Here are just four among the many types of definitions:
(1) Definition by synonym;
(2) Ostensive definitions;
(3) Stipulative definitions, and
(4) Analytical definitions.
The appropriateness of a definition is measured by its usefulness. There are contexts in everyday life where somebody may offer you a definition, and you may think, “Gee, that’s funny. This person just gave me a definition, and I still don’t have the answer to my question.”
(1) For example, you may be talking to somebody about a fairly serious matter, like capital punishment. In the course of such a conversation, the issue of justice may arise. Feeling that you are getting nowhere on the topic, suppose you say, “Hey, could you define what you mean by justice, so that I can have a clearer understanding of what you mean?” Your interlocutor, or partner in conversation, may then say: “Sure. Justice is fairness. There – you asked me for a definition, and I’ve given you one.”
Do you sense that there’s a problem with the above definition? Actually, the problem with this definition is a standard weakness of definitions by synonym. Briefly, the problem is that if you don’t already have a fairly clear and robust understanding of the word (or words) being used to define the word you want defined, then the word being defined is still going to be unclear or (to use a visual metaphor) “un-illuminated” for you. In other cases, however, where you do know the meaning of the word(s) used to define the word you want defined, definitions can be quite useful indeed. So, for example, if you are reading for a part in a play, and the stage directions instruct you to “move with alacrity across the stage,” it does help to know that ‘swiftness’ is a synonym for alacrity. This latter, then, is a context that makes clear the strength of definitions by synonym. Remember, then, that it is the context that determines the appropriateness of the type of definition used, and that this is determined by its usefulness within it.
Did you notice in the above paragraph how hard it was to refer to the word being defined, and the words used to define it? It is for this reason that we substitute the word definiendum for ‘the word to be defined’, and the word definiens to refer to the words that actually illuminate the definiendum. As a mnemonic device, you might think of the definiendum as the “dumb word,” or the word about which you are initially ignorant, and for which you hope to acquire some enlightenment or understanding. We can now say that the strength of a definition by synonym is that if you know the meaning of the definiens, then you add the definiendum to your vocabulary; while the weakness of a definition by synonym is that if you do not know the meaning of the definiens, then this kind of definition is useless since it will not enlighten you regarding the meaning of the definiendum.
(2) Ostensive definitions are definitions by example. An example of such definitions that is often used in Introduction to Philosophy courses is a quote from Euthyphro, an acquaintance of Socrates, who said: “Piety is what I am doing, namely prosecuting a wrongdoer.” Notice that this is an example of an intangible or abstract idea – piety. Ostensive definitions are not limited to such contexts, of course: I could very easily explain the meaning of the word ‘cup’ by pointing to a cup, and that too would then be functioning as an ostensive definition. The strength of such definitions is that they give the inquirer a literal example of the definiendum, and one example is usually – but not always – better than none. Moreover, there are contexts in which such a definition is in fact the most desirable kind, since there are some contexts in which knowing quickly what something means, is the surest way of accomplishing the task at hand. Can you think of one such context?
There is a very important weakness associated with ostensive definitions, however: ostensive definitions do not tell us what features of a definiendum are the ones that are relevant for the example’s inclusion in the class of objects (or abstract ideas) being defined. Because of this, it is theoretically possible to include items in the definiendum class, which should be kept out of it; and it is likewise possible to allow into the class, items which should be kept out. Below is an example that illustrates this weakness.
Suppose Xylo [pronounced like “sigh-low,” only with an initial “z” sound] is from the planet Quantum, and Xylo has just recently acquired a fairly good grasp of English and of Earthling cultures. Somehow, however, until today Xylo has never before heard the word ‘cup’. So Xylo asks you, “What is a cup?” and, quite reasonably, you show Xylo a cup and hope he quickly grasps the definition of a cup. The next day, however, Xylo approaches you with a pair of sunglasses and says, “Thank you for teaching me the meaning of the word ‘cup’. I too, now, have a cup. Here is my cup,” and Xylo thereupon holds up his sunglasses for you to inspect. What has gone awry? To complicate matters more, suppose that you point to a cup and Xylo says, “But that cannot be a cup.” Why might Xylo do this? Think hard about the limitation of ostensive definitions in order to answer these two questions. One tidy way of summarizing the weakness of ostensive definitions is to say that they fail to state either the necessary or the sufficient conditions for inclusion in the definiendum class.
(3) Stipulative definitions are definitions that amount either to coinages of new words (called neologisms), or that define familiar words in ways so different from ordinary usage, that they might almost appear to be new words (although strictly speaking, their meaning is what is new, rather than they themselves). Take the word ‘mouse’. Today we associate this word with external devices used to move the cursor to various locations on a computer monitor. A generation or so ago this would have been thought insane (and unmarketable)! The word ‘mouse’, used in this way, was then stipulated (by Steven Jobs?) to refer to this device, sometime in the nineteen-eighties, I believe. In a rather similar vein, in philosophy programs at colleges, we stipulate that ‘validity’ means the property possessed by those arguments in which, if the premises are all assumed to be true, then the conclusion must be true as well. Notice how wildly different this usage of the words ‘valid’ and ‘validity’ is from everyday usage! Now, philosophers don’t regard their definition as stipulative, although it is recognized by them to deviate from general social usage. Therefore, we might say that whether or not a given definition is stipulative, is to some degree a matter determined by the exclusiveness of the group using it.
Does the above constitute a weakness of stipulative definitions? Actually, it may be both the strength or the weakness of stipulative definitions. This requires an explanation: On the one hand, by saying exactly how you are using a word, you are assisting your interlocutor (conversation partner) in following along with whatever you are discussing. On the other hand, if your goal is to make a clear case for something by appealing to a special definition you apply to a term, then you aren’t going to be terribly successful making your case in situations where your meaning is highly idiosyncratic. Suppose, for example, that you define ‘murder’ as ‘the taking of life’. Can you do this? Sure! You can define a word any way you wish to! But if you are discussing a serious moral issue, and you define murder this way, and then accuse your friends of being murderers because they take the life of vegetables by picking them off their vines, you are unlikely to persuade them. Why? Because this is a context in which a stipulative definition is not useful, and it is for that reason that it is inappropriate. It doesn’t help you solve the problem you want to solve. (Did you see the romantic comedy Notting Hill, starring Julia Roberts and Hugh Grant? In this movie, Grant’s character winds up on a date with a woman who declares herself a fruitarian – she regarded it as complicity in murder to eat anything that hadn’t fallen off of a tree of its own accord.) Identify at least three popular neologisms, and then invent one of your own (see question 10 below). Try, too, to give expression to a clear context in which a stipulative definition has failed because of its deviation from normal usage.
Stipulative definitions may be given of abstract terms like ‘justice’, as well as of physical objects like a mouse. Furthermore, they may be given to familiar words, like the foregoing two examples, and they may also be applied to concepts or objects that have not been distinguished from others, or -- just because it’s enjoyable to make up new words – to concepts or objects for which words already exist. All words begin by being stipulated; social acceptance determines when they cease to be neologisms. Dictionaries and social discourse both help us determine the status of such words. When in doubt, it is usually a good practice to stipulate the way in which you are using a word (or phrase).
(4) Analytical definitions are the definitions most commonly prized by mathematicians and Western philosophers and scientists. The reason is that these definitions state the necessary and sufficient conditions for the definiendum – that is, they do precisely what ostensive definitions inherently fail to do. In the West, their strength has often been thought to be that if you have given a genuine analytical definition of a concept, then by the same token, you guarantee genuine understanding of the definiendum. In other words, to successfully analyze a concept, is (at least by Western standards) to have knowledge of the definiendum. Ask yourself if knowing something is always a matter of “breaking a thing down” into its parts.
The weaknesses of such definitions are that they are extraordinarily hard to arrive at, and even if you do, one might wonder how you would know that you had done so! (John Rawls, a well-known political philosopher, tried to give an analysis of justice in his famous book published in 1971, A Theory of Justice. Visit your library to see how many pages it took him to do so!) This idea, or ideal, of analysis is manifest in the general method of science. Those practices attempt to solve problems by “breaking them down” into their constituent parts, and then breaking the constituent parts down into their constituents, and so on and so forth, until no more division is possible. By clearly understanding each “part” (whether abstract or physical in nature), the idea is that if you can isolate precisely what it takes to be such a part, then there is no way of confusing it with any other part, and there is likewise nothing left to say about it in isolation. This is tantamount to arriving at the essence of the definiendum. A statement of the essence of something answers the question: “What is it that makes this thing the thing that it is, and nothing other than that?” If you know the answer to this question, of any given thing, could you possibly say any more about it, or would that constitute certain knowledge of what that thing is?
Questions to answer:
1. What determines the appropriateness of a definition-type?
2. What is the strength of a definition by synonym?
3. What is the weakness of a definition by synonym?
4. What is the strength of an ostensive definition?
5. What is the weakness of an ostensive definition?
6. What is the strength of a stipulative definition?
7. What is the weakness of a stipulative definition?
8. What is the strength of an analytical definition?
9. What is the weakness of an analytical definition?
10. Invent three neologisms, and explain how you came up with them.
11. Give three examples of analytical definitions. (Hint: Mathematical examples tend to be the easiest, but try doing one for, say, mayonnaise! Maybe “wheel” would be a fun one, too.)
12. Try to answer the question of whether you think the Western assumption is correct or incorrect, being sure to say why you do or do not.