The Elements of Arguments PDF

# The Elements of Arguments ## An Introduction to Critical Thinking and Logic ### By Philip Turetzky ## Chapter 1 - Basic Definitions and Structure of the Text * **Part 1: Arguments** For our purposes, the central concept of logic is that of an argument. In the sense the term is used in critica...

# The Elements of Arguments ## An Introduction to Critical Thinking and Logic ### By Philip Turetzky ## Chapter 1 - Basic Definitions and Structure of the Text * **Part 1: Arguments** For our purposes, the central concept of logic is that of an argument. In the sense the term is used in critical thinking and logic, an argument is not a quarrel or fight between people, but rather consists of propositions, including both a number of premises and one conclusion. Premises give reasons that are supposed to support the truth of a single proposition, the conclusion. Arguments can be presented by a single person and even presented anonymously; that is, they and their content and their evaluations are independent of who, if anyone, presents them. To argue for a conclusion is to present reasons for that conclusion to be true; to argue from one or more premises is to present them as reasons for thinking that the conclusion being argued for is true. An argument thus consists of the whole, including the reasons, the premises, the conclusion those reasons are supposed to support, and the relationship of support that is supposed to hold between the premises and the conclusion. An example of an argument is the following: * **Example 1:** When it snows, the road gets slippery, and it has been snowing all night. So, the road will be slippery. This argument gives reasons that are supposed to support the proposition that the road will be slippery. Those reasons are both that it has been snowing all night and that when it snows, the road gets slippery. We can make this clear by rewriting the argument in what we shall call premises and conclusion form (see below) as follows: 1. When it snows, the road gets slippery, and it has been snowing all night. Therefore, 2. The road will be slippery. Where (1) is the reason or premise and (2) is the conclusion which is supposed to be supported by (1). We define argument rigorously as follows: * **Definition of Argument:** Something is an argument if and only if it is a set of propositions such that the truth of one (called "the conclusion") is supposed to be supported by the truth of the others (called "the premises").¹ This definition is complex and in need of clarification. Accordingly, we will divide up the material covered by this text in a way that corresponds to the separate elements of this definition. First, arguments consist of propositions. The term "proposition" is used here in a specific sense that requires considerable clarification. Chapter II will explore what, for the purposes of logic and critical thinking, a proposition is and how propositions are to be distinguished from other seemingly similar things. Chapter II will also sort out some typical confusions about the nature of propositions and will examine some common errors in reasoning that arise because of these confusions. Having sorted out these confusions, we will then be able to see in greater depth why logic and critical thinking skills are important. Chapter III will continue the exploration of propositions begun in Chapter II by identifying several important types of propositions and showing some logically important ways in which complex propositions can be constructed from simpler propositions. Chapter III will also consider some common errors that arise out of misunderstanding these types of complex propositions. Second, arguments consist of sets of propositions. Even though some arguments may be expressed in a single sentence, arguments must always contain more than one proposition. If an argument is expressed in a single sentence, that sentence is always complex and expresses a relationship between at least two propositions. That every argument includes at least one premise and exactly one conclusion demonstrates this point. The conclusion of an argument is the proposition being argued for; that is, the conclusion is that proposition whose truth the truth of the other propositions, the premises, are supposed to support.² * **Definition of Conclusion:** A proposition is the conclusion of an argument if and only if it functions in that argument as the proposition whose truth is supposed to be supported by the argument's premises. For example, the following sentence contains an argument. * **Example 2:** Sue will get the promotion because she is the best qualified for the job, and whoever is best qualified for the job will get the promotion. Although this argument is expressed in a single sentence, it contains the proposition that expresses the conclusion * **Sue will get the promotion** and the complex proposition that expresses the premise, * **She is the best qualified for the job, and whoever is best qualified for the job will get the promotion.** The complex premise in Example 2 can be divided into two separate premises, since the two propositions that compose the premise are connected with "... and..." or what we shall call logical conjunction (see Chapter III) as follows: 1. Sue is the best qualified for the job. 2. Whoever is best qualified for the job will get the promotion. Notice that these propositions can each be expressed in separate complete sentences. A sentence is a grammatical structure belonging to a particular language and forming a complete unit, while a proposition is the meaning or content that may be expressed in a sentence (we will define "proposition" more rigorously in Chapter II). By convention we count the number of arguments by counting the number of conclusions, for each argument has exactly one conclusion. The premises are the other propositions in the argument: those propositions whose truth is supposed to give support to the truth of the conclusion. Arguments can have any number of premises. * **Definition of Premise:** A proposition is a premise of an argument if and only if it functions in that argument as a proposition whose truth is supposed to give support to the truth of the argument's conclusion. For example, the following sentence contains an argument. * **Example 3:** I won't miss any of the course work, because if I go to class, then I won't miss any of the course work, and I do go to class. Although this argument is expressed in a single sentence, it contains a complex proposition that expresses its premise, * **If I go to class, then I won't miss any of the course work, and I do go to class,** and the proposition that expresses the conclusion, * **I won't miss any of the course work.** The premise in Example 3 can be divided into two separate premises, since the two propositions that compose the premise are connected with "... and ..." (see Chapter III) as follows: 1. If I go to class, then I won't miss any of the course work. 2. I do go to class. While premise (1) is complex, since it contains the two propositions "I go to class" and "I won't miss any of the course work," this premise cannot be broken up and separated into its parts as with the propositions connected with "... and...." We shall see why this is in Chapter III. What makes a proposition count as a premise or as a conclusion is how the proposition functions as part of an argument. A proposition need not be part of any argument at all, in which case we simply call it a proposition, but when a proposition is part of an argument, then it should instead be called a premise or a conclusion depending on how it functions in that argument. Since each argument alleges that there is a connection between the truth of its premises and the truth of its conclusion, it is important to study how the truth or falsity of one claim may depend solely upon the truth or falsity of another. Such dependencies are called logical relations. Chapter IV explores various types of logical relations, as well as some important consequences that follow from the fact that the truth or falsity of some propositions depends solely on the truth or falsity of others. The connection between the premises and the conclusion of an argument is supposed to be one of support. As the definition states, the truth of an argument's conclusion is supposed to be supported by the truth of its premises. This aspect of arguments is both the most important and the most challenging. It is crucial to notice that the definition of argument does not say that the premises of an argument do support its conclusion; it only says that the premises of an argument are supposed to support its conclusion. The reason for this is that not all arguments are good arguments. In a good argument the premises do support the conclusion. But bad arguments still count as arguments; they still make the claim that their premises support their conclusion, even though their premises may actually fail to do so. So in giving a definition of argument we are careful to say that the premises are supposed to support the conclusion, so that our definition includes all arguments regardless of whether they are good arguments or bad ones. However, good arguments differ in definite and distinguishable ways from bad arguments. The primary tasks of logic and critical thinking are to discover, explain, and apply methods for determining of any argument whether it is good or bad. These three tasks are related to one another. The study of logic and critical thinking seeks to provide explicit methods for identifying which arguments are good and which are bad. Most people reason well some of the time, but because they seldom reflect explicitly on how they are reasoning, they often develop bad habits and consequently fall into error and confusion without noticing that they do so. Part of the difficulty is that we are usually and for the most part concerned with what we are reasoning about, the specific subject matter, rather than with how and how well we are reasoning about that subject matter. Studying logic and critical thinking helps us become more aware of these pitfalls and urges us to take a reflective step back so as to explicitly examine how-that is, by what methods-we are reasoning, rather than what we are reasoning about. So studying logic and critical thinking provides us with explicit methods that we may apply to actual arguments to sort out which arguments are good and which are bad. However, in order to use such methods, we must develop and discover which methods work reliably. This is what logicians-people who study logic-do: they seek to discover methods that work reliably to sort out which arguments are good and which are bad. We are fortunate to be able to draw on over 2,000 years of such studies. Finally, if we are to have methods that reliably sort out which arguments are good and which are bad, then we must be able to explain why those methods work, so as to justify the reliability of those methods and understand their power, scope, and limits. Chapter V will identify some important types of arguments, explain the standards for evaluating them, and develop some methods for testing some types of arguments to see if they meet these standards of evaluation. The types of arguments investigated in Chapter V will be presented through formal models designed to be clear and simple and to make the standards for evaluating arguments easier to grasp. However, such clarity and simplicity necessitate a certain amount of abstraction and simplification. When we confront arguments in our everyday lives, they are seldom presented in these neat and rigorous forms. First, we are ordinarily confronted with and produce arguments that are expressed in a disjointed and fragmentary way; they are not expressed in rigorous or formal language. In addition, the arguments we ordinarily come across or produce ourselves tend to be mixed in with other things we do and say, and they appear in the context of other activities and other concerns (many things that are said or written are neither arguments nor parts of arguments). This means that to apply the insights and methods of logic to ordinary arguments requires that we develop skills in reading, interpreting, and translating between ordinary discourse and the more formal models we explore in Chapter V. The task of Chapter VI is to provide some tips and rules of thumb for applying the methods and insights developed in previous chapters to arguments as they appear in ordinary discourse. This text is organized as we have just outlined. We will concentrate on and emphasize the elements of arguments in the indicated order: 1. Throughout this book, we will focus exclusively on how examples of reasoning work and will never be concerned about what is actually true or false with regard to any subject matter (see Chapter II).