The Art of Reasoning | Audiobook: A Practical Guide to Logic & Argument

Pedram Keshavarzi

Audiobook of Kelley & Hutchins’s acclaimed logic text—clear lessons on arguments, fallacies, symbolic logic, and cognitive biases to sharpen critical thinking. bypedram.substack.com

Episodes

  1. 1.7 Propositions and Word Meaning

    1 DAY AGO

    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

    17 min
  2. 1.6 Constructing Definitions

    1 DAY AGO

    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 sho

    27 min
  3. 1.5 Rules for Definitions

    3 DAYS AGO

    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 cert

    28 min
  4. 1.4. Definitions: Their Nature and Function

    5 DAYS AGO

    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

    12 min
  5. 1.3. Levels of Organization

    5 DAYS AGO

    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

    11 min
  6. 1.2 Rules of Classification

    4 OCT

    1.2 Rules of Classification

    What is classification? Classification is the process of sorting items into categories. The whole set you’re classifying — animals, college courses, tools, or anything else — is the genus; your job is to subdivide that genus into species so each item has a clear place. There are often many possible ways to divide a genus, but some divisions are better than others. The rules of classification help us choose the best, most useful divisions. Why good classification matters A good classification makes it easy to find, compare, reason about, and act on items. Bad classification causes confusion: overlapping categories, gaps that leave items unassigned, or groupings that tell you almost nothing useful about the members. Rule 1 — Use a consistent principle (mutually exclusive & jointly exhaustive) The first rule in any system of classification is consistency in the principle you use to divide the genus. Two formal standards follow from that: * Mutually exclusive: Different species should not overlap. Every item must belong to only one species under the chosen principle. If categories overlap (e.g., art and introductory when classifying courses), you cannot assign certain items unambiguously. * Jointly exhaustive: The species taken together should cover the entire genus. Every item must fall into one of the species; otherwise the classification leaves gaps. When you diagram a classification you can show the guiding principle in brackets under the genus name (for example: Furniture [function] → table | bed | chair). The species then reflect consistent differences with respect to that single principle. Common failures to follow Rule 1 An inconsistent classification mixes different dividing principles (ownership, condition, training, shape, etc.). Such mixes produce overlapping and chaotic categories that are useless for clear reasoning or action. Rule 2 — Prefer essential attributes when possible The second rule helps choose among multiple consistent divisions: base your classification on essential attributes rather than superficial ones. * An essential attribute is a fundamental property that makes a thing what it is. Classifying by essentials groups items that are fundamentally similar and separates things that are fundamentally different. * A non-essential attribute (superficial) — such as color, transient condition, or arbitrary ownership — may cluster items together that otherwise have little in common, making the classification unhelpful. Examples: animals and furniture * Animals: Biologists classify animals by essential principles—mode of reproduction (egg-laying vs. live birth), internal physiology (vertebrate vs. invertebrate), thermoregulation (warm-blooded vs. cold-blooded), means of locomotion (swimming, flying, crawling). These reflect fundamental biological functions (survival and reproduction), so groupings are informative: similar groups tend to share many attributes. * Color-based animal groups: Classifying animals by color (gray, red, green…) puts together elephants, mosquitoes, and certain sharks just because of superficial similarity — a classification that tells you little of value about the animal’s behavior, needs, or risks. * Furniture: For man-made objects the essential attribute is usually function: knowing a tool’s purpose explains its shape, material, and structure. Interior designers, however, may legitimately choose style as essential for their purpose (Danish vs. Colonial furniture). When multiple principles are necessary Complex phenomena often require multiple consistent principles (e.g., biologists use anatomy, behavior, genetics). That’s fine — but be careful: when using several principles, structure the taxonomy so species remain mutually exclusive and jointly exhaustive. Multiple principles must be applied in a disciplined way (hierarchical or multi-axial classification) rather than mixing unrelated criteria randomly. A cautionary illustration (Borges’ faux taxonomy) Jorge Luis Borges’ imaginary categories (animals that belong to the emperor; those drawn with a very fine brush; those that tremble as if mad; etc.) show what goes wrong when classification lacks a consistent principle. Categories overlap, many items fit several headings, and the single catch-all “others” hides the absence of coherent principles. This is exactly what to avoid. Applying rules of classification to people and institutions Classification is not inherently problematic — we classify students, applicants, products, and organizations all the time. The ethical and practical problem arises when we classify by attributes that are not essentially related to the purpose at hand. * Example: Employment — A fair employer classifies applicants by ability, training, and character (attributes essentially related to job performance) rather than by race or sex (non-essential for performance). * Example: Corporations — Classifying companies by function (producer vs. service; non-profit vs. for-profit) is usually essential and useful. A classification by CEO height would be superficial and useless. Determining what is “essential” often requires expertise and judgment; there is no mechanical test. Reasonable people may disagree. Still, seeking essential attributes generally improves clarity and usefulness. The role of purpose in choosing essential attributes Classification serves a purpose — your goal influences what you take as essential. For general biological understanding, anatomy and reproduction are essential. For an interior designer, style may be essential. Both classifications can be valid within their purposes; the key is to be explicit about the guiding principle and to follow it consistently. Quick checklist: building a good classification (summary of rules) * Decide your purpose — What will this classification be used for? * Choose a principle (or coherent set of principles) that serves that purpose. * Ensure mutual exclusivity — species should not overlap under your principle(s). * Ensure joint exhaustiveness — every member of the genus should be assignable. * Prefer essential attributes when they are available and relevant. * When using multiple principles, structure them hierarchically or orthogonally so categories remain non-overlapping and complete. * Be explicit — name the principle(s) in diagrams or labels so users understand the logic. Final note on judgment and disagreement There is no mechanical shortcut to distinguish essential from non-essential features in every domain. Some domains (like chemistry) have deep research to justify essentials; others (human institutions, policy) require normative judgment. Expect debate — but aim for clarity: state your purpose, be consistent about principles, and prefer fundamental attributes that make the classification useful. 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

    19 min
  7. 1.1 Concepts and Referents

    1 OCT

    1.1 Concepts and Referents

    Part one: Language and reasoning. Part one is concerned with the basic elements and standards of reasoning. Later sections will deal with the details of specific forms of reasoning, but here we will cover the elements and standards that pertain to reasoning in general, and that will be of value in all your studies as well as everyday life. Language is the medium in which we think, communicate, and reason. Words expand the range of our senses, bring order to our experiences, allow us to learn from the experiences of others, and preserve the thoughts of preceding generations. In learning to speak, each of us has acquired an amazingly powerful and versatile set of tools. But the tools will not do what we want unless we know how to use them properly. So before we turn to reasoning. We need to master these tools. We need to know how to define the concepts our words expressed and how they combine into statements, which we analyze in terms of the proposition they assert. That will be the focus of chapter one. Language, concepts and propositions. Chapter two, we will introduce the basic unit of reasoning, which in logic is called an argument. We learn how to identify the premises and the conclusion of an argument, and begin our study of how to analyze and then evaluate Its logical structure. Chapter three is concerned with fallacies. Various arguments in which the premises may appear to support the conclusion but do not really support it. We are going to review some of the more common fallacies and learn how to spot them in everyday thought and speech. In chapter four, we will add to our understanding of potential pitfalls in reasoning by reviewing some of the psychological factors that give rise to errors. Chapter one language. Concepts and Propositions. Learning objectives. On successful completion of the chapter. You will able to understand differences in levels of abstraction among concepts. Learn rules for organizing concepts in classification hierarchies. To learn to evaluate and construct definitions of concepts. Understand how words and grammatical structure determine what assignment does and does not assert. One of the major functions of language is to divide the world up into categories, except for proper names. Most words stand for groups of things; Tigers, tables, tests, and so forth. Or common features of things. Their characteristics, actions, etc.. Organizing a set of things into groups is called classification, and the word that stands for such a group expresses a concept. In the first three sections of this chapter, we will learn the rules of classifying things in the most effective way, and will see how concepts can be arranged in hierarchies of species and genus. To use concepts with precision and to understand the relationships among different concepts. We need to define them in sections one point four through one point six. We will learn how to evaluate and construct definitions in the final two sections. We will see how to identify propositions and how to tell whether two statements assert the same or different propositions. One point one. Concepts and reference. Suppose that we asked you to classify the courses you’ve taken in college. You might classify them by subject matter or biology, history, etc. or you might classify them by level. Introductory. Intermediate. Advanced. Whichever way you choose, you are grouping together courses that have something in common and distinguishing them from other courses. In effect, you are creating a set of file folders in your mind and then putting each course into the proper folder. Classifying things together into groups is something we do all the time, and it isn’t hard to see why. Imagine trying to shop in a supermarket where the food was arranged in random order on the shelves. Tomato soup next to the white bread in one side. Chicken soup in the back next to the double A batteries on brand of cream cheese in front and another in assault eight near the Oreos. The task of finding what you want would be time consuming and extremely difficult, if not impossible. In the case of a supermarket, someone had to design the system of classification. But there is also a ready made system of classification embodied in our language. The word dog, for example, groups together a certain class of animals and distinguishes them from other animals. Such a grouping may seem too obvious to be called a classification, but this is only because you have already mastered the word. As a child learning to speak, you had to work hard to learn the system of classification your parents were trying to teach you before you got the hang of it. You probably made mistakes like calling the cat a dog. If you hadn’t learned to speak, the whole world would seem like the unorganized supermarket. You would be in the position of an infant for whom every object is new and unfamiliar. In learning, the principles of classification, therefore, will be learning about the structure that lies at the core of our language. Whenever we classify we makers of concepts ideas that represent classes of things we have grouped together. In classifying your courses, you use the concepts such as art, history and introductory. We will use capital letters to indicate a concept. To learn the word dog you had to acquire the concept dog. A scientist who discovers a new phenomenon forms a concept for that class of thing, and expresses the concept in a new word, for example quark. As these examples illustrate, concepts and words are intimately related. A concept is an idea. A word is the linguistic vehicle we use to express the idea. And the things that a concept stands for are called the reference of the concept. The reference of dog, for example, are all the individual dogs in the world. We can diagram the relation between a concept and its reference as follows. The diagram consists of the word dog with large rocket on either side, enclosing a row of five dots. Two dots appear outside the brackets on either side. The black dots stand for individual objects. The bracketing lines indicate that certain objects Mali, the next door neighbor’s dog, etc. are included within the concept. There are the references of dog, while other things are excluded. My cat, the Taj Mahal and everything else in the world that is not a dog. Now consider the concept animal. We could diagram this separately, and the diagram would look like the one we just did for dog. But these concepts are obviously related. Dogs are a type of animal that means we can represent both concepts in the same diagram. The diagram consists of the word animal with a large bracket on either side enclosing its two types dog and cat. Dog and cat appear beside each other at the bottom of the diagram. Each type has the animal name along with a pair of smaller brackets each. A row of dots are enclosed within the brackets of dog, cat, and animals at the bottom of the diagram. Notice that all the references included in Doc are also included in animal, but animal includes many other things as well. Cats. As the diagram indicates, skewers, fish, and all the other types of animals. Animal is a broader concept because it includes more than the narrower concept dog. Whenever we encounter this relationship, we use the term genus for the broader concept and the term species for the narrower one. A genus is a class of things regarded as having various subcategories. Its species, thus dog and cat are both species within the genus animal. If a species is a file folder, a genus is a file drawer containing many folders. You may be familiar with the idea of genus and species from biology, where they are part of an elaborate system of classification with many levels species, genus, family, etc.. In logic, however, the term genus and species have a more flexible meaning. Here a genus can be any group to which a species belongs. That’s why we said animal is a genus. In biology it’s a kingdom, and species can be any subcategory within a given genus. Genus and species are relative terms like mother and daughter. Your mother is also a daughter in relation to her parents. In the same way, a given concept can be either a genus or a species, depending on our perspective. Dog is a species in relation to animal, but it’s a genus in relation to the narrower concept. Beagle. The diagram consists of the word animal with a large bracket on either side enclosing its two types dog and cat. Dog and cat appear beside each other at the bottom of the diagram. Each type has the animal name, along with a pair of smaller brackets, each within the brackets for the type. Beagle appears with a smaller pair of brackets. A row of dots are enclosed within the brackets of dog. Beagle, cat and animal at the bottom of the diagram. By using the genus species relationship, we can create very complex systems of classification. For instance, the item in your house can be classified as tables, chairs, etc. these are a species of the genus furniture, which in turn is a species of the genus. Man made objects or artifacts. If you classified your courses by subject matter, art, history, economics, physics, you might go on to classify these disciplines into wider groups such as humanities, social sciences, and physical sciences. Indeed, every concept can be placed within some hierarchy of genus and species, and as we will see, most concepts can be placed within many different hierarchies. The reference of our concepts are concrete. Each is a single individual object. If we have separate names for each reference, as we do in the case of people or cities, the names would also be concrete, but the concepts such as people or city is abstract. The word abstract here means two things. It means first, that a concept refers to a group of objects, not just to a single thing as a name does. The concept people includes all human beings. City includes all cities. Second concept is abstract because it groups together things

    19 min
  8. The Art of Reasoning - Introduction To Logic

    SEASON 1 TRAILER

    The Art of Reasoning - Introduction To Logic

    What Is Logic? This book is about thinking, and more precisely, it is about the role of logic in thinking. In its broadest sense, thinking refers to anything happening in our minds—memories, daydreams, questions, worries, or plans. But in a narrower and more purposeful sense, thinking means activities such as solving a problem, planning an action, preparing for an exam, or defending a position in a debate. Logic distinguishes this purposeful, goal-driven mental activity from other processes such as emotions or daydreams. Feeling and reasoning both play important roles in life, but logic gives structure to thought, ensuring clarity and precision even in the presence of strong emotions. Logic as Science and Art Logic can be understood both as a science and as an art. As a science, it offers a body of knowledge, like physics or history. As an art, it is a skill to be mastered, like playing the piano or carpentry. This book approaches logic primarily as a practical art, while still introducing essential scientific principles. Just as a carpenter must understand wood and a pianist must understand musical theory, the student of logic must know key principles of reasoning. However, the aim here is not abstract theory but practical application—learning how to think clearly and apply logical standards in real situations. Why Practice Logic? Logic is like tennis: to improve, you must both study the rules and practice the moves. In reasoning, the “moves” are methods such as forming sound arguments, testing assumptions, and evaluating evidence. The more you practice applying logic, the more it becomes a habit of thought, shaping everyday decisions as well as academic work. Reasoning always involves inferences. We take what we know and use it to reach further conclusions. For example, if your car won’t start but the headlights still work, you can infer that the problem is not the battery. Logic gives us the standards for making valid inferences and distinguishing good reasoning from bad. Logic in Action: Real-Life Questions Logic provides methods for analyzing real issues. Consider debates about seatbelt laws: * Supporters cite statistical evidence that seatbelts save lives. * Opponents cite rare cases where not wearing a seatbelt saved someone. The real question is not just statistical safety but also the role of government in mandating behavior. Logic helps us separate these sub-issues—safety versus personal freedom—and evaluate what kind of evidence is relevant for each. This ability to break down issues is essential not only in politics but also in philosophy, literature, and daily decision-making. Logic helps us identify when people are talking past each other, often because they confuse moral and legal issues or use the same word with different meanings. Concepts, Definitions, and Miscommunication Another essential role of logic is clarifying concepts and definitions. Miscommunication often occurs because people use the same word with different meanings. For instance, two people debating whether student work should be “graded” may mean letter grades versus any kind of evaluation. More abstract terms such as democracy, freedom, or love carry even greater risk of confusion. Logic provides tools for making concepts explicit, reducing vagueness, and defining terms clearly. Even if perfect clarity is impossible, logical methods improve communication, argumentation, and learning across disciplines. Analysis and Synthesis in Logic Good reasoning requires both analysis and synthesis. Analysis means breaking arguments into parts and distinguishing related concepts. Synthesis means putting ideas together into larger frameworks. For example, ideas from philosophy may interact with economics, politics, or psychology. Logic enables us to recognize when ideas support or contradict each other across different fields, helping us integrate knowledge. Objectivity Through Logic At its core, logic cultivates objectivity. Objectivity has two main elements: * A commitment to truth—recognizing that reality exists independently of what we believe or feel. * A disciplined process of reasoning—avoiding bias, wishful thinking, and errors by applying logical standards. Being objective does not mean being neutral or indifferent. It means being fair: listening to opposing arguments, considering evidence carefully, and communicating ideas clearly. Logic strengthens our ability to step outside our own perspective and evaluate arguments critically, which is essential in both writing and discussion. Logic as a Tool for Communication Logic, like language, is a shared framework for communication. Writing in particular requires logical clarity because readers cannot stop to ask for clarification. Many writing problems are, in fact, problems of reasoning: vague assumptions, unclear definitions, or missing arguments. Practicing logic therefore strengthens both thinking and communication. Exercises to Strengthen Logic Just as physical training builds muscle, practicing logical exercises strengthens mental clarity. The book provides three types of exercises: * Skill-building exercises: focused practice within a section. * Integrative exercises: combining skills from multiple sections. * Putting it all together: challenging applications to real-world examples. Developing logical skill takes effort, but the reward is a sharper, more disciplined mind. The payoff is the ability to think critically, communicate persuasively, and navigate complexity with clarity. Conclusion: Why Logic Matters Logic is more than academic theory—it is the art and science of reasoning. It helps us avoid confusion, clarify concepts, weigh evidence, and think objectively. Whether in personal life, education, politics, or professional work, logic gives us tools to reach better conclusions and communicate more effectively. The study of logic is therefore both a discipline and a practice, a way to build mental strength and clarity. Like any skill, it improves with effort, and the clarity it provides is invaluable in a world full of complexity and competing perspectives. 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

    24 min

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