Chapter 3: Definitions of Critical Thinking

Definitions 

• Definitions are very useful in explaining and clarifying meaning. A typical definition has two parts:
• The definiendum: (the term being defined) <a word>
• The definiens: (the words that define the definiendum) <definition>
• For Example, bachelor (definiendum) = unmarried man (definiens)
  People often use is instead of the equality sign in giving definitions—for example, a bachelor is an unmarried man. 
• A term is a referring expression in a language made up of one or more words, such as The United Nations, Beethoven, mammals, purple, etc.
• The referent of a term is what the term refers to. So the terms listed above refer respectively to an organisation, a person, a class of animals, and a particular shade of colour. A term such as Mount Everest refers to a real physical thing in the world, but other terms such as truth and 13467 refer to more abstract things. The set of things a term refers to is known as the extension of the term. So dolphins, humans, donkeys, gorillas, etc. are all within the extension of mammals.
• The concept associated with a term is an idea that encapsulates our understanding of the term. Although a term is made up of words, a concept is not. Agua is a Spanish word distinct from the English word water. They have different spelling and pronunciation, but they have the same meaning and express the same concept.
• Definitions can be divided into three kinds according to their purpose: stipulative, reportive, and precising.

1. REPORTIVE DEFINATION

• A reportive definition is also known as a lexical (relating to words) definition. It reports the existing meaning of a term. Here are some examples: 
• Prime number = any integer (a whole number) greater than 1 and divisible only by 1 and itself. 
• WTO stands for "The World Trade Organisation". 
• Sushi is a kind of food made with vinegar rice with some meat or vegetable topping.
• Reportive definitions are useful for learning new words in a language. The main criterion for evaluating a reportive definition is that the meaning of the definiens should match the meaning of the definiendum exactly. This means the definition should not be inconsistent with the existing usage of the term in question.
• Suppose someone consults a very old dictionary that defines a computer as "a person whose job is to carry out mathematical calculations." This definition was before modern electronic computers were invented. It is inconsistent with how we actually use the word computer today, and so it is no longer a good reportive definition. 
• A correct reportive definition should not be too wide or too narrow. A definition is too wide if the definition applies to things that the definiendum does not apply to. 
• For example, defining an airplane as a flying machine is too wide, since helicopters are also flying machines but they are not airplanes. There are plenty of flying machines within the larger circle that are not airplanes, such as helicopters, rockets, and airships. 
• A definition is too narrow if the definition fails to include things to which the definiendum applies.
• Consider the definition of religion as any belief system that includes worshipping a god who created the universe. This definition is too narrow since it excludes religions that do not suggest a creator, such as Jainism and certain versions of Buddhism.
• A definition can be too wide and too narrow at the same time. Suppose someone defines bravery as "not running away from danger". 
• The definition is too wide because even a coward might fail to run away from danger. Perhaps he is immobilised by fear, or perhaps he does not even realise that he is in danger. 
• The definition is also too narrow because a person can be brave even if he avoids dangerous situations. Bravery does not require stupidity. There is no reason why a fireman who escapes from a burning building cannot be brave. 

2. STIPULATIVE DEFINATION (stimulate)

• A stipulative definition is used to assign a new meaning to a term, whether or not the term has an existing meaning. If the stipulative definition is accepted, then the term is used in the new way that is prescribed. Suppose we agree to define IBM to mean "incredibly boring movie". Once this is accepted, we can then say things like "Cable TV is showing another IBM right now.”
• Stipulative definitions are not just for secret codes and acronyms. They are also used to introduce new technical terms—for example, quark (physics), priori (biology), risk premium (economics). 
• In a stipulative definition, the meaning of the definiendum is completely determined by the meaning of the definiens, whatever it is, so the question of whether it is too wide or too narrow simply does not apply. 
• NOTE: If you define a term more than once, make sure that the definitions are equivalent. Otherwise, confusion might arise due to inconsistent definitions. 

3. PRECISING DEFINATION

• A precising definition is something in between reportive and stipulative definitions. 
• The function of a precising definition is to make the meaning of a term more precise. Suppose a bus company wants to give discounts to old people. If the company simply declares, "old people pay only 50% of the full fare," this would be too vague because it is not clear when a person becomes old. Some people might say that being 60 is old, but others might disagree. To avoid disputes and uncertainty, the company might define an old person to mean "any person of age 65 or older.”
• One major function of precising definitions is to make laws and regulations more precise, so there is less uncertainty regarding their application.
• Precising definitions are also useful in resolving verbal disputes. The American philosopher William James (1842-1910) once told this story about some hunters in a forest. 
• One of the hunters was standing on one side of a tree and there was a squirrel climbing on the other side of the tree trunk. The hunter tried to look at the squirrel by walking around the tree, but the squirrel kept moving around the tree as well and always stayed on the opposite side of the tree trunk. Now the hunter certainly circled the tree, and the squirrel was on the tree. But did the hunter go around the squirrel or not? The hunters entered into a heated debate about this, and it was left to James to resolve. He explained that it all depends on what go round means: 
• This is a dispute that a precising definition can resolve. The ordinary meaning of go round is not precise. Verbal disputes are contrasted with factual disputes, which are disagreements about facts rather than meaning. If someone thinks Sydney is the capital of Australia and others disagree, then this is a factual dispute that can be resolved by checking the facts.
• Many disputes are a mixture of verbal and factual disputes, and we should separate them out to advance the discussion. 
• Take the question of whether nonhuman animals have language. To answer this question, we should be more precise about what language means. If it refers to any system of communication, then obviously birds and other animals have languages, since they do communicate with each other. 
• On the other hand, language might also be used in a different sense, requiring the use of words to form sentences according to a system of grammar or being able to communicate about random objects and situations, including those that might be far away and distant in time. Given this definition, many animal communication systems do not qualify as languages. It is of course possible that some mammals such as chimpanzees might possess language in this more sophisticated sense. 
• Precising definitions allow us to refine questions, so we can gain a better understanding of how to answer them. 

CRITERIA FOR GOOD DEFINITIONS

• In the previous section, we said that a reportive definition should not be too wide or too narrow. Here are more criteria for evaluating all kinds of definitions, not just reportive ones. 
• Use Intensional Definitions if Possible
• There is a distinction between the extension and intention of a term (or concept). The extension of a term is the set of things to which the term applies. For example, the extension of a prime number is a set of numbers {2, 3, 5, 7, 11, 13,...}. 
• The intention of a term is its meaning. The intention of a prime number would be "any integer larger than one which is completely divisible only by one and itself." 
• When we define a term, should we define it by extension or intention? It depends, but we should use an intensional definition where possible. 
• A term such as human being has a very large extension. It is impossible to define the term by listing all the human beings there are. An intensional definition is better. 
• However, in some situations, an intensional definition might not be available. The seven deadly sins, for example, is understood as referring to pride, greed, envy, anger, lust, gluttony, and sloth. There is of course a long story about the history of the term and why it is these seven sins that appear on the list. However, this history is not relevant to the definition of the list. 
• Avoid Circularity
• A good definition should avoid circularity. A circular definition is one where the definition cannot be understood without knowing the meaning of the definiendum. Consider the definition of time as "a quantity measured by clocks or watches." 
• This definition is circular because we cannot fully explain what clocks and watches are without taking them as instruments that measure time. 
• Similarly, sometimes people say "the meaning of life is to search for the meaning of life." This sounds profound, but taken as a definition, it is hopelessly circular and does not make much sense. 
• If the meaning of life is to search for the meaning of life, then it follows that the meaning of life is to search for a search for the meaning of life, which is to search for a search of the meaning of life, and so on. 
• Avoid Obscurity (unimportant)
• Definitions should avoid obscure and metaphorical language as far as possible. "Science is searching for a black cat in a dark room" might convey an amusing image of the difficulty of scientific research, but as a definition, it is too obscure to tell us much about the nature of science. 
• However, a reportive definition should not be more precise than the term that is being defined. A ship might be defined as a vessel of considerable size for navigating on water. This definition is vague because it is unclear what considerable size means (But this is in itself not a good objection to the definition, because our concept of a ship is vague in exactly the same way). 
• Defining a ship as a vessel longer than 30 meters will make the definition too precise and end up distorting the ordinary meaning of the word. 
• Avoid Persuasive Definitions 
• Definitions should also avoid inappropriate emotional connotations. A persuasive definition is a definition that attaches a positive or negative emotional meaning to a term when there is in fact no such association. 
• For example, if someone defines democracy as "dictatorship by the poor and the uneducated," obviously such a person does not think very highly of democracy. But whether democracy is a good or bad thing should depend on further arguments and not be decided solely by a definition. 
• Similarly, consider the definition "abortion is the termination of pregnancy by murdering an unborn child." This definition assumes that abortion is wrong because it classifies abortion as murder. But it is surely possible to understand abortion in a more neutral way. 
• The biased definition that is proposed distorts the ordinary meaning of the term. This is not to deny that a persuasive definition can be a useful rhetorical tool. They are often used in debates and political speeches, but we should avoid them in a rational and fair-minded discussions.

DEFINITION TECHNIQUES

Some of the different ways of formulating a definition are listed below:

• Definition by Synonym: In a definition by synonym, a word (or a short term) is defined by giving another term that has exactly the same meaning—for example, physicians = doctors, lawyer = attorney, ameliorate = improve, and prognosticate = predict.
• Definition by Ostension: An ostensive definition explains the meaning of a term by giving examples, as when we explain the meaning of red to children by pointing to examples of red things. Or someone might explain a professional as "people like doctors, lawyers, and accountants." 
• Ostensive definitions are useful when it is difficult to explain the meaning of a term precisely. But an ostensive definition is a form of definition by extension, and intensional definitions can explain meaning better if they are available. 
• Definition by Genus-Differentia: The genus-differentia method is a very useful tool for constructing definitions. According to this approach, when we want to define a term, first we identify the broad category that the term is supposed to apply to. This category is known as genus. 
• To define a mule, we note first of all that a mule is an animal. 
• Of course, there are many kinds of animals other than mules. So the next step is to identify the differentia. This is the property that separates the items in the genus into two groups—those that fall within the extension of the definiendum, and those that do not. In the case of mule, this would be the property of being the offspring of a male donkey and a female horse. Putting the two parts together, we arrive at the full definition: 

A mule is an animal that is the offspring of a male donkey and a female horse. 

• Definition by Genus-Differentia: This type of definition is useful because it informs the audience about the kind of thing the definiendum applies to, even if the complete definition is difficult to remember and understand. Here are more examples of this kind of definition, with the genus part underlined: 

Ice = frozen water. 

Witness = a person who testifies under oath at a trial or deposition. 

Vitamin = a low molecular weight organic compound required in trace amounts for normal growth and metabolic processes. 

Bear market = a prolonged condition of the financial market in which investment prices fall and are accompanied by widespread pessimism. 

Phoneme = the smallest unit of sound in a language. 

Three Misconceptions About Definitions

• Some people claim that we should define all the words we use. But this is far too extreme. First of all, we do not have to be precise and clear all the time. 
• Many words are difficult to define. We learn words like green, warm and cold through examples and not complete definitions. 
• Other words like time and existence seem so basic and hard to define even though we understand them well enough in everyday life. In any case, it is surely impossible to define all the words we use without circularity since our language contains only a finite number of words
• A second misconception about definitions is to think that dictionaries provide the most accurate and authoritative definitions. Dictionary entries often describe only the main usage of a term. An entry might also include extra factual information that is not part of the meaning of the term.
• According to The Pocket Oxford Dictionary of Current English, a cat is a small soft-furred four-legged domesticated animal. As a definition, it is both too wide and too narrow, because a small furry dog is not a cat, and a cat that has become large as a result of hormonal injection does not thereby cease to be a cat. 
• Another point to remember is that a lot of terms have technical meanings, such as inflation in economics and mass in physics. A general dictionary might not give you the correct explanation. You need to consult a more specialised dictionary for that particular discipline.
• The definitions of many abstract concepts can be controversial. Think of art, justice, knowledge, rationality. A short dictionary entry might be a good start to help us think more deeply about these concepts, but we should not expect a dictionary to give us the final word on their proper understanding. 
• The third misconception about the definition is the belief that to know the real meaning of a term, we have to find its original definition or meaning. 
• Many people like to explain X by beginning with the history of the word X. The etymological fallacy is the mistaken idea that we always need to look at the history and original usage of a term to decide what its current meaning is. 
• For instance, the word passion derives from a Latin root that means "suffering." The current meaning of a word depends on how it is actually used.

End of the Part!