1.5 Rules for Definitions

1.7 Propositions and Word Meaning

One point seven. Prepositions and word meaning. Consider the following statements. Most cars have four wheels. The Empire State Building is over one thousand feet tall. Jack is a Baptist. The theory of relativity in physics has been well confirmed by experiments. Each of these statements has a linguistic form as an English sentence, and each of sentences has a meaning. It expresses a thought. The meaning or thought is a. Prepositions. When we engage in reasoning, the units of thought are propositions. Understanding propositions is a vital skill in reasoning. When we take a position on an issue, we are asserting that a certain proposition is true. if we can’t distinguish between propositions that are similar but not identical, then we don’t really know what we believe and we can’t tell whether someone else’s position contradicts our own. When we weigh the evidence for and against some conclusion, we need to use the principles of logic that we are going to cover in later chapters. And these principles identify certain relations among propositions. In this section, we will study propositions, what they are and how to tell them apart. A proposition is a complete thought normally expressed in a complete sentence, making a statement that it is either true or false. The first proposition, for example, uses the concept car which designates a category of things. But the sentence also says something about cars, something that is either true or false. In the same way, the phrase the Empire State Building names a certain structure in New York City, but does not say anything about it, whereas the second proposition does make a definite statement. And even if you don’t happen to know whether the statement is true or false, you know that it must be one or the other. Propositions and the sentences that express them must have a subject and a predicate. The subject term refers to something or class of things, and the predicate says what the subject is or does. A proposition must have this basic structure, subject, and predicate in order to be complete. A subject without predicate or predicate without subject is not a complete thought that is either true or false. For example. Game one in the playoffs. The Pillsbury boy ran too fast for me to catch him was to block south of the library. The first two examples might serve as subjects, the second two as predicates, case, but none of them by itself is a proposition. A proposition, to summarize, is the thought that the sentence expresses, or more precisely, the content of that thought. While a sentence is the linguistic vehicle we use to express it just as an individual word is the linguistic vehicle we use to express a concept. This term statement, finally is usually understood to mean a proposition as expressed linguistically. When we are not focused on the difference between thought and expression, we will use statement interchangeably with proposition. But it is important here at the outset that you understand the difference. Two different sentences may express the same proposition, just as two different words may express the same concept, and a single sentence may express more than one proposition. In this section, we will see how individual words contribute to the meaning of a sentence, and how variations in the words it uses can affect the proposition it asserts. Then we’ll turn to the grammatical structure of the sentence and see how the rules of grammar allow us to formulate more and more complex sorts of thoughts. Suppose we have two sentences that differ only in one word. Jack is an ex and Jack is y. If x and y express the same concept, then these two sentences asserts the same proposition. If the words express different concepts, then the sentences assert different propositions. That’s a general rule, and it’s often easy to apply. If the two words are synonyms, the resulting sentences make the same statement. Jack is a lawyer. Jack is an attorney. Lawyer and attorney are different words, but they express the same concept. So both sentences express the same proposition despite the different words. If the words are unrelated, the sentences make different statements. Jack is tall. Jack is married, tall and married. Obviously expressed different concepts, so these sentences express different propositions. The tricky cases are those in which the words are related but not identical in meaning. Jack is a Baptist. Jack is a Christian. Baptists are one denomination of Christians, so the propositions are related. If the first is true, then the second must also be true. But Christian is a more abstract term. It is a genus that includes other denominations besides Baptists. So here again the sentences express different propositions. There is no single rule for determining whether two words express the same concept. We need to use our understanding of word meanings, including what we’ve learned about classification and definitions, to ask whether the word pick out the same class of things and if so, whether they isolate those things on the basis of the same distinguishing properties. But it will help to consider two specific issues. Word connotations and metaphors. One point seven eight. Connotations. Two words that express the same concept are usually considered to be synonyms. Couch and sofa, car and automobile. Owen and passes, and so on. But sometimes words that express the same concept have different connotations. They convey different images or feelings. They elicit different associations in our minds. They express different attitudes. For example, in a letter of recommendation for a student, I could make the same point with either of two sentences. Felicia has firm command of the subject matter. Felicia has a true understanding of the subject matter. These sentences assert the same proposition because the italicized phrases express the same concept, but the first conveys the image of power and control over the material, whereas the second is more bland. It doesn’t really convey any image at all. A good writer makes use of such differences in connotation to achieve a desired effect. What we shouldn’t be misled by different connotations into thinking that different propositions have been asserted. This is especially important when the connotations involve strong positive or negative attitudes. On the negative side, we have derogatory slang terms for racial and ethnic groups and for professions to pick two of the less offensive ones. Cop used to be a derogatory term for a policeman. Shrink is an impolite term for a psychotherapist. In each case, the slang term stands for exactly the same class of people as the more polite term, and expresses the same concept. the only difference is in connotation. On the positive side, the clearest examples are Euphemism. Sanitary engineer describes the same occupation as garbage collector, but has a more Dignified sign. In an earlier age when people were more delicate in discussing bodily functions. It used to be said that animals sweat, men perspire, ladies glisten. We need to be careful, though. Words that differ in connotation may also differ in literal meaning, they may not express the same concept. An unmarried couple who shared the same address or sometimes described as living together, sometimes as living in sin. There is an obvious difference in meaning here. One phrase implies a moral judgment by classifying the couple with sinners, the other does not. Before we decide that two words differ merely in connotation, therefore, we should make sure that they do not also differ in meaning. We should ask whether the attribute different properties to their reference or classify them in different ways. One point seven metaphors. A special problem arises in the case of metaphors. Strictly speaking, a metaphor is a particular figure of speech in which one thing is equated to another in order to bring out some point of similarity, as in the example we discussed earlier. Life is a cabaret in this strict sense, metaphors are distinguished from other figures of speech, such as similes. Life is like a box of chocolates, but we will use the term metaphor more broadly here to include any non-literal use of language. We have seen that metaphors are not appropriate in definitions, but they are extremely valuable in other contexts, and we use them all the time. They allow us to make our language more colorful and interesting. They convey similarities and shades of meaning that would otherwise be difficult to express. For that very reason, however, it is often difficult to interpret a metaphorical sentence to formulate in literal terms the proposition it asserts. For example, when the poet Robert Burns said, my love is like a red red rose, he was making a comparison. But in what respects? He wasn’t making a biological comparison. He didn’t mean that he was dating a form of plant life. Presumably, he meant his love was beautiful. That is the literal meaning of the metaphor. Yet the two statements. My love is like a red, red rose. And my love is beautiful do not express quite the same proposition. Beautiful is a very abstract word. The point of this metaphor is to convey the particular kind of beauty she has. The dark and delicate, regal beauty of a red rose. Not the more exotic beauty of an orchid or the sturdier, sunnier beauty of a daffodil. And roses have thorns. So perhaps the poet also means to say that his love is prickly and temperamental. Pimento, you can see that it would be extremely hard to find a literal statement that asserts exactly the same proposition. Why do we have to find a literal translation? Why can’t we just say that the poet is expressing the proposition? My love is like a red rose. Well, sometimes we can let it go at that. We can savor the metaphor without analyzing it in the context of reasoning. However, where we are concerned with the logical relationships among propositions, a literal translation is usually necessary to know how a given proposition is logically related to others. We have to know exactly what the proposition does and doesn’t say. If two people are using metaphorical terms in an argument, we won’t know whether they are really talking about the same issue until we formulate their positions in literal terms. For example, she you always keep your feelings bottled up inside. He. You want me to let everything just hang out there? In these situations, we have to interpret metaphors. And the only rule we have is a fairly vague one. We should give as full, sensitive, and reasonable an interpretation as we can. Usually it is not difficult to find a reasonable interpretation. In our example, the literal meaning behind the metaphors of bottled up and hang out there is being less or more emotionally expressive and responsive. Few of the metaphors we encounter are as rich in meaning as the ones we find in poetry. For example, to describe something as a band aid solution is to say that it doesn’t solve the underlying problem, but is only a short term or superficial treatment. This is a one dimensional metaphor and is easily put into literal terms. Our language is also filled with dead metaphors. Words so often used to express an idea Metaphorically that they now contain the idea as part of their literal meaning. Thus, we often speak of grasping a fact. Grasp is a physical metaphor for the mental act of understanding, but it has been used so often that understanding is now considered one of the literal meanings of the word. In the same way, we often describe pains as sharp people, as dense as spicy food, as hot relationships as stormy, and so on. If you think about it, you can see that each of the italicized terms is based on a metaphor that is now incorporated into its literal meaning. In such cases, there is no need for interpretation at all. Solve words in propositions to determine whether two sentences assert the same proposition. Use techniques of classification and definition to identify the concepts the words express. Ignore differences in connotation. Find the literal interpretation of all metaphors. This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit bypedram.substack.com [https://bypedram.substack.com?utm_medium=podcast&utm_campaign=CTA_1]

1.6 Constructing Definitions

Definitions do not appear out of thin air. It’s up to us to construct our own. To come up with definitions that satisfy the rules we’ve learned, we need a procedure we can follow—a technique for constructing definitions. Of the six rules of definition, the first three are the most important. If you can find a genus and differentia that, together, are neither too broad nor too narrow, and that state the essential attributes of the referents of the concept, you can be pretty sure that your definition will satisfy the remaining three rules. We can think of those other rules as backup tests. To define a concept, therefore, the first step is to find the genus. Then look for a differentia that states the essential attributes of the referents and distinguishes them from other species of the same genus. Finally, double-check your definition by looking for counterexamples and by making sure that your definition is not circular, negative, or unclear. Let’s look a little more closely at each step. Then we’ll apply our techniques to a particular case. If we start by finding the genus, it will make the rest of the job easier. Suppose we want to define CUP. We would use what we know about classification to locate the concept in a genus–species hierarchy: The diagram is titled, drinking vessel, with a large bracket on either side. It encloses its three types, namely: cup, mug, and glass. Now we know that our definition will have the form, “A cup is a drinking vessel that ___.” And we’re in a good position to fill in the blank—to find the differentia. We know we have to distinguish cups from mugs and glasses, so we’ll look for properties such as shape or function that will best do the job. In defining a term, we are concerned only with its literal meaning, not with any metaphorical use. A metaphor typically applies a concept from one genus to things in some other genus. An army, for example, is a military organization, but the term “army” is used metaphorically to describe nonmilitary groups that are similar in one way or another, such as an army of ants. If we tried to define ARMY in such a way as to include these metaphors, we couldn’t use MILITARY ORGANIZATION as the genus. Indeed, there is no genus we could use, because we could not possibly anticipate every metaphorical use of the term. But we don’t need to include the metaphorical uses. The purpose of a definition is to give the literal meaning of a concept. When we choose a genus, we need to consider the appropriate level of abstraction. As noted, the genus of CUP would be DRINKING VESSEL. But a drinking vessel is a kind of utensil, which is a kind of tool, which is a kind of man-made object. Each of these terms is more abstract than the one before and covers a wider range of things. Any of them could serve as the genus. Why choose the narrowest one, DRINKING VESSEL? The answer lies in the rule that a definition should state essential attributes. If we choose UTENSIL as the genus for CUP, then our differentia would still have to include the information that a cup is a utensil used for drinking. That’s the function of a cup, and the function explains why a cup has a certain size and shape. The function is an essential attribute, so we might as well include it in the genus. In contrast, we used ANIMAL as the genus in defining HUMAN, but this is not the narrowest genus. Humans are also vertebrates, mammals, and primates. Each of these terms is narrower, less abstract, than the one before. Again, any of them could serve as the genus. Why choose the wider genus, ANIMAL? Once again, we consider which features of humans are essential. The feature we share with other vertebrates, for example, is a spinal column. However important that feature of our anatomy may be, it is not as fundamental as the biological attributes we share with all animals: being alive, having needs for sustenance, reproducing, etc. Our similarities to other primates, mammals, or vertebrates are not as essential as our similarity to all animals. So unless we have a specialized purpose, as biologists do, there is no need to mention these other similarities. Remember that a definition is selective. Its purpose is to condense the information we have about a concept by stating only the fundamental facts. The main thing to keep in mind when you look for a differentia is that it should distinguish the referents of the concept from the referents of other species in the same genus. It should name an attribute possessed by all the referents of the concept and not possessed by members of the other species; this will ensure that the definition is neither too broad nor too narrow (rule 2). You may be able to find many attributes shared by all the referents, but you should not include them all unless they are all necessary to distinguish the concept from other species in the genus. Once again, a definition should be selective, so look for the essential attribute (rule 3). When we apply rule 2, we should keep in mind the possibility of borderline cases. Suppose we’re defining CITY. Cities are distinguished from other municipalities mainly on the basis of population. Our definition should thus include any place large enough to be considered a city and exclude any place too small. A place with 1,000 residents is obviously a village or town, while a metropolis of 2 million is clearly a city. But there is no sharp line between a large town and a small city. So how would we define CITY? We have two choices. If we do not have any specialized need for precision, then we should define a city simply as a large metropolis. The term “large” clearly includes the metropolis of 2 million, it clearly excludes the village of 1,000, and it leaves the borderline area unclear. Thus it matches the content of the ordinary concept, including the indefinite areas around the borders. In general, we can expect a definition to help clarify boundaries, but we cannot expect it to set more definite boundaries than the concept itself has. However, if we do need a concept with a precise borderline, as we may if we are taking a census or doing economic research, then we will have to specify a precise criterion of population size and turn the concept into a technical one. A definition of this type is sometimes called a “precising definition.” A precising definition is a special case of a more general type: the stipulative definition. A stipulative definition introduces a new word by specifying that it shall mean such and such. We may need to do this in the case of new technological products (e.g., blockchain software), new scientific discoveries (e.g., quarks), new professions (e.g., programming), and so forth. We may also need to give a new meaning to an old word; in physics, for example, “work” is defined as the product of the force applied to an object and its displacement in the direction of that force. Stipulative definitions are not subject to rule 2. Because the term being defined has no antecedent meaning, the definition cannot be too narrow or too broad. But this does not mean that such definitions are arbitrary. They are appropriate only when the referents of the new term are important enough, and distinctive enough, to require their own concept. And once we have created the new concept, its definition is still subject to rule 3: It should state the essential attributes of those referents. When we apply rule 3 to a definition (whether stipulative or ordinary), there’s another qualification to keep in mind. As we have seen, an essential attribute is one that underlies and explains other attributes of the referents. One of the goals of science is to identify such attributes. But it is not always appropriate to incorporate scientific theories when we define a concept for ordinary use. We can define water as the substance with the chemical structure H2O, because that chemical structure, which explains many of the other properties of water, is so well established that it has become common knowledge. But it would not be appropriate to define man as the animal with the most complex brain—even though that complexity is likely to be what gives us our capacity for reason. The problem here is that the relationships between the brain and reason are not very well known yet; the available theories are speculative and incomplete, and it wouldn’t serve our purpose to incorporate them into a definition. So the rule of essentiality must be qualified: The differentia should name the most essential attributes that are fairly well understood. SOLVE Constructing Definitions To construct a definition for a concept C: Find the genus of the concept—the broader concept that includes C and other, related concepts from which one needs to distinguish C. Choose a differentia that distinguishes C from other concepts in the same genus. If there is more than one distinguishing attribute, choose the most essential one. Check to make sure that the resulting definition is not circular, unnecessarily negative, or unclear. Look for counterexamples to your definition. For the same reason, it is not a good idea to include controversial information in a definition. Our concepts, and the definitions we give them, provide the framework for thought and discussion. Ideally, the framework should be a neutral one, so that people on opposite sides of an issue can rely on a common understanding of the relevant concepts in presenting their arguments and thus understand each other. I may be convinced, for example, that psychological depression results from repressed anxiety, but this theory about the unconscious cause of depression is controversial. If I’m going to discuss the matter with a psychologist who rejects that theory, we should define depression in terms of properties we can agree on, such as the conscious feelings involved. Once we have established the genus and differentia, the final step is to test our definition. We should make sure that it is not circular, that it is not negative (unless the concept itself is a negative one), and that it does not use vague, obscure, or metaphorical language. And we should make an effort to find counterexamples. That is, we should look for things that are included in the concept but would be excluded by the definition: They would prove that the definition is too narrow. And we should look for things that are not included in the concept, but would be included by the definition; in that case, our definition is too broad. If we have looked for counterexamples and haven’t found any, then we can be more confident that our definition is correct. Let’s see how the general procedure works in practice by trying to define the concept GAME. This is a fairly abstract concept, covering indoor games played with cards, boards, or dice; outdoor games played with balls; races of all kinds; and even simple things like throwing a ball against a wall and catching it before it hits the ground. Let’s see whether we can come up with a definition that covers all of these diverse activities. As usual, we should start by looking for the genus. A game is a kind of human activity, so we need to contrast it with other human activities. The first thing that should occur to us is that games can be contrasted with jobs. There’s a basic difference between working and playing; games belong in the second category. Of course, people sometimes describe their jobs as games, as in “I’m in the real-estate game.” But this is clearly a metaphor: It’s intended to startle the listener precisely because a job is not literally a game. So games belong in the genus we’ve described as “play.” To make it clear that we are talking about the leisure activities of adults as well as children, let’s use the term recreation. What else does this genus include? In addition to games, RECREATION includes activities such as hobbies and pastimes, vacation traveling, and dancing. Our classification now looks like this: The diagram for Recreation with a large bracket on either side, encloses four types, namely: Games, Hobbies, Vacation, and Dancing. These types have a pair of smaller brackets each and appear beside each other at the bottom of the diagram. The diagram for Work, with a large bracket on either side, is blank. This is not an exhaustive list of recreational activities. (Can you think of any others?) And of course recreation and work are not the only activities that human beings engage in. Among other things, we have left out family and social life. But this classification is enough for our purposes. Before we turn to the differentia, let’s pause to consider the nature of the genus we have isolated. Recreation is an activity and so is work. The difference clearly has something to do with goals and rewards. It will help us to understand games if we explore this difference a little further. What goal does one pursue in work? Take a doctor as an example. In one respect, a doctor’s goal is restoring people to health: That is the function of medicine. In another respect, a doctor’s goal may be to make money, or to help people, or to use his mind in solving problems. Notice that the first goal is common to all doctors: Restoring health is a goal intrinsic to medicine; it is the function of medicine. However, the personal goals that doctors have are not intrinsic to medicine as a profession. They vary from one doctor to another; they’re a matter of the individual’s motivation. We could draw this same distinction between function and motivation in any line of work. Now let’s consider recreation. Here, too, personal motivation differs from one individual to another. Some people play to relax, while others play to prove themselves; professional athletes and gamblers play for money. The common element in any given type of recreation, therefore, will have to be a goal intrinsic to the activity itself—a goal analogous to the function of a given line of work. This is where the essential difference lies between work and recreation. In any type of work, the function is producing a good or service that has value in its own right, apart from the activity of producing it. In recreation, the intrinsic goal is not productive in that sense. The activity is an end in itself, something we do merely for the sake of doing it. This would be true even for a professional athlete, who is being paid to play the game, to create an exciting spectacle that other people want to see. In that sense the athlete is working, not playing. But the game itself (football, golf, or whatever) is still a form of recreation because the goals internal to the game (getting a touchdown, sinking the putt) are not valuable in and of themselves. They have value only as elements in an activity that people value for its own sake. Keeping all this in mind, let’s try to find a differentia that will distinguish games from other types of recreation. Some games are played with cards, others with balls, others with boards; some are physical, some are mental; some involve mostly skill, others mostly luck. So none of these properties can serve as our differentia, which has to be a property common to all the referents. What about competition between players? Most games do have a competitive element, but this definition would still be too narrow, because some games do not involve competition. Solitaire and sudoku are counterexamples. Couldn’t we say, though, that in these cases we are competing against ourselves? We often do describe solitary games this way. The problem is that this description is metaphorical. If we took it literally, it would mean that you are your own opponent. If you are competing against yourself, and you win, who loses? But let’s not give up yet. When you play solitaire, you may not literally be competing, but it’s still true that you can win or lose. That’s because the rules of the game set a certain goal, such as turning up all the cards; if you achieve the goal, you win. Here we have something that looks like a universal property, and an essential one. What would a game be without rules? In every game, there is a set of rules that says what the goal is (the object of the game) and also says what means you can use to achieve the goal. This is what creates the challenge of a game and leads us to use the metaphor of competing with ourselves. Even in competitive games, the existence of rules is a more essential attribute than competition, because the rules create the competition: They specify the number of players and the terms on which they will compete. Our definition, then, might be stated as follows: A game is a form of recreation constituted by a set of rules that specify an object to be attained and the permissible means of attaining it. Notice the word “constituted” here. It was carefully chosen to convey the idea that the very structure of the game depends on the rules. Notice also that the differentia fits in well with our analysis of the genus. We saw that recreation should not be distinguished from work in terms of personal goals. Either activity can be done for fun or profit. They should be distinguished rather in terms of the goals intrinsic to the activities. And our differentia tells us where a game’s internal goal comes from. Let’s test the definition by looking for counterexamples. Is it too broad? Would it include anything that is not a game? It’s certainly true that other recreational activities are governed by rules. In skiing, there are traffic rules—you shouldn’t bump into other people. In stamp collecting, stealing the stamps you want would violate the law. But each of these rules is superimposed on an activity that could be done without them. They do not give the activity its goal; they merely impose external constraints on the means one can use. So these activities are not constituted by rules in the way our definition requires. Is the definition too narrow? Would it exclude any games? What about throwing a ball against a wall and catching it? Well, in a sense, there is a rule here that specifies a goal and the permissible means: “Throw the ball against the wall and catch it before it bounces.” That isn’t much of a rule. But then this isn’t much of a game. It is not clear whether this activity satisfies our definition, but it’s equally unclear whether the activity should be considered a game. What we have here is a borderline case, and, as we have seen, we cannot demand that a definition have sharper boundaries than the concept it defines (unless we need to turn the concept into a technical one). All we can ask is that the definition include everything that is clearly a member of the concept, exclude everything that is clearly not a member, and leave the same set of borderline cases uncertain. So far as we can see, therefore, our definition is a good one. You’ll have to decide for yourself whether you agree—perhaps there is something we have overlooked. But regardless of whether we agree on the outcome, the process of reasoning behind it illustrates the technique to follow in defining a concept. This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit bypedram.substack.com [https://bypedram.substack.com?utm_medium=podcast&utm_campaign=CTA_1]

1.5 Rules for Definitions

If we’re looking for a definition, why not just use the dictionary? Isn’t that what dictionaries are for? Well, yes and no. A dictionary is a good place to begin our search for a definition. But dictionaries are concerned with words. They often give nothing more than synonyms and rarely provide the full context we need to understand the concept that a word expresses. To define a concept, we usually have to go beyond the dictionary. Logicians have identified six rules for constructing a type of definition that is suitable for general purposes: A definition should include a genus and a differentia. A definition should be neither too broad nor too narrow. A definition should state the essential attributes of the concept’s referents. A definition should not be circular. A definition should not use negative terms unnecessarily. A definition should not use vague, obscure, or metaphorical language. 1.5A Genus and Differentia 1. A definition should include a genus and a differentia. The most common way to violate this rule is to leave out the genus. And the usual sign of this omission is the use of the word “when,” as in “fear is when you think you’re in danger.” What’s missing in this definition is the genus: Fear is the emotion one feels in response to the awareness of danger. The word “where” is sometimes used in the same way, as in “a denouement in a story is where the conflict is resolved and the story ends.” Here again, the genus is missing. This definition does not tell us what kind of thing a denouement is—namely, an element or a stage in the plot of a literary work. Like the differentia, the genus need not be specified by a single word. If we define an automobile as a motor vehicle intended for personal transportation, the genus is contained in the phrase “motor vehicle.” A definition of USER SESSION might be: “A user session at a website occurs when a unique user is present on a site for a specified length of time,” which distinguishes it from a hit, which occurs each time a user views a different page at a site. This definition includes a genus even though it uses the word “when,” because it describes the user session as a unit of measure for usage of a website, in contrast with another measure, a hit. From a logical standpoint, user sessions and hits are two species of the genus “unit of measure for website usage.” The definition makes this clear. When we define a concept that designates an action, we often use a verb phrase, as in “to practice is to perform an activity for the sake of improving one’s skill.” The genus here can be restated as “an activity one performs.” The English language gives us many ways to specify a genus. To identify the genus, we need to look for the element in a defining statement that refers to a wider class. A definition by genus and differentia builds on what we have learned about classification. The genus not only helps us identify the referents of a concept, but also conveys a great deal of information about them. If you don’t know what a peso is, for example, the most useful thing I can tell you is that it’s a unit of Mexican currency. In the same way, the statement that humans are animals locates our species within the biological order and conveys a vast amount of information in summary form—that we are living beings, that we are mortal, that we have specific needs for survival and reproduction, and so on. 1.5B Co-Extensive and Essential Attributes 2. A definition should be neither too broad nor too narrow. A definition is too broad if it includes things that are not referents of the concept. For example, the definition “Humans are two-legged animals” is too broad because the defining phrase “two-legged animal” includes birds as well as humans. We can represent this problem in a diagram: The diagram is titled, Two-legged Animals, with a large bracket on either side. It encloses Human, which appears with a pair of smaller brackets. A row of dots appears at the bottom of the diagram, enclosed within Humans and Two-legged Animals. Two dots enclosed within Two-legged Animals are labeled, birds. A definition is too narrow if it fails to include things that are referents of the concept. An example would be “Humans are religious animals.” This definition is too narrow because, no matter how widespread religious belief may be, some people are atheists. We can see this by drawing a diagram: “Religious animals” has a pair of brackets. “Humans” appears below it as follows. The left bracket of “Humans” appears outside “Religious animals,” while the right bracket is enclosed inside it. A row of dots appears at the bottom of the diagram, enclosed within “Humans” and “Religious animals.” Two out of the three dots enclosed within “Humans” are labeled, atheists. Being too narrow and being too broad are opposite flaws in a definition. But both involve the relation between the concept and its referents. One purpose of a definition is to identify the referents of a concept. A definition that does not pick out the right referents—one that includes too much or too little—is not doing its job. It is like an incompetent doorkeeper at a party, letting in people who weren’t invited or turning away people who were. We can tell whether a definition is too broad or too narrow by looking for counter-examples. A counterexample is a particular instance that proves a definition wrong. If a definition is too narrow, a counterexample is something that belongs in the concept but is excluded by the definition. Atheists are counterexamples to the definition of humans as religious animals. If a definition is too broad, a counterexample is something that does not belong in the concept but is included in the definition. Birds are counterexamples to the definition of humans as two-legged animals. Let’s look at a few other cases. “A college is a degree-granting educational institution.” A counterexample would be a law school. Law schools are degree-granting educational institutions, but they are not colleges. So this definition includes too much; it’s too broad. “A cigarette is a sheaf of chopped tobacco rolled in white paper.” What about the brands that are rolled in brown paper? They are counterexamples proving that the definition does not include enough; it’s too narrow. We should notice, finally, that a definition can be simultaneously too broad and too narrow. Suppose, for example, that we define murder as the act of killing another person outside a military context. By this definition, killing someone in self-defense would be an act of murder, but it isn’t. So this definition is too broad. But it is also too narrow. Suppose a soldier kills another member of his own regiment in cold blood. This would be murder, but the definition would exclude it because it occurred in a military context. So the same definition can violate the rule in both ways: It can be both too broad and too narrow. The diagram has overlapping brackets. The text, “killing another person outside a military context,” has a pair of brackets. “Murder” appears below it as follows. The left bracket of “Murder” appears outside the brackets of the above statement, while the right bracket is enclosed inside it. A row of dots appears at the bottom of the diagram, enclosed within “Murder” and “killing another person outside a military context.” One dot is enclosed between the left bracket of Murder and the left bracket of “killing another person outside a military context,” which is labeled, one soldier murders another in same regiment. Two dots enclosed between the right bracket of Murder and the right bracket of “killing another person outside a military context,” are labeled, self-defense. 3. A definition should state the essential attributes of the concept’s referents. The referents of a concept often have many attributes in common. Some are relatively superficial, some are essential. As we saw in discussing classification, “essential” means fundamental: an essential attribute causes or explains the existence of other attributes. For example, the heart makes a certain thumping noise, so we might try to define it as “the organ that goes lub-dub, lub-dub.” But the “lub-dub” sound is a superficial trait; it is merely a by-product of the heart’s essential function, which is to circulate the blood. This essential function explains many of the heart’s other properties: the way it beats, the way it is hooked up to the veins and arteries, even the sound it makes. But explanation is a one-way street. The “lub-dub” sound does not explain the heart’s function. Remember that one purpose of a definition is to condense the knowledge we have about the referents of a concept. Defining by essential attributes is the best way to achieve this purpose, because then you convey not only the particular attributes named in the definition, but also the ones they underlie and explain. The rule of essentiality applies to the genus as well as the differentia. Dogs, for example, belong to various wider groups: they are animals, they are playmates, they are a means of self-defense. But ANIMAL would be the best genus to use for general purposes in defining DOG, because a dog’s animal nature is more fundamental and explains more about it than does the fact that it can play with human beings or defend them. In regard to the differentia, the rule of essentiality will help us choose among attributes when there is more than one that would differentiate a concept from other species of the same genus. Consider the concept HUMAN. Many attributes, in addition to the faculty of reason, are common and distinctive to humans: language, social institutions, the accumulation of knowledge from one generation to the next, laws, moral codes, certain complex emotions such as reverence, a sense of humor, a brain of a certain size and complexity, a certain physical shape and posture. But reason is the common element, the underlying cause, for many of these attributes. Not for all of them—reason doesn’t seem to have much connection with our physical shape and posture. But it is reason that allowed us to develop abstract language and technology, to create social institutions based on general rules and laws, to pass along knowledge to the next generation, and so forth. Reason gives us a differentia that condenses the greatest amount of knowledge about the concept HUMAN. As with choosing an essential principle in classification, there is no hard and fast rule for determining which attributes are essential. Our view of what is essential to a class of objects may change as we acquire more knowledge about them, and it may involve controversial issues on which people disagree. The rule of essentiality means this: Pick the most essential attribute you can, given everything you know, using your best judgment. And the guidelines to follow are the ones we have already discussed: Look for the attribute that explains the most. For man-made objects, actions, and institutions, look for the basic function. For objects in nature, such as biological species or physical substances, look for underlying traits that cause and explain the more superficial attributes. 1.5C Other Rules 4. A definition should not be circular. Suppose we define ownership as the legal relation between people and the things they own. Because this definition uses the word “own,” it defines the concept OWNERSHIP in terms of itself. Instead of explaining what it means to own something, it assumes that we know this already. It tells us how the concept relates to itself, but not how it relates to other concepts or to reality. This definition doesn’t go anywhere; it just moves in a circle. The same problem arises if we use synonyms in a definition. Suppose we define ownership as the legal relation between people and things they possess. “Own” and “possess” are synonyms, different words that express the same concept. In terms of concepts, therefore, the definition is still circular: The concept OWNERSHIP is still being used to define itself. The same objection would apply if we define man as the human animal, large as the attribute possessed by something that is big, or folly as a foolish act. In each case, the italicized words are synonyms. To avoid such circularity, it is useful to ask: What contrast is the concept intended to draw? For example, what is the difference between owning a dress and borrowing it or trying it on in the store? How are humans different from other animals? What makes an action a folly as opposed to a wise action? Circularity can take an even subtler form when two different concepts are used to define each other. Suppose that we define a doctor as a professional who offers medical services to patients. So far, so good: DOCTOR and PATIENT are distinct concepts. But if we now define a patient as a person who receives the services of a doctor, then we have a circular pair of definitions. A better approach would be to define the doctor–patient relationship first; then we could define both DOCTOR and PATIENT in terms of that relationship. 5. A definition should not use negative terms unnecessarily. At the beginning of the 20th century, the automobile was described as a “horseless carriage.” That phrase certainly does describe the automobile, but it would not be a good definition. The differentia “horseless” tells us about one source of power that automobiles do not use. But there are many sources of power automobiles do not use; what we want to know is the source they do use. As another example, suppose that when we introduced the term “differentia,” we defined it as the part of the definition that is not the genus. That would not have been much help to you in understanding what a differentia is. In general, negative definitions should be avoided because knowing what a thing is not doesn’t tell us much about what it is. For that reason, a negative definition usually violates the rule of essentiality as well. Some concepts, however, are inherently negative and thus require negative terms in their definitions. A bachelor is a man who is not married; failing means not succeeding; an empty space is one with nothing in it. How do we know whether a concept is negative? In some cases, a suffix or prefix gives us a linguistic clue: immortal, worthless, asymmetric. In the absence of such clues, you will have to use your judgment. There are no hard and fast rules, but it’s a good idea to look first for a positive attribute, then fall back on a negative one only if the search fails. 6. A definition should not use vague, obscure, or metaphorical language. We might think of this as the “clarity” rule. The purpose of a definition is to clarify our understanding of a concept. At the very least, therefore, the language we use in a definition should not be less clear than the concept being defined. Unfortunately, there are too many ways of being unclear to list them all here, but vagueness, obscurity, and metaphor are the three most common. A vague definition is unclear because it does not give any precise criterion for membership in the concept. Suppose we define maturity as the stage of psychological development in which a person becomes well-adjusted. How do we tell whether a person is well-adjusted? Does adjustment mean passive acceptance of the social environment, or can it include a critical outlook? Is it primarily a set of cognitive skills, an emotional state, or both? As these questions indicate, the term “well-adjusted” is vague. It’s unclear who belongs in the class of well-adjusted people and who doesn’t; the class has highly indefinite boundaries. Of course, the concept MATURITY itself has indefinite boundaries, but a definition shouldn’t make the problem worse. An obscure definition is unclear because it uses abstract or technical language that is more difficult to understand than the concept itself. An example would be a definition of death as the cessation of one’s participation in finitude. The problem here is not necessarily one of vagueness. In the appropriate context of a philosophical theory about human life and afterlife, this definition might have a perfectly clear and definite meaning. But that’s the problem: it has a clear meaning only in a specialized context. For general purposes, the defining terms are too obscure to be useful. The same is true of many technical definitions in law, science, or other specialized areas. Such definitions may be perfectly clear to specialists, but if the concept is employed outside the specialty, then we also need a general-purpose definition that is intelligible to laymen. A metaphorical definition is unclear because it doesn’t convey the literal meaning of the concept, but only an analogy that we have to interpret. A famous Broadway musical maintained that “Life is a cabaret.” Like any good metaphor, this one uses a simple image to convey a complex thought that would take many paragraphs to explain in literal terms. But for a definition, we need the literal terms. A metaphor leaves too many questions unanswered. In exactly what ways is life like a cabaret? How far does the analogy extend? Is this the essential truth about life or just one perspective? Metaphors are valuable tools of thought and communication, but they can’t do the work of definitions. Altogether, then, there are six rules of definition. These rules give us standards for evaluating definitions proposed by other people and guidelines for creating definitions—as we will see in the next section. REVIEW Rules for Definitions * A definition should include a genus and a differentia. * A definition should not be too broad or too narrow. * A definition should state the essential attributes of the concept’s referents. * A definition should not be circular. * A definition should not use negative terms unnecessarily. * A definition should not use vague, obscure, or metaphorical language. This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit bypedram.substack.com [https://bypedram.substack.com?utm_medium=podcast&utm_campaign=CTA_1]

1.4. Definitions: Their Nature and Function

Concepts serve as mental file folders that help us organize our knowledge about classes of similar things. Definitions tell us what is in the folder. In the case of simple, relatively concrete concepts such as table or running, we can get along pretty well without definitions. We can tell just by South whether something is a table, whether someone is running, but most concepts are more abstract and more complex by telling us what they stand for and how they relate to other concepts, definitions are an important tool of knowledge. To see more clearly why definitions are so valuable, let’s look at some of the problems they help us to solve. First, a definition can clarify the boundaries of a concept. A child who has just learned the concept plant can point to some obvious and clear cut examples, such as houseplants or other shrubs. Such cases are called paradigm or prototypical examples. But it will take a while before the child understands the full range of the concept plant, which includes trees, moss, and so on. At a more advanced level, a person might understand that the category of social sciences includes such examples as economics, but not be sure whether geography fits. One major function of definitions is to tell us what is and is not included in a concept by giving us a test is or rule for membership. Some people argue that a concept can never have completely sharp borders on the color spectrum. For example, orange lies on the border between red and yellow, and it isn’t clear which way to classify it. Nor can we solve the problem by treating orange as a separate category between red and yellow, because then there would be colors on the borderline between red and orange. In biology, the one celled organism Euglena sits on the border between plants and animals. It has chlorophyll and engaged in photosynthesis like a plant, but it also has flagella for swimming like an animal. Fortunately, we do not have to settle the theoretical issue of whether concepts can or should have completely sharp borders. The important point is that there are degrees of precision in understanding a concepts, boundaries and definitions help us to become more precise. A second function of a definition is to clarify the relationships among concepts. Concepts are not isolated, self-contained units. They form networks of interrelated ideas. We have already seen that they fit together into genus spacious hierarchies, but there is more to it than that. A concept groups things together into classes on the basis of similarities. In some cases, like table, the objects and their similarities are perceptible. You can literally see the similarity among tables. In such cases, we can employ what is sometimes called an ostensive definition, pointing and saying things like that. More often, however, the reference of a concept and the attributes they have in common are not directly observable, and we have to learn about them by means of other concepts that we already understand. Consider the concept of government. If you were trying to explain this concept to someone, what concrete object could you point to? A police officer? The flag, the white House? These are merely symbols or instruments of government and would convey only a child’s understanding of the concept. Actual examples such as the US government are not things you can literally point to. You would have to explain in abstract language that the concept government refers to an institution with the authority to make laws, for a society to enforce those laws, and to protect its citizens against foreign threats. These words expresses a concept necessary for understanding what governments have in common. It is a link in a long chain that connects the concept government to its reference in reality. If the chain is weak, if the person doesn’t understand the intervening concepts, then he won’t really understand the concept government either. Our ability to acquire new concepts on the basis of old ones is Enormously valuable. It allows us to expand our knowledge and to profit from discoveries made by other people. But it poses the danger that will occur, a concept only as a vague idea, without any clear understanding of the class of things it actually stands for. It also poses the danger that different people using the concept will have radically different ideas of what the concept includes. Definitions help us ward off these dangers. They keep a concept tied to its reference by relating it clearly to other concepts that serve as links in the chain. A third function of a definition is to provide a summary statement about the reference of our Or concepts. If we think of a concept as a file for there, where we put all the information we have about a certain class of things, then we have to realize that these folders may contain enormous amount of information in one way or another. For example, virtually all knowledge in the humanities and social sciences is relevant to the concept. Human definitions help us keep our filing system in order by giving us summary statements about what is in each folder. A good definition condenses the knowledge we have about the reference of a concept, giving us just the highlights, the key points, the essence. Because it performs this service, a definition is valuable even in cases such as human, where we already know what class of things the concept stand for. Now, let’s review the main functions of definitions. Definitions are one. State the criteria for membership in the class of reference. Two. Indicate the relationship between a concept and other concepts. Three condense the knowledge we have about the reference of a concept within the broad framework of the functions we have discussed so far. Definitions can serve a variety of more specific purposes. We are going to be concerned primarily with definitions of concepts that we employ frequently in everyday thought and language. But for specialized purpose in science, law, and other technical fields. We may also need to introduce a new word or give a new meaning to an old word. We may need to give more precise boundaries to a concept, or we may need to clarify the role that a concept plays in a complex story. As we will see, however, the type of definition that works well for ordinary concepts can also be adapted to these other contexts. This type is called a definition by genus and differentia. To understand what this means, consider a classic example. Humans are rational animals. Notice that the definition has two parts. The term animals names the wider class to which humans belong. It classifies us as a species of the genus. Animal A genus is a class of things regarded as having various subcategories. It’s spacious the term rational species can attribute that distinguishes us from other species of the same genus. This part of the definition is called the differentia. It differentiates humans from other animals. In effect, we are assuming a classification of animals in terms of the principal mode of cognition, and then defining our species by our rational mode of cognition. A differentia can really be expressed in a single word, like rational, but it always serves the same function of differentiating a concept from other species within the same genus. Thus, the genus is like your last name, which indicates the family you belong to. The differentia is like your first name, which distinguishes you from other members of your family. In light of what we have said about the functions of a definition and about its genus Differentia structure, we can now define the very concept of definition itself. A definition is a statement that identifies the reference of a concept by specifying the genus they belong to and the differential, the set of essential characteristics that distinguishes those references from other species in the genus along one or more principles of divisions. This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit bypedram.substack.com [https://bypedram.substack.com?utm_medium=podcast&utm_campaign=CTA_1]

1.3. Levels of Organization

So far, we have treated classification as if it were always a matter of sorting things into categories or dividing a genus into a species. Two ways of describing the same operation. And this is indeed the task we face when we start from scratch. But we do not always start from scratch. We often deal with concepts that reflect pre-existing classifications. And the task we face is to locate the concepts at the right level of species genus hierarchy. Suppose you were studying religious affiliations. People describe themselves as Baptists, Methodists, Catholics, Jews, Muslims, and so forth. These are indeed different religious groups, but they do not all belong on the same level of classification. They are not all species of a single genus. Jews, for example, should not be compared directly to Methodists. They should be compared to Christians, a category that we did not include in the list. And Catholics should be compared to Protestants. Another term missing from the list. Thus the classification might look like this. The diagram consists of the word religious with a large bracket on either side. The index. Doctrine and practice appears within square brackets below. Religions. Religions. Encloses the three types Christian, Jewish, and Muslim. Christian is enclosed by parenthesis. The three type have a small pair of brackets each. Jewish and Muslim are blank, enclosed within Christian or the types Protestant and Catholic. Protestant is enclosed by parenthesis. These types have a pair of even smaller brackets, each enclosed within Protestant or the type Baptists and Methodists Catholic is blank. This diagram illustrates several points. First, concept on the same level of organization should have roughly the same degree of abstractness. It is clear in this case that Catholic and Protestant belong on the same level, and that Baptists and Methodists are narrower, less abstract subregions within the category Protestant. Second, when it’s necessary to separate levels in this way, we must often add concepts that were not given to us originally. The new concepts in this case are Protestant and Christian, and we indicate that they were not on the original list by putting them in parentheses. Finally, the diagram gives us ideas about ways in which we might want to flesh out the classification. Are there other religions besides Christianity, Judaism, and Islam? Are there other branches of Protestantism? Other categories within the major religions? This sort of analysis is often required when you are learning a new subject, and have to learn a new set of concepts. Separating the different levels of organization will help you understand the concepts much more clearly than if you try to master each concept as an isolated unit in a course in Lego theory. For example, you might encounter concepts like felony trespass, Misdemeanor homicide and tort. See the diagram that follows. In order to grasp these concepts, you would need to understand that felonies and misdemeanors are the two species of crimes regarded as offenses against public order and prosecuted by the state, and that tort, such as trespass, is considered a civil lung and offense for which a private individual must bring suit. The diagram is titled offenses, which is in parentheses with a large bracket on either side. The text private versus public appears within square brackets below. Offenses. It encloses two types, namely civil wrongs and crimes. Both types are enclosed by parentheses. The text reappears within square brackets below. Crimes. Enclosed within Civil Lines is torts with a pair of smaller brackets. Torts encloses trespass. Crimes is diagrammed as follows. Its left bracket leads to missed minors below. Misdemeanors, has a pair of smaller brackets, and is enclosed between misdemeanors, and the right bracket of crimes is felonies, which also has a pair of smaller brackets. Felonies encloses homicide. In addition to clarifying the new concepts, this diagram would provide a skeleton or outline for organizing all the other crimes and offenses you learn about. Notice that one of the concepts we had to fill in here was the genus offenses. This is the first case we’ve seen in which the genus was not given at the outset, but it is not an uncommon case. When you are learning a new set of concepts or organizing an old set. You’ll often have to find an overarching concept for the entire domain. Such generic concepts will, of course, be more abstract than concepts for the corresponding species, and it may help to be familiar with some of the highest level abstractions we use to organize our knowledge of the world, or fundamental distinction is between living and non-living animate versus inanimate objects. Another distinction is between natural objects, living or non-living, and man made ones. Yet another basic division is between physical and mental phenomena. The external world of material things versus the internal world of thoughts and feelings. Mental phenomena, in turn, are often divided into cognitive and affective states. Thinking versus feeling. Perhaps the most abstract set of generic concepts is one devised by the ancient Greek philosopher Aristotle. He divided the world into things in the sense of whole objects. Actions. Relations. Quantities. Times and places. When you are looking for a genus, it may help to remember these fundamental concepts. You may not need anything so abstract, but if you are stuck, they may help you get oriented. Solve organizing concepts. To organize related concepts into a classification diagram one. Find the highest level, most abstract genus two. Identify concepts that are species of that genus. They should all have the same degree of abstractness three identify the principle of division that applies to the concepts in step two. Put the principle in brackets. for for each concept in step two, identify any other concepts that are it’s suspicious and identify the principle of division. The single principle by which the concept has been divided into species. Five. Repeat step four for as many levels as necessary. One final word of warning classification is the process of dividing a genus into its species. This is not the same as breaking an object down into its parts or elements. Engines and driveshafts are parts of cars, but they are not themselves types or species of cars. In this case, the point is pretty obvious, but it’s easy to get confused when we are learning new concepts. This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit bypedram.substack.com [https://bypedram.substack.com?utm_medium=podcast&utm_campaign=CTA_1]