk for their young”; “Reptiles are cold-blooded and have scales, not fur or feathers”, etc.).
The goal when making a distinction is usually to provide a proper distinction.
“Exhaustive” means that everything in the domain falls into at least one category. Nothing is left out.
Suppose we tried to distinguish between morally obligatory and morally prohibited actions. This distinction would not be exhaustive, as there are some actions which are neither obligatory nor prohibited—they are permitted but not obligatory.
“Mutually exclusive” means that nothing from the domain falls into more than one category. Nothing meets the criteria to be in multiple categories.
Suppose we distinguished between “actions with good consequences” and “actions with bad consequences”. This distinction would not be mutually exclusive, because some actions have both good and bad consequences, so would fall into both categories.
Taken together, exhaustiveness and mutual exclusivity mean that a proper distinction places everything in the domain into one and only one category.
Evaluating a distinction
When we see distinctions being drawn in philosophical work, we should ask two questions:
- Is it exhaustive?
- Is it mutually exclusive?
Sometimes, to answer this question, we’ll have to spell out the distinction in more detail. Often, the criteria or the domain are left vague. It’s very important to do this with the Principle of Charity in mind.
Look for things which fall into multiple categories, and things which do not fall into any category. If a distinction is not exhaustive or mutually exclusive, then a philosophical argument based upon it might fail.
To show that a distinction is not exhaustive, we need only to show that there is something which doesn’t fit into any category. A single example will usually suffice. For example, suppose a philosopher writes: “There are three kinds of philosopher: German idealists, British empiricists and Ancient Greeks.” These categories are mutually exclusive, as no philosopher can fall into two or three of them. But it is not exhaustive. A single French philosopher, for instance, will show as much.
Why does it matter if a distinction is not exhaustive? Distinctions are often drawn in arguments in order to prove a claim category-by-category, or to create a dilemma. But if the distinction is not exhaustive, it risks posing a false dichotomy.
There is a cheap and easy way to ensure that a distinction is exhaustive: by adding a catch-all category, such as “Others”. If there is such a miscellaneous category, the distinction is exhaustive, but it will be very difficult to say anything meaningful about the members of that category, making the distinction less valuable for philosophical work.
To show that a distinction is not mutually exclusive, we must provide an example of something from the domain that fits into multiple categories. For example, if I divide all actions into ‘Morally obligatory’, ‘Morally permissible’ and ‘Morally prohibited’, then there may be a problem: it seems that obligatory actions must also be permissible. So, many actions will fall into both of those categories.
Mutual exclusivity may or may not be a needed property for a distinction. But if a distinction does allow this kind of overlap, then philosophers making use of it must be careful about the claims they make to ensure that they are consistent.
Not every distinction which fails to meet the criteria for a proper distinction lacks value or is worthy of criticism as a result. If the distinction can still fulfill its purpose despite lacking exhaustiveness and/or mutual exclusivity, then that is fine. But it is important to be aware of the consequences of lacking these properties and to scrutinise such distinctions and arguments based upon them.
The Celestial Emporium of Benevolent Knowledge
The fiction of Jose Luis Borges is fertile ground for interesting philosophical curiosities. In one of his essays, Borges invents an encyclopedia known as The Celestial Emporium of Benevolent Knowledge, which divides all the animals of the world into these categories:
(a) those that belong to the emperor,Jose Luis Borges (1942) ‘The Analytical Language of John Wilkins’ in Otras Inquisiciones (Sur)
(b) embalmed ones,
(c) those that are trained,
(d) suckling pigs,
(f) fabulous ones,
(g) stray dogs,
(h) those that are included in this classiﬁcation,
(i) those that tremble as if they were mad,
(j) innumerable ones,
(k) those that are drawn with a very ﬁne camel’s hair brush,
(m) those that have just broken a ﬂower vase,
(n) those that resemble ﬂies from a distance.
Is this baffling assortment of categories a proper distinction? Take a moment to decide whether it is exhaustive and mutually exclusive.
The Celestial Emporium does not provide a proper distinction of animals. Many of the categories have significant overlap (which was Borges’ point) – there could be a stray dog which has just broken a flower vase, an embalmed suckling pig which belongs to the emperor, and so forth. But the distinction is exhaustive – there is a catch-all category “(l) others” which ensures this.
But actually things get more complicated: there is also category “(h) those that are included in this classification”. This means that in fact everything which appears in at least one category will appear in multiple categories. A suckling pig is also included in the classification, so appears in (d) and (h). This creates an interesting philosophical paradox! We have “(l) others”. What are ‘others’ if not things which aren’t included anywhere else in the classification? So if something belonged to no category, it would belong in (l) – but that would mean it now qualifies for (h)! And now, since it’s part of (h), it would no longer qualify for (l). But if it doesn’t qualify for (l), it can’t qualify for (h) – and so on.
It turns out that distinctions can also become paradoxical! The most common source of paradox within distinctions is self-reference. Where categories refer to other categories or to the classification itself, we can get into serious trouble.
Try analysing the following distinction to check your understanding. Are they exhaustive, mutually exclusive, both or neither?
Categories: Mammals, Fish, Sheep, Others
Domain: Planets of the solar system
Categories: Rocky planets, Gas giants
Domain: Living things
Categories: Animals, Fish, Plants
Latest edit: 05/11/2021 by CJ Blunt