Critical Thinking and Logical Reasoning PDF

CRITICAL THINKING AND LOGICAL REASONING BY DR. CLETUS KWAKU MBOWURA © 2024 1 Unit 1: Arguments and Non-Arguments in Logic Unit Introduction Hello! Welcome to the study of Unit 1, which focuses on arguments and non-arguments in logic. Logic focuse...

CRITICAL THINKING AND LOGICAL REASONING BY DR. CLETUS KWAKU MBOWURA © 2024 1 Unit 1: Arguments and Non-Arguments in Logic Unit Introduction Hello! Welcome to the study of Unit 1, which focuses on arguments and non-arguments in logic. Logic focuses on arguments, and the study of logic does not only introduce students to the analysis of arguments, it also equips students with many useful skills. In ordinary sense, the term argument is used to refer to divergent opinions of people about something. In logic, the term argument refers to a set of statements, known as premises, with a conclusion. Premises form the building blocks of arguments in logic. Premises are the statements that provide evidence in support of the conclusion in an argument. Arguments in logic can be subjected to analysis to determine their strengths or weaknesses, validity or invalidity. It is significant to note that, it is not always the case that a set of statements qualifies as an argument. For a text or set of statements to qualify to be called argument in logic, there should be an inferential relationship between the premises and the conclusion. A set of statements without a conclusion or from which a conclusion cannot be inferred, whether explicitly or implicitly, is called a non-argument in logic. You will learn all arguments and non-arguments in this Unit, how to analyze them, as well as all the terms associated with them. This Unit is made up of the following sections: Section 1: Logic and Critical Thinking: Meaning and Significance Section 2: Basic Terms in Arguments: Premises, Propositions and Statements Section 3: Inference and Conclusion in Arguments Section 4: Arguments in Logic Section 5: Analyzing Arguments in Logic Section 6: Non-Arguments in Logic Objectives By the end of this unit, you should be able to: Define logic and account for the skills needed in studying critical thinking. Explain the significance of studying logic and critical thinking. Differentiate between an argument in ordinary sense and an argument in logic. Distinguish between arguments and non-arguments in logic. Explain basic terms in arguments such as premise, propositions, inference, and conclusion. Recognize and analyze arguments in texts. Differentiate between good arguments and bad arguments. Identify and analyse the various types of non-arguments in logic. 2 Section 1: Logic and Critical Thinking: Meaning and Significance Introduction Welcome to this section. This section focuses on the meaning and significance of logic and critical thinking. You often hear people say that “your argument is not logical” or that “you do not engage in critical thinking.” Have you taken the pain to know what they meant by such statements? If you have not, do not worry because this section will give you the meanings of such statements. Join me to learn the meaning and significance of logic and critical thinking. Objectives Upon a successful completion of this section, you should be able to: Define logic and use its meaning appropriately in your daily conversations. Explain critical thinking in your own words. Account for the skills needed in studying critical thinking. Explain the significance of studying logic and critical thinking. Logic: Meaning and Focus What is logic and what is its focus? In commonsense, logic means an idea that makes sense. It is used to refer to an idea that appeals to the senses of people. People often use the term to refer to any idea or list of statements that make commonsense or an idea or series of statements that are coherent in meaning or can stimulate the minds of others. However, logicians do not use the term ‘logic’ the way it is used in commonsense. To logicians, the focus of logic is on arguments. In other words, “logic deals with arguments. Logic is the field of study concerned with analyzing arguments and appraising their correctness or incorrectness” (Salmon, 2013, p. 12). Logic can also be defined as “the organised body of knowledge, or science, that evaluates arguments” (Hurley, 2015, p. 1). Copi, Cohen and McMahon (2014, p. 2) define logic as “the study of the methods and principles used to distinguish correct from incorrect reasoning.” In other words, logic is the study of methods of evaluating premises/propositions of an argument to determine whether or not they adequately support a conclusion. Therefore, “the aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own” (Humphrey and Watson, 2018, p. 1). It is not easy for beginners to evaluate arguments successfully. Given its definition and focus, studying “logic can be a challenging subject to beginners” (Hurley & Watson, 2018, p. xxii). Despite this difficulty, it is important for students to study logic. Critical Thinking The words, “critical”, “criticism” and “critic” are derived from the Greek word kritikos, meaning, to be “able to judge or discern” (Butterworth & Thwaites, 2013, p. 6). To be critical means to make evaluative judgements about something. Critical Thinking can, therefore, be defined as “the 3 systematic evaluation or formulation of beliefs, or statements, by rational standards” (Vaughn, 2008, p. 4). Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, analyzing, synthesizing, and evaluating information gathered from observation, experience, reflection, reasoning, or communication. It involves the ability to think clearly and rationally, understanding the logical connection between ideas, and systematically solving problems by considering different perspectives and outcomes. Critical thinking has some characteristics. First, it is rational in character because it “operates according to rational standards” (Butterworth & Thwaites, 2013, p. 5). Second, “critical thinking is systematic because it involves distinct procedures and methods” (Butterworth & Thwaites, 2013, p. 5). Third, critical thinking “entails evaluation and formulation because it's used to both assess existing beliefs (yours or someone else's) and devise new ones” (Butterworth & Thwaites, 2013, p. 5). Skills Needed for Critical Thinking Analytical skill There are some skills that a student needs to possess in order to be able to be successful in critical thinking. In the first place, a student needs an analytical skill. At the core of critical thinking as a discipline is analytical skills. Reasoning is rational, and rationality requires that one is able to break down complex issues into parts that can be easily comprehensible. As a skill, analysis enables a person to reason through issues to identify relationships and identify relevant and irrelevant information. Hence, a student who intends to be a critical thinker must be analytical. Interpretative skill Another skill that a student needs to be a critical thinker is interpretation. Interpretation is the skill that enables a person to be able to understand situations and explain their meanings and relevance clearly. No matter the complexity of situations, the skill of interpretation enables a person to dissect complexities and comprehend complex situations in simple terms. Inferential skill Inferences are at the core of arguments in logic and critical thinking. An inference is the process of drawing a conclusion from an argument. In simple terms, “to infer something means to draw it as a conclusion, usually from some evidence or information” (Butterworth & Thwaites, 2013. p. 74). Inferences must be sound or safe because “a sound or ‘safe’ inference is one that is adequately supported by the information. Otherwise, it is unsafe … ‘unjustified’ or ‘unwarranted’ …” (Butterworth & Thwaites, 2013. p. 74). Sometimes, the pattern of the argument is such that it is easy to make an inference. Some arguments are complex, and the inference may not be very clear and simplistic. Whatever the nature of the argument, you need the skill of inference to be able to identify the conclusion in an argument, irrespective of whether the conclusion is explicit or implicit. 4 Evaluative skill Evaluative skill is needed to examine and dissect arguments in logic and critical thinking. Evaluation is the processing of assessing the credibility and relevance of information and sources. It also requires the skill to make judgement based on the strength and validity of arguments. In the case of inductive arguments (you will learn them later), the application of the skill of evaluation to the arguments is needed to determine any assumptions, biases and fallacies they may contain. Explanative skill Arguments in logic and critical thinking contain explanations. Arguments are structured in such a way that they contain evidence in support of a conclusion. A student of logic and critical thinking needs the skill of explanation to be able to articulate the reasons or evidence in support of a conclusion succinctly. Arguments that lack clarity of the explanation of the reasons or evidence in support of a conclusion are usually said to be logically bad or weak arguments. On the other hand, logically good or strong arguments contain sufficient explanation of the reasons, and they provide a coherent logical relationship between the reasons/evidence and the conclusion. Reasons in an argument “are expressions which tell us why something is as it is. Their primary function is to explain” (Butterworth & Thwaites, 2013. p. 58). In good arguments, there must be “reasons for believing, or agreeing with, the conclusion” (Butterworth & Thwaites, 2013. p. 58). Problem-solving skill Critical thinking requires problem-solving skills. It requires a person to have the skills to identify problems and determine the pathways to solve or overcome them. Problem-solving is at the heart of critical thinking. With problem-solving skills, you are able to use “some sort of strategy – a method of proceeding from the beginning which may be systematic or may involve trial and error. This development of strategies is the heart of problem solving” (Butterworth & Thwaites, 2013. p. 79). Creative skills It is not always the case that problems are solved by employing a systematic method to evaluate situations. As Butterworth and Thwaites (2013, p. 98) put it, “some problems may not always be resolved by using direct methods of calculation.” Other times, there are multifaceted approaches to the problem. This is because some “problems do not have a single solution, but many, and we need to find one that represents a maximum or minimum” Butterworth & Thwaites, 2013. p. 98). Hence, there is the need for a problem-solver to sometimes think outside the box to find novel solutions. Activity 1.1 What does the commonsense or ordinary sense of the term ‘logic’ mean? Differentiate between logic as used by logicians and ordinary people. 5 Importance of Studying Logic and Critical Thinking You now know the definition of logic and what it deals with. Why is it significant to study logic and critical thinking? There are many reasons why it is important for students to study logic and critical thinking. First, logic and critical thinking improves the reasoning skills of people. By studying logic and critical thinking, students learn the techniques of reasoning, making and evaluating arguments. It equips students with the skills of constructing logical proofs, which ultimately “hones the skills needed” (Hurley & Watson, 2018, p. xxii) in constructing logical arguments in our everyday activities. In short, “learning the various techniques of logic improves and perfects that very reasoning ability that is so essential to our being human” (Hurley & Watson, 2018, p. xxii). Second, studying logic and critical thinking is significant because it introduces students to the various types of logical inferences. In your daily routine activities, you make inferences (reasoning) from sets of claims or statements. You may not be aware of the type of inferences you have made. When you study logic and critical thinking, you learn the various types of inferences such as modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, etc. (you will study them later). You may have been making the above inferences without any formal knowledge. Studying logic and critical thinking would give you formal knowledge of how to make these inferences and, obviously, enable you to use those inferences very well in arguments in your daily activities. In short, studying logic will make explicit the rules of inference (reasoning) that are already a part of your everyday life (Hurley & Watson, 2018, p. xxii). Third, “logic is primarily concerned with distinguishing good reasoning from bad reasoning” (Humphrey & Watson, 2018, p. xxii). By studying logic and critical thinking, you would be equipped with the technique of discerning or distinguishing good reasoning from bad reasoning. The extent of the success of a lot of things we do in our daily routine activities depends on our reasoning. While good reasoning would normally advance the course of our activities, bad reasoning may not. In all our endeavours and careers, we need to apply good reasoning skills to all the issues we face. Whether you are a banker, lawyer, politician, marketer, teacher, surgeon, judge, accountant, security officer, etc. you need to apply good reasoning skills in all the issues you are confronted with. Studying logic and critical thinking equips you with the skill to good make arguments (reasoning), as well as distinguish between good reasoning from bad reasoning. Fourth, logic and critical thinking as a discipline lays a good foundation that would improve the performance of students in other disciplines. This is because “a strong foundation in making good inferences (doing logic) will improve your performance” (Humphrey & Watson, 2018, p. xxiii) in other disciplines. How? If you are a science student, for instance, you will need to know how to design experiments, test hypotheses and draw good conclusions (Humphrey & Watson, 2018, p. xxiii). Logic and critical thinking will build your skills in them. If you are studying any humanities discipline (law, economics, political science, management, accounting, etc.), you also need logic and critical thinking. Logic and critical thinking provides you the surest way of analyzing data and drawing conclusions from them. If you are studying literature, “engaging with a text critically means evaluating its coherence, its development of characters and their motivations, and many other things, almost all of which involve logic. In short, logic teaches and improves the kinds of 6 knowledge and basic skills that are relevant to almost everything you do or want to study” (Humphrey & Watson, 2018, p. xxiii-xxiv). Finally, studying logic and critical thinking can be fun. From time to time, you need fun. Having fun can revitalize your faculties, make you happy and active all the time. Logic and critical thinking provides students with intriguing realities about arguments, fallacies and controversies that serve as a means of entertainment to alleviate boredom. Activity 1.2 State and explain three reasons why the study of logic and critical thinking is significant. Summary You have come to the conclusion of this section. Congratulations! In this section, you learnt that logic focuses on arguments. You also learnt that critical thinking focuses on the evaluative mechanisms applied to the analysis of arguments. Furthermore, you learnt that there are some skills needed to make a person become a critical thinker. The skills include analytical, evaluative, inferential, interpretative, explanative, creative and problem-solving skills. Finally, you learnt that it is important for a student to learn logic and critical thinking for a number of reasons. 7 Section 2: Basic Terms in Arguments: Premises, Propositions and Statements Hello! Welcome to the study of the basic terms in arguments. Studying logic and critical thinking is significant. Its argument forms help to build your skills in constructing arguments. It also builds your critical thinking skills. There are a number of terms in logical arguments. Terms such as premises, propositions, statements, inferences and truth-value are often used in the analysis of logical arguments. Join me in this section as I take you through the basic terms or concepts in arguments. Objectives Upon a successful completion of this section, you should be able to: Construct arguments or engage in arguments with others about how logic equips learners with reasoning skills and the skill to distinguish between good reasoning from bad reasoning. Demonstrate knowledge on the concept premise in arguments. Distinguish between a proposition and a non-propositional statement. Premises in an Argument A premise is a proposition that makes a claim, provides evidence or sets forth the reasons that serve as the basis of a particular conclusion. According to Copi, Cohen & McMahon (2014, p. 4), a premise is “what is typically asserted by a declarative sentence, but not the sentence itself.” In any argument, “the propositions upon which inference is based; the propositions that are claimed to provide grounds or reasons for the conclusion” (Copi, Cohen & McMahon, 2014, p. 6) are called premises. The following propositions or statements are examples of premises: 1. Kofi is a brilliant student. 2. GCTU offers IT and Computer Science programs. 3. Accra is the capital of Ghana. 4. I am Nana James Tweneboah Prekope I. 5. Some politicians in Ghana are corrupt. All the above propositions make some claims that can serve as a basis upon which a conclusion can be drawn. Characteristics of Premises Premises have a number of characteristics. Join me as I take you through the characteristics of premises. All premises have truth-value. Truth-value is a term used to refer to the truthfulness or falsity of a proposition. Every claim in a proposition can be analysed to determine whether 8  it is true or false, though, in some cases, its truthfulness or falsity may be undetermined. Truth-value asserts that something is the case or it asserts that something is not. As Copi, Cohen and McMahon (2014, p. 4) rightly put it, “we may affirm a proposition, or deny it – but every proposition either asserts what really is the case, or it asserts something that is not. Therefore, every proposition is either true or false.” If you make statements such as “it is raining”, “Kofi is a brilliant student”, “Accra is the capital of Ghana”, you or any person should be able to determine their truth-value, i.e., determine whether each statement is true or false. Any statement that does not have a truth-value (cannot be said to be true or false) does not qualify to be a premise. For instance, the statements “is it raining?” and “come here, Kofi!” cannot be said to be true or false; hence, they are not premises. Questions and commands assert nothing, and therefore they are not premises. Premises are either simple or compound propositions. A simple premise is a proposition that makes a single claim. For instance, the statements “Kofi is dancing Kpalongo” and “it is raining” are simple premises because each contains a single claim. Compound premises are propositions that make two or more claims. For instance, the statements “Kofi is dancing Kpalongo and Ama is singing”, “I will go to church today or go to school” and “if it rains today, I will plant corn” are compound premises because each contains two claims. Note that a premise can also be a compound premise when a proposition contains other propositions within itself (Copi, Cohen & McMahon, 2014). For instance, the statement “the Forest Zone in Ghana makes up 30% of Ghana’s vegetation, harbours a lot of animals and attracts more rainfall than any other vegetational zone in Ghana” is a compound statement because it asserts three propositions about the Forest Zone in Ghana, namely, the landmass of the Forest Zone, what it habours and what it attracts. Premises either make particular or general claims. A premise makes a particular claim when the claim it makes is not general. For instance, the statements, “it is raining in Kpandai”, “Kofi is dancing Kpalongo and Ama is singing”, “some politicians are corrupt” and “if it rains, I will plant corn” are particular premises because they do not make general claims about the objects in reference. On the other hand, a premise makes a general claim when it makes a universal claim about an object or issue. For instance, the statements “all humans are mortal”, “no politicians are corrupt”, and “all men are womanizers” are general premises because they make universal claims about the objects in reference. Premises may be explicit or implicit. Explicit premises are propositions in an argument that are clearly stated. You do not need to figure out the premises in an argument. Take a look at the following argument: All men are mortal. Kofi is a man. Therefore, Kofi is mortal. The first two statements are premises, and both were clearly stated in the argument. Hence, they are explicit premises. On the other hand, some premises are implicit. Implicit premises 9  are propositions in an argument that are not clearly stated, but have to be figured out based on the logical structure of the argument. Take a look at the following argument: Mbowura is a philanthropist, who offers a lot of assistance to people in his community. This proves that a person does not have to be a politician to be a philanthropist. In the above argument, the first statement is a premise, which was clearly stated. The second statement is the conclusion of the argument. But the second premise in the argument is implicit, which can be figured out from the structure of the argument. The implicit premise in the above argument is that “Mbowura is not a politician.” Activity 2:1 Take any newspaper of your choice. Identify and two arguments with implicit premises. Write down the arguments in the spaces below and state their implicit premises. Argument 1 ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Argument 2 ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… 10 Propositions versus Statements Logicians use the terms proposition and statement interchangeably. The usage of the terms proposition and statement is a matter of preference to logicians. As Copi, Cohen and McMahon (2014, p. 4) argued “the term statement is not an exact synonym of proposition, but it is often used in logic in much the same sense. Some logicians prefer statement to proposition, although the latter has been more commonly used in the history of logic. Other logicians eschew both terms as metaphysical, using only the term sentence.” In this write-up, I prefer to use them differently. What is a proposition? According to Humphrey and Watson (2018, p. 5), a proposition, in the narrow sense, is the meaning or information content of a statement. Goranko (2016, p. 2) defines a proposition as “a sentence that can be assigned a unique truth value: true or false.” In other words, it is a statement that can be determined as true or false. It is important to note that all propositions in arguments are statements but not all statements qualify as propositions. A statement is said to be a proposition if it contains or makes a claim that contains a truth-value (can be said to be true or false). On the other hand, a statement that does not contain any factual claim (true or false) in it is not a proposition. In other words, a statement that does not contain a truth-value does not qualify as a proposition. Hence, it is a non-propositional statement. Take, for example, the following statements: 1. It rained in Kpandai today. 2. Kofi is dancing Kpalongo while Mensah is drumming. In the above examples, 1 and 2 are propositions because they contain claims that can be analyzed to determine whether the claims are true of false. You can gather evidence to determine whether it is true or false that it rained in Kpandai today. Similarly, based on available experiential evidence, you can determine whether it is true or false that the dance Kofi was performing is Kpalongo; you can also use your experiential evidence to determine whether it is true or false that Mensah was drumming. Some statements cannot be said to be true or false. Statements in the form of proposals, suggestions, opinions, commands, questions and exclamations cannot be said to be true or false. Hence, such statements do not qualify to be propositions. Here are some examples. 1. Is it raining in Kpandai today? 2. Stop what you are doing. 3. Let’s show them love. 4. I suggest we go to Mensah’s house tomorrow. 5. Praise the Lord! 6. Grace loves me. In example 1 above, the statement, “is it raining in Kpandai today?” is not a proposition. Rather, it is a non-propositional statement because it does not make any claim that can be analyzed to determine its truth-value. The statement is a question, which cannot be logically subjected to analysis to determine whether the statement is true or false. Similarly, the statement in example 2, “stop what you are doing” is a command, but not a statement of claim that can be said to be true 11 or false. Example 3 is a statement of opinion, and does not qualify to be a proposition because its truth-value cannot be determined. Similarly, the truth-value of example 4 cannot be determined because it is a suggestion. Example 5 is an exclamation, which cannot be said to be true or false. In example 6, the statement “Grace loves me” depends on who the particular “Grace” is and who uttered the statement. Hence, it is not a proposition because no truth-value can be consistently assigned to it. Rather, it is a non-propositional statement which qualifies as a moral value statement. It is important to emphasize that the determiner of a propositional statement and a non- propositional statement is a statement of claim. A propositional statement, or simply a proposition is typically a declarative statement or a sentence component that could stand as a declarative sentence (Humphrey & Watson, 2018, p. 2). In short, a proposition should contain a statement of claim; a non-propositional statement is a statement that does not contain a claim. Given that some statements qualify as propositions and some do not, it is not always accurate to use the term “statement” as a synonym of the term “proposition.” As Copi, Cohen and McMahon (2014, p. 4), “the term statement is not the exact synonym of proposition …” Activity 2:2 Construct ten statements of which five are propositions and the remaining five are not. State the reason(s) why you consider some of the statements as premises and some not premises. Summary In this section, you also learnt that arguments contain premises, which are statements that make claims. You learnt that premises have truth-value, propositions are particular of general, propositions are implicit or implicit, propositions are simple or compound propositions. You also learnt that there are some passages that can be identified as non-arguments. 12 Section 3: Inference and Conclusion in Arguments Introduction Welcome to this section. In the previous section, you learnt about premises, propositions and statements in arguments. This section focuses on two key terms in arguments, namely, inferences and conclusions. Arguments in logic, unlike arguments in ordinary sense, contain conclusions. The premises of the arguments provide evidence for the conclusion. Conclusions in arguments come alongside with inferences, that is, the process of drawing a conclusion. Objectives Upon a successful completion of this section, you should be able to: Explain what a conclusion in an argument entails. Identify the process of drawing a conclusion in an argument. Identify premise and conclusion indicators in arguments. Inference You draw conclusions from your daily routine activities. According to Goranko (2016, p. 2), “an inference, in the narrow sense of the term, is the reasoning process expressed by an argument.” In the broad sense of the term, “inference” is used interchangeably with “argument.” An inference is the process of drawing a conclusion from a proposition or propositions. It is the process of affirming one proposition on the basis of others. According to Copi, Cohen and McMahon (2014, p. 5), an “inference is a process that may tie together a cluster of propositions.” In other words, it is the process whereby a person examines “propositions with which the process [argument] begins and with which it ends” (Copi, Cohen and McMahon, 2014, p. 5). In short, an inference is “a process by which one proposition is arrived at and affirmed on the basis of some other proposition or propositions” (Copi, Cohen and McMahon, 2014, p. 5). In simple language, drawing a conclusion from a proposition or number of propositions is called an inference. Conclusion Let’s now turn our attention to a conclusion in an argument. A conclusion in an argument is “the proposition to which the other propositions in the argument are claimed to give support, or for which they are they are given as reasons” (Copi, Cohen and McMahon, 2014, p. 5). In other words, a “conclusion is what the argument is trying to prove (Waller, 2012, p. 17). Take a look at the following argument: All men are mortal. Kofi is a man. Therefore, Kofi is mortal. The conclusion in the above argument is that “Kofi is mortal” because it is the proposition that the first two propositions provide support or provide reasons for. 13 A conclusion in an argument can be explicit or implicit. In the above example, the conclusion (“Kofi is mortal”) was explicit because it was clearly stated. On the other hand, an argument could contain an implicit conclusion. An implicit conclusion is a conclusion in an argument that is not clearly stated, but has to be figured out from the structure of the argument. Take a look at the following example: I had a revelation that one of the two of us would pass the exam in Logic and Critical Thinking. I will be the one who will pass the exam. In the above example, the argument contains an implicit conclusion. In other words, the conclusion is not clearly stated; you need to figure out the conclusion based on the structure of the argument. In the above example, the implicit conclusion is that “you will fail the exam in Logic and Critical Thinking.” Where to Find a Conclusion in an Argument Where does a conclusion appear in an argument? Conventionally, the conclusion in an argument appears at the end of the argument. For instance, in the argument, “all men are mortal. Kofi is a man. Therefore, Kofi is mortal”, the conclusion Kofi is mortal appeared at the end of the argument. However, it is not always the case that the conclusion appears at the end of the argument. The conclusion can appear anywhere (beginning, middle or end) of an argument. Take a look at the following arguments: Argument 1 Liverpool is an inconsistent football club. They beat Manchester United 7-0, but lost 1-0 to Bournemouth in the following week. It was so embarrassing. Argument 2 We made all attempts to fix the problem. We could not have done any better than we did. We did far better than Kofi and his group who tried many days to fix the problem. We succeeded in fixing the problem in a day. In example 1, the conclusion is Liverpool is an inconsistent football club. The conclusion is at the beginning of the argument. In example 2, the conclusion is We could not have done any better than we did. The conclusion appeared in the middle of the argument. 14 Activity 3.1 Construct your own argument in the spaces below. Your argument must contain a conclusion. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Inference Indicators How do you know whether a proposition in an argument is a premise or conclusion? It is tasking for a student to identify premises and conclusions in arguments. As Humphrey & Watson (2018, p. 3) put it, “one of the most important tasks in the analysis of arguments is being able to distinguish premises from conclusions. If what is thought to be a conclusion is really a premise, and vice versa, the subsequent analysis cannot possibly be correct.” Many arguments contain inference indicators (also known as premise and conclusion indicators), which will help you to determine the premises and conclusion in an argument. What is an inference indicator? An inference indicator is a word or phrase that shows the role of a proposition in an argument. They are “indicator words that provide clues in identifying premises and conclusion” (Humphrey & Watson, 2018, p. 3). A proposition performs two roles in an argument. It performs the role of a premise and a conclusion. To borrow the words of Copi, Cohen and McMahon (2014, p. 11), words or phrases that typically serve to signal the appearance of an argument’s conclusion or of its premises” are called inference indicators. A word or phrase that shows that a proposition performs the role of a premise in an argument is called a premise indicator. A word or phrase that shows that a proposition performs the role of a conclusion in an argument is called a conclusion indicator. Below is a partial list of premise indicators and conclusion indicators. Table 1: Table of premise and concluding indicators Premise indicator Conclusion indicator Because Therefore Since Hence Granted that Thus Assuming that So Seeing that Which proves that Inasmuch as For this reason The facts are that Accordingly Evidentially Consequently In evidence As a result On the account that We may infer As shown by; in lieu of In conclusion It follows from; in view of the fact that; the Which shows that; which entails that; which reason is that; for that reason; for this reason proves that; which implies that 15  May be inferred from; May be deduced from; In consequence may be derived from Reference: Copi, Cohen & McMahon, 2014, pp. 11 & 12. Note that the above words and phrases are not always premise or conclusion indicators, but they usually do. These words or phrases would help you to identify a premise and a conclusion in an argument. Activity 3.2 1. Scrutinize the following argument, and point out its implicit conclusion. Hajia Memuna wears biker shorts. This proves that a lady does not need to need to be a slay queen to wear biker shorts. A. Hajia Memuna is not a slay queen. B. Hajia Memuna is a slay queen. C. Hajia Memuna deserves to be a slay queen. D. Hajia Memuna did not know that people see her as a slay queen. 2. Consider the argument: “You achieved good results because you worked together as a team. You would probably not have achieved good results if you did not work together as a team.” The conclusion of the argument is: A. You achieved good results. B. You worked together as a team. C. You would probably not have achieved good results. D. You did not work together as a team. 3. Consider the following line of argument, and determine the implicit premise it contains. “Mr. Kals Tuffuor resides at Virginia, and had never travelled to California. It could not have been Mr. Kals Tuffuor who used his credit card to shop at California.” A. Mr. Kals Tuffuor’s credit card was used for shopping in Virginia. B. Someone used Mr. Kals Tuffuor’s credit card to shop in California. C. Someone used Kals Tuffuor’s credit card to shop in both Virginia and California. D. Mr. Kals Tuffuor personally used his credit card to shop in both Virginia and California. 4. Consider the argument: “one of us will clean the dishes. It won’t be me.” Which one of the following statements is the correct implicit conclusion of the argument? A. You or I would clean the dishes. B. Both you and I would clean the dishes. C. You would clean the dishes. D. No one would clean the dishes. 16 Summary In this section, you learnt that inference is the process of drawing a conclusion from a set of premises. Furthermore, you learnt that words or phrases that provide clues of the role of a proposition in an argument are called inference indicators. You also leant that inference indicators are subdivided into premise indicators (words or phrases that show that a statement performs the role of a premise in an argument) and conclusion indicator (words or phrases that show that a statement performs the role of a conclusion in an argument). Furthermore, you learnt that a conclusion in an argument is the statement in an argument that all other statements provide reasons in support of it. You also that a conclusion can appear anywhere in an argument (beginning, middle or end of an argument). Bravo! You have successfully completed the study of this section. 17 Section 4: Arguments in Logic Introduction Have you ever engaged in an argument? What do people mean when they use the term ‘argument’? This section focuses on arguments in logic. You have learnt in Section 1 of this Unit that logic focuses on arguments. You have also learnt in Section 2 of this Unit that premises form the building blocks of arguments. This section explains the meaning of argument in logic, its form, structure and ways of recognizing arguments. Objectives Upon a successful completion of this section, you should be able to: Differentiate between an argument in ordinary sense and an argument in logic. Identify ways to recognize arguments in texts. Determine the form that arguments in logic take. What is an Argument? In ordinary usage, an argument is a disagreement between people. It is used to refer to a situation of dispute between two or more people. The Advanced Oxford English Dictionary defines an argument as “an exchange of diverging or opposite views, typically a heated one.” It also defines an argument as “a reason or set of reasons given with the aim of persuading others that an action or idea is right or wrong.” Logicians do not use the term argument to mean the ordinary usage of the word. According to Woods, Irvine and Walton (2004), logicians use the term argument in both broad and narrow senses. Broadly, logicians use the term argument to mean “a presentation of reasons or evidence in support of some claim. It is an attempt to build a case in favour of a conclusion” (Woods, Irvine & Walton, 2004, p. 2). According to Woods, Irvine and Walton (2004, p. 2), “arguments in the broad sense are social exchanges between two or more parties in which premisses (sic) are offered in favour of a conclusion according to a given set of rules or standard. These rules or standards will vary from context to context, but typically determine whether, in a given situation, an arguer justified (or proved) his or her conclusion.” In the narrow sense, arguments are “simply sequences of propositions, one of which is the argument’s conclusion, the rest of which are the argument’s premisses (sic)” (Woods, Irvine & Walton, 2004, p. 2). Generally, logicians use the term argument to mean a sequence of statements of which one is the conclusion while the others are premises that provide reasons or evidence for the conclusion. In other words, “an argument offers a conclusion and supports that conclusion with reasons (premises)” (Waller, 2012, p. 14). The Form of An Argument The arrangement of arguments may take different forms. Take a look at the arrangement of the arguments below. Example 1 All men are wealthy. Kofi is a man. Therefore, Kofi is wealthy. 18 Example 2 All men are wealthy. Kofi is a man. Therefore, Kofi is wealthy. Example 3 All men are wealthy. Kofi is a man Kofi is wealthy All three examples contained arguments made up of two parts, namely, premises and conclusion. In all the three examples, the conclusion is Kofi is wealthy. The other two statements in the arguments are the premises that provide evidence for the conclusion drawn. It is not necessarily the case that an argument should have two premises. An argument can have one premise, two or more premises. Carefully observe the arrangement of the three examples of the arguments given above. Note that each of the arguments was arranged differently, yet they remained the same argument with same premises and same conclusion. Hence, the type of arrangement of the argument does not affect its structure and logical basis. You can decide how you arrange your argument in a different way from the way others arrange their arguments. As a result, “… there are many ways in which an argument can be expressed …” (Butterworth & Thwaites, 2014, p. 28). Given that there are many ways of arranging arguments, “it is convenient to have one standard form for setting arguments out. The customary way to do this … is to place the reasons in a list, and to separate them from the conclusion with a horizontal line. The line performs the same function as words such as ‘therefore’ or ‘so’ in natural reasoning” (Butterworth & Thwaites, 2013, pp. 28-29). Take a look at this example of the standard form of arranging argument. All men are smart Mbowura is a man Mowura is smart From the above example, you can see that the first two statements are the premises, and they are separated from the conclusion with a horizontal line. Note that, when you use a horizontal line to separate the premises from the conclusion, you do not have to precede the conclusion with 19 conclusion indicators such as ‘therefore’, ‘so’, ‘thus’, ‘consequently’, etc. This is because the horizontal line replaces and performs the function of such conclusion indicators. Activity 4.1 In the spaces below, differentiate between an argument in ordinary sense and an argument in logic. ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… Recognizing Arguments You have learnt that a set of statements of which one is a conclusion and the others provide evidence for the conclusion is called an argument. But it is not all sets of statement that qualify as arguments. For you to identify an argument or come to the conclusion that a set of statements is an argument, you need to observe the set of statements carefully. The first step in the analysis of arguments is the identification of a passage or set of statements as an argument. As Copi, Cohen and McMahon (2014, p. 11) put it, “before we can evaluate an argument, we must recognize it. We must be able to distinguish argumentative passages in writing or speech. Doing this assumes, of course, an understanding of the language of the passage.” Since logic deals with arguments, “it is important [for you] to be able to distinguish passages that contain arguments from those that do not. In general, a passage contains an argument if it purports to prove something; if it does not do so, it does not contain an argument” (Humphrey & Watson, 2018, p. 14). Take a look at the following passages. The second principle is to conduct or apply a partial test to the passage. You apply a partial test to a passage if the passage does not have any conclusion indicator linking the conclusion to the premises. In this case, you insert a conclusion indicator such as ‘therefore’, ‘so’, etc. “between the sentences and asking: Does it make sense? If it doesn’t make sense, then there is no argument – although the converse does not necessarily apply” (Butterworth & Thwaites, 2013, p. 33). Take a look at the following examples: 20 Example 1 We went to the market today. GCTU students will go to the market today. There were many people buying and selling in the market. Example 2 You answered only three out of ten questions in the examination. Your answers are poor and did not attract high marks. You failed the examination. Let’s conduct a partial test on example 1 by inserting the conclusion indicator ‘therefore’ in the passage to read as: We went to the market today. GCTU students will go to the market today. Therefore, there were many people buying and selling in the market. OR GCTU students will go to the market today. There were many people buying and selling in the market. Therefore, we went to the market today. OR We went to the market today. There were many people buying and selling in the market. Therefore, GCTU students will go to the market today. In all three instances, you can see that even after inserting the conclusion indicator ‘therefore’, there is still no logical connection between the statements for two reasons: There is no conclusion in the passage, as none of the statements in the passage functions as a conclusion. No two statements in the passage were designed by the author to serve as evidence in support of a conclusion. Now, let’s conduct a partial test on example 2. You answered only three out of ten questions in the examination. Your answers are poor and did not attract high marks. Therefore, you failed the examination. 21 You can see straight away that, by inserting the indicator ‘therefore’ before the last statement, you can establish a logical connection between the statement and the preceding two. Hence, the passage passes as an argument containing two premises providing evidence to a conclusion. The third principle to apply to the passage to determine whether it is an argument or not is to scrutinize the passage to determine or decide “whether or not the author meant or intended one of the claims to be a conclusion, and the others to be reasons” (Butterworth & Thwaites, 2013, p. 33). As you scrutinize the passage, find out if there are inference indicators such as ‘because’, ‘since’, ‘so’, ‘therefore’, etc. The presence of such indicators may signal that the passage is an argument. However, it is not always the case that the presence of such indicators signals that the passage is an argument. This is because the indicators may have other functions (Butterworth & Thwaites, 2013, 33). Hence, “just finding two sentences joined by ‘so’ or ‘since’ does not automatically identify a reasoned argument” (Butterworth & Thwaites, 2013, 33). For instance, the following passages are not arguments even though they contain some inference indicators: Example 1 You are so cute. You are so beautiful. And you are so admirable. Example 2 I haven’t eaten since yesterday. In the two examples above, the words so and since in the passages do not perform the functions of inference indicators. They are performing functions as adverbs, but not providing indications of a conclusion drawn. Activity 4.2 In the spaces below, construct a series of statements of not more than ten sentences. Apply a partial test to the set of statements to determine whether it is an argument or not. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… 22 Summary In this section you learnt the meaning of arguments in logic. You learnt that: An argument is made up of premises and a conclusion. There are many ways of arranging arguments, but the standard form is to list the premises and separate them from the conclusion with a horizontal line. There are ways of identifying a passage as an argument or a non-argument. This includes identification, conducting a partial test, and scrutinizing the passage to determine whether it contains premise and conclusion indicators or not. 23 Section 5: Analyzing Arguments in Logic Introduction This section deals with how to analyse arguments. Upon critical scrutiny of the premises of an argument, their strength, weakness, validity and invalidity, arguments can be identified as good arguments or bad arguments. Both deductive and non-deductive (inductive) arguments can be subjected to critical analysis to determine whether they are good or bad arguments. Objectives Upon a successful completion of this section, you should be able to: Identify good arguments and bad arguments. Differentiate between good arguments and bad arguments. Teach others about how to identify good arguments and bad arguments. Apply the lessons drawn from this section to construct good arguments in routine daily activities. Good verses bad arguments Arguments can be categorized into good arguments and bad arguments. Good arguments are also known as sound or cogent arguments. These are arguments that provide valid, strong basis for the conclusion. The evidence adduced from the premise can be said to support the conclusion completely or that the evidence they provide give a high probability for the conclusion. Take a look at the following examples: Example 1 All humans are mortal. Kofi is a human being. Therefore, Kofi is mortal. Example 2 I will go to school or go to church today. I did not go to school today. Therefore, I went to church today. The above two examples are good deductive arguments. A deductive argument is said to be good for three reasons: If its premises and conclusion are true. In the case of the above examples, the premises and the conclusions are true. Take example 1, for instance, it is true that all humans are mortal. It is true that an individual called Kofi is a human being. It is also true that the individual called Kofi is mortal so long as he is a human being. A deductive argument is said to be good if because its inference is valid. The conclusion is logically derived from the premises. In other words, the premises supported the conclusion completely. Now take a look at examples 3 and 4. Example 3 24  All victims of the conflict in Bawku received relief items of one kind or the other. Azeez Ayeebo should receive the relief items because he is a victim of the conflict in Bawku. Example 4 Every one of my classmates has to attend the party. All my colleagues are already at the party. I am the only one absent. My father, you have to let me go to the party. Examples 3 and four and non-deductive arguments, known as inductive arguments. The examples are good inductive arguments for two reasons. The arguments are strong because the premises provide sufficient basis for the conclusions. If it can be proven that all the premises are true, then they provide a highly probable basis for the conclusions. Activity 5.1 In the spaces below, construct two arguments of your own. Analyze the arguments to determine whether they are good or bad arguments. Provide reasons for your answer. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Bad arguments Some arguments are bad. Bad arguments are arguments which do not provide sufficient evidence for the conclusion. Bad arguments are invalid arguments, or valid arguments with false premises. 25 Example 1 If it rains, I will plant corn. I planted corn. Therefore, it rained. Example 2 All birds have tails. All animals with tails have beaks. Therefore, all birds have beaks. The examples above are bad deductive arguments. In example 1, it is possible that the premises are true, but the argument is invalid. The conclusion does not follow deductively from the premises. Example two is also a bad deductive argument. The argument is deductively valid but one of its premises (all animals have beaks) is not true. Hence, deductive arguments can be valid but they can be bad arguments because all the premises or at least one of the premises is false. Let’s turn our attention to bad inductive arguments. An inductive argument is said to be a bad argument if the premises provide weak evidence for the conclusion. Furthermore, inductive arguments can be said to be bad if the premises are false though the premises provide strong evidence for the conclusion. Take a look at the following examples. Example 1 The cow in Manu’s house is brown. The cow in Belinda’s house is brown. Conclusion: Therefore, all cows are brown. Example 2 There are some men in Ghana who have tails. The tail-bearing men in gay are gays. Ghana should identify all the men with tails if the country seeks to stamp out the activities of gays. In the case of argument 1, it is a bad inductive argument because, though the premises are true, they do not provide sufficient basis for the conclusion. In other words, the premises provide weak evidence in support of the conclusion. In Example 1, for instance, the evidence that the cow in Manu’s house is brown, and the evidence that the cow in Belinda’s house is brown is not enough for us to jump to the conclusion that all cows world-wide are brown. It may be true that the cow in Manu’s house is brown. It may also be true that the cow in Belinda’ house is brown. But the conclusion that all cows are brown is false because the premises provide weak evidence to lead us to the conclusion. In the case of argument 2, it is a bad argument because at least one of the premises is false. Based on the evidence of the premises, the argument could be a strong argument but it is a bad one because one of its premises (there are some men in Ghana who have tails) and its conclusion (Ghana should identify all the men with tails if the country seeks to stamp out the activities of gays) is equally false. 26 Activity 5.2 In the space below, define good and bad arguments, and distinguish between them. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Summary In this section, you learnt there are good and bad arguments in logic. You learnt that good arguments provide strong basis for the conclusion drawn or that they support the conclusion completely. Furthermore, you learnt that some arguments can be considered as bad arguments, and that bad arguments do not support the conclusion completely or provide weak basis or reason for the conclusion. 27 Section 6: Non-Arguments in Logic You have learnt in previous sections that an argument in logic contains premises and that the premises serve as proof for the conclusion. The basic test to tell whether a passage is a non- argument is to apply the test of an argument to it. Find out if it has premises and if the premises prove the conclusion. The premises are said to prove the conclusion if there is an inferential relationship between statements. There are many passages that do not qualify as arguments. Let’s delve into the passages that do not qualify as arguments in logic. Objectives Upon a successful completion of this section, you should be able to: Identify passages that are non-arguments. Critique passages and explain why they are non-arguments Differentiate between an expository passage that is a non-argument and one that is an argument. Distinguish arguments from example and illustrations that are non-arguments. Use the knowledge acquired and lessons learnt from this section to impart knowledge to people and society about non-arguments. Non-inferential passages A passage that does not contain an inferential relationship between statements is known as a non- argument. Such a passage lacks “a claim that anything is being proved” as the conclusion (Hurley & Watson, 2018, p. 17). With non-inferential passages, it is possible the passage to contain premises or a conclusion or both, but it may lack “a claim that any potential premise supports a conclusion or that any potential conclusion is supported by premises” (Hurley & Watson, 2018, p. 17). Non-inferential passages include the following: Warning Warnings are non-inferential passages. They only provide information that seeks to put someone on the alert against a possible danger, problem or unpleasant situation. A warning could also be in the form of statements that seek to caution someone. Though warnings may contain propositions/statements, they may not necessarily contain a conclusion or that they do not make inferential relationship between the propositions/statements. Take a look at the examples below. Example 1 Be careful you do not get involved in the armed conflict. No matter your interest in the outcome of the conflict, don’t try to risk your life by participating in it. Example 2 Your attitude to work is appalling. If you do not change, you will be sacked. In the above examples, there is no evidence that the statements are intended to prove something as the conclusion. It is rather a series of connected statements without any inferential relationship. 28 Advice A piece of advice contains statements without any inferential relationship between them. In other words, though the statements of the advice may be connected to each other to convey a sense or message of the advice, the statements do not contain an inferential relationship or do not prove a particular conclusion. A piece of advice takes the form of a guidance or recommendation. Take a look at the example below. You need to keep things simple if you intend to win the match. Pass the ball to your teammate where necessary. Dribble or shoot where it is appropriate to do so. The above example only contains a series of connected statements, but none of them sets out to prove another as the conclusion. As such, the passage does not qualify to be an argument. A statement of belief or opinion Another non-inferential passage is a statement of belief or opinion. A statement of opinion simply states what you think, and a statement of beliefs states your beliefs. Such statements may not contain a conclusion or do not make any inferential relationship between statements. Take a look at the following passages: Example 1 I believe in God, the Father Almighty. Creator of heaven and earth. And in Jesus Christ His only Son our Lord who was conceived by the Spirit. Born of the virgin Mary. Suffered under Pontius Pilate. Example 2 Kofi thinks the best way to train students in this modern era is to train them improve their reading skills. In my view, we need to train students to be critical-minded instead. You may have a different view. Just like warning and a piece of advice, statements of opinion and belief, as shown in the two examples above, do not contain inferential relationships between the statement. The series of statements do not prove a conclusion. Reports Reports seek to convey information about an event, phenomenon, subject matter and any other issue of interests. Reports do not make inferential relationships between statements. Reports may contain premises, but if the author of the report fails to make a claim that they prove a particular conclusion, they do not qualify to be regarded as arguments. Take a look at the example below. Yesterday, the President of Ghana commissioned the Ameri plant that was relocated to Kumasi. The commissioning was a colourful event. Lots of dignitaries including the Asantehene Otumfuo Osei Tutu II attended the commissioning ceremony. Other dignitaries that attended the ceremony included the Vice President Dr. Mahmoud Bawumia, the Minister for Energy, and many other ministers of state. 29 The above example contains statements that qualify as premises but the passage did not make any inferential relationship between the statements. In other words, it did not set out to prove that the statements or a set of the statements provide evidence for a conclusion. Loosely associated statements A passage contains loosely connected statements when the statements in the passage are unconnected to create a logical pattern desirable of an argument. The statements may be about the same subject matter, “but they lack a claim that one of them is proved by the others” (Hurley & Watson, 2018, p. 17). Take a look at the example below. Kofi and Ama are in class. Some of the students are also in class. The teacher just entered the class to start today’s lessons. In the above example, you can see that the statements are about the same subject-matter, but they are loosely connected or that they did not prove a particular conclusion. Activity 6.1 Listen to reports by journalists or newscasters in radio and television news in Ghana. Write down any two reports. Analyze the reports to determine whether they are arguments or not. Explain the reasons for your answer. Expository Passage An expository passage does not qualify as an argument. An expository passage is a passage that starts with a topic sentence (i.e., a sentence in a paragraph that states the idea in the paragraph) and it is followed by other sentences that explain the idea in the topic sentence in detail. The sentences that explain the topic sentence (the major and minor supporting sentences) break the idea in the topic sentence into its component parts, provide further and better particulars, as well as provide examples about the idea in the topic sentence. However, the supporting sentences do not prove a conclusion; they only throw more light on the idea in the topic sentence. Hence, expository passages are not arguments. See the example below. The Government of Ghana has tasked organizations and institutions to make upward adjustment of the salaries of staff annually. However, the Government of Ghana is aware that some institutions/organizations increase the salaries of their workers quarterly. The Government is also aware of exceptional cases where some institutions and organizations provide hefty monthly allowances to their staff to cushion them against rising cost of living. On the other hand, there are reports that some organizations fail to adjust the salaries of their staff annually, and the government has done nothing to ameliorate the plight of the staff of such organizations. The above passage is an expository passage. It sets out with a topic sentence (The Government of Ghana has tasked organizations and institutions to make upward adjustment of the salaries of staff annually). The rest of the sentences in the passage provided further explanation of the topic sentence. The passage with started the topic sentence, “and the remaining sentences merely develop and flesh out this topic sentence” (Hurley & Watson, 2018, p. 19). Hence, it is not an argument because it lacks an inferential claim. 30 In some cases, however, an exposition may qualify as an argument if the explanations it contains seek to prove a conclusion. This is the case when the subsequent sentences in the expository passage seek to prove the topic sentence, rather than merely explaining it. Take a look at the passage below. There are many reasons why Ghana is one of the most peaceful countries in Africa. First, Ghana is one of the countries in the world with the lowest crime rate. Crimes such as kidnapping, murder and raids, which are common in most countries, are absent or low in Ghana. Second, Ghana is free from the activities of militant groups. There are no Islamic insurgency groups in Ghana. Unlike Nigeria and other countries in the Sahel region in West Africa, Ghana does not experience the activities of terrorists. Finally, Ghana has a stable democratic system. The country has experienced peaceful change of governments through the ballot box. Even where there were electoral disputes, those disputes were settled in court. The above expository passage qualifies as an argument. It began with a topic sentence (There are many reasons why Ghana is one of the most peaceful countries in Africa). The rest of the sentences sought to prove the topic sentence. Hence, the expository passage is an argument. Sometimes, it is difficult to distinguish between an expository passage which is not an argument and one which is an argument. Hurley and Watson (2018, p. 19) provide a way out in deciding whether an expository passage is an argument or not. According to them, “in deciding whether an expository passage should be interpreted as an argument, try to determine whether the purpose of the subsequent sentences in the passage is merely to develop the topic sentence or also to prove that it is true” (Hurley & Watson, 2018, p. 19). However, there may be instances that this test fails to help you make a decision. In such a situation, “the only alternative may be to say that if the passage is taken as an argument, then the first statement is the conclusion and the others are the premises” (Hurley & Watson, 2018, p. 19). Illustration Generally, an illustration does not qualify as an argument. An illustration also seeks to provide examples in support of a point. They do not serve as new points that seek to prove a conclusion. Take a look at the example below. There are talented musicians in Ghana. Some of such talented musicians in Ghana include Stone Bwoy, Shatta Wale, Daddy Lumba, Wendy Shay and Kwabena Kwabena. In the above example, the first statement makes a point, but the second statement does not make a new point. Rather, it provides an illustration in support of the first point. The passage did not set out to prove a conclusion but to make a point and to provide an illustration of it. Hence, the passage is not an argument. There are borderline cases between examples (illustrations) and evidence. Sometimes, the example serves as evidence to prove a particular conclusion. Take a look at the example below. 31  Some Ghanaian and Nigerian celebrities die at a young age. For instance, Junior Pop died in his early thirties. Another example is Suzzy Willaims, a young movie star in Ghana, who died in her late twenties. Three other young, but extremely talented, Ghanaian celebrities who died at young age in their late twenties were Ebony Reigns, Terry Bonchaka and Castro da Destroyer. In Nigeria, celebrities such as Bisi Komolafe (aged 26), Dagrin (aged 25) and Mohbad (aged 27) died at young age. In the above example, the first statement (Some Ghanaian and Nigerian celebrities die at a young age) is a conclusion, which is proved by the subsequent sentences. Though the subsequent sentences are illustrations, they sought to prove a conclusion. Hence, there is an inferential relationship between the illustrations and the point they sought to prove (the conclusion). Therefore, the above illustration qualifies as an argument. Illustrations that can be taken as arguments are known as arguments from example. Explanations Explanations are a statement of account that seeks to make a particular issue clearer. Hurley and Watson (2018, p. 20) define an explanation as “an expression that purports to shed light on some event or phenomenon. The event or phenomenon in question is usually accepted as a matter of fact.” An explanation is made up of two parts, namely, the explanandum (the word, event or phenomenon that is the subject of explanation) and the explanans (the statement of account that explains the word, event, phenomenon, etc. under consideration). Take a look at the following examples: Example 1 Ghanaians are hospital because they take good care of visitors and strangers. Example 2 Rent in Ghana is expensive in recent times due to the high cost of living and the depreciation of the Ghanaian currency over the past two years. The above two examples are explanations, but not argument. In example one, the explanandum is the phrase Ghanaians are hospital, and the explanans is the clause they take good care of visitors and strangers. In example 2, the explanandum is the clause rent in Ghana is expensive in recent times, and the explanans is the clause the high cost of living and the depreciation of the Ghanaian currency over the past two years. Both examples are explanations, not arguments. Sometimes, students are tempted to see explanations as arguments because they contain conclusion indicators such as ‘because’, ‘due to’, etc. Hurley and Watson (2018) have provided a formular to distinguish explanations from arguments. According to them, “to distinguish explanations from arguments, identify the statement that is either the explanandum or the conclusion (usually this is the statement that precedes the word “because”). If this statement describes an accepted matter of fact, and if the remaining statements purport to shed light on this statement, then the passage is an explanation” (Hurley & Watson, 2018, p. 21). 32 Conditional statements Conditional statements are statements couched in the “if …then” form. They are not arguments. Conditional sentences are made up of two parts – antecedent and consequent. Take a look at the statement, “if it rains, then I will plant corn.” The antecedent of this conditional sentence is the “if clause”, i.e., “if it rains.” The consequent is the “then clause”, i.e., “then I will plant corn. Sometimes, conditional sentences do not contain ‘then.’ For instance, the above conditional sentence can be written as “if it rains, I will plant corn.” Though the link between the antecedent and consequent resembles the inferential link between the premises and conclusion of an argument”, conditional statements are not arguments because they do not prove any conclusion. For a conditional statement to qualify as an argument, there should be another statement that proves its “if clause” or disproves its “then clause.” Take a look at the following examples: If it rains today, I will plant corn. It will rain today. Therefore, I will plant corn today. If it rains today, I will plant corn. I will not plant corn today. Therefore, it will not rain today. Both examples are valid arguments because parts of the conditional sentences were either affirmed or denied in the subsequent non-conditional statement to serve as a basis for the conclusions drawn. Activity 6.2 Construct two expository passages of which one is a non-argument and the other an argument. Critically analyze the passages and point out the reasons why one is said to be a non-argument and the other an argument. Give your activity to your peer (classmate) to assess you. Summary This section explained passages that are non-arguments. It explained that non-inferential passages such as a piece of advice, warning, reports, statements of opinion or belief, and loosely associated statements are not arguments because they do not contain inferential relationship between the statements they contain. You have learnt that, in few cases, reports qualify as arguments only when they set out to prove something. You also learnt that illustrations, explanations and expository passages are generally not arguments because they lack proof of a conclusion, but in few cases, they qualify as arguments only when they set out to prove something as the conclusion. Finally, you learnt that a conditional sentence by itself alone does not qualify as an argument unless it is followed up by other statements that sought to prove or disprove part of the conditional sentence. 33 Unit Summary You have come to the conclusion of this unit. Congratulations! In this unit, you learnt the meaning of logic, the meaning of critical thinking, the skills needed to study logic and critical thinking as a course, and the significance of studying logic and critical thinking. You also learnt the meaning of arguments and the basic terms such as premise, proposition, premise indicator, inference, conclusion and other terms associated with argument. Furthermore, you learnt that there are ways of identifying a passage as an argument or a non-argument. You also learnt that arguments in logic can be subjected to analysis to determine whether they are good or bad arguments. Finally, you learnt that non-inferential passages such as a piece of advice, warning, reports, statements of opinion or belief, and loosely associated statements are not arguments because they do not contain inferential relationship between the statements they contain. Assignment 1 1. Distinguish between arguments and non-arguments in logic. 2. Define arguments in logic and explain they are analyzed. 34 Unit 2: Language and Definitions Unit Introduction Welcome to the study of Unit 2. This unit focuses on language and definitions. It explains the functions and forms of language. It also seeks to explain how language is used to express thoughts through the construction of various types of statements – interrogative, imperative, declarative, emotive and exclamatory statements. The unit explains the various analytical mechanisms that can be applied to statements to arrive at some logical or illogical conclusions. Furthermore, the unit explains the various types of definitions available, explains their structure, and the techniques that can be used to produce definitions and analyse them. Unit 2 is divided into the following sections: Section 1: Functions, Forms of Language and Interrogative Sentences Section 2: Imperative Sentences Section 3: Declarative and Exclamatory Sentences Section 4: Types of Definitions Section 5: Structure of Definitions: Intensions and Extensions Section 6: Analysing Definitions Unit Objectives By the end of this unit, you should be able to: Distinguish between the functions and forms of language. Explain the principles and characteristics associated with imperative statements. Analyse texts to identify declarative, emotive expressions, exclamatory expressions and value judgements. Differentiate between lexical and precise definitions. Distinguish between stipulate definition and theoretical definition. Define, identify and apply extensional and intensional definitions in routine daily communications. Critically diagnose definitions to determine the causes of their inaccuracies. 35 Section 1: Functions, Forms of Language and Interrogative Sentences This section focuses on the functions and forms of language. Language is a tool for communication. It enables people to express their ideas. Therefore, “when people reason, they typically do so using language ….” (Copi, Cohen & McMahon, 2014, p. 68). Language “…serves various functions in our day-to-day lives” (Hurley & Watson, 2018, p. 81). Language performs informative, expressive, directive, performative and ceremonial functions. Apart from the functions it performs, language is designed to enable individuals express their ideas in different grammatical forms. One of the grammatical statements that language enables us to construct is an interrogative sentence, a sentence which purposively asks questions. There are a number of principles that are applied to the analysis of questions vis-à-vis the answers they seek to elicit. Objectives Upon a successful completion of this section, you should be able to: Distinguish between the functions and forms of language. Establish ways to deal with complex questions. Acquire knowledge on the principle to apply to a question before answering it. Teach students and other people how to answer questions. Functions and Use/Forms of Language Languages are designed to enable people express ideas. If you survey your language, you will find that the language contains words that you can put together to express your thoughts. The thought you express could be in the form of constructing interrogative, declarative and imperative sentences. Thoughts are ideas which are communicated in language, usually expressed in sentences. Sentences perform different functions in English. Sentence function refers to a speaker’s purpose in uttering or communicating a specific sentence. A sentence function answers the question: “why has this been said?” Language is designed to perform a number of functions. These are: Informative function (i.e., “or denying propositions, formulating or evaluating arguments, and so on (Copi, Cohen & McMahon, 2014, p. 69)). Statements such as “Ghana is a peaceful country”, “GCTU offers IT and computer science programs”, “Yaw is a teacher”, etc. are examples of the informative function of language. Expressive function (i.e., to express an idea, opinion or belief, conveys reports and feelings). Statements such as “Kofi said he is unhappy”, “I love Grace”, etc. are examples of the expressive function of language. Directive function (i.e., to provide directives, make request and commands). Statements such as “shut the door”, “stop what you are doing”, “give the money to Kofi”, etc. are examples of directive function of language. 36  Performative function (i.e., the language that is purported to perform an action which it reports). When taking marriage vows, when the bride and groom respond, “yes I/we do” or we say in a swearing-in ceremony, “I/we accept”, those statements are examples of the performative function of language. Ceremonial function of language (i.e., statements that are not necessarily informative or expressive). Statements such as “honourable members of parliaments”, “I apologize for my mistake”, “I accept the offer”, “thank you for your assistance”, “His Excellency the President of Ghana” are examples of the ceremonial function of language. We are not interested in the functions of language in this section. Rather, we are interested in the uses of language. We are interested in the grammatical forms of language. Grammatical forms of language deal with the types of sentences constructed in a language. According to Copi, Cohen and McMahon (2014, p. 70), “the grammatical forms of language are essentially four: declarative, interrogative, imperative, and exclamatory.” Activity 1.1 In the spaces below, construct sentences to illustrate the following functions of language: Informative function of language ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Expressive function of language ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Transformative function of language ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Ceremonial function of language ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Directive function of language ……………………………………………………………………………………………………… 37 ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… Interrogative sentence Interrogative sentence is a sentence that asks a question. An interrogative sentence is spoken to get information. Interrogative sentences are couched in the form of questions and they end with a question mark. Let’s now examine the elements of an interrogation. 1. An interrogation does not have a truth-value. In other words, an interrogative sentence cannot be said to be true or false. Rather, a question is measured based on whether it is successful or not depending or whether or not it attracts a correct answer. For instance, if I ask you the question, “are you intelligent?” the information the question conveys cannot be said to be true or false. Rather, it is the answer to the question that can be said to be true or false. If a person asks you the question in Twi “w’oa gyimi ana?” (to wit, “are you a fool?”), the person did not insult you. The person simply asked you a question. You can decide to answer it in the affirmative or in the negative. 2. The nature of a question (whether affirmative or negative) does not determine the nature of an answer to it. Take a look at the following questions: a. Are you a fool? b. Are you not a fool? The first question is an affirmative question; the second is a negative question. If you answer “yes” to the question, it means you have answered that you are a fool. If you answer “no”, it means you have answered that you are not a fool. The same applies to the second question. If you answer “yes” to the second question, it means you have answered that “yes, I am a fool”; if you say “no”, it means you have answered that “no, I am not a fool.” Note that “yes” does not go with not. For instance, in your answer to example 2, you cannot say “yes, I am not a fool.” It is grammatically unacceptable. In short, whether a question is couched in the affirmative or negative form, “yes” means affirmative, “no” means negative. 3. As much as possible, the answer to a question is shaped by the demand, objective or import of the question. Every question has a demand or objective or import, which it seeks to achieve. Ensure that your answer is formulated to meet to the demand/objective/import of the question. Do not go beyond the boundaries of the demand of the question to add superfluous information to it. Such superfluous information is, by and large, unnecessary, unless in extreme cases where the one interrogating you seeks additional information beyond the scope of information the question seeks to elicit. In some rare cases, the superfluous information in the answer could have dire consequences. For instance, the police may ask you the question “are you a thief?” Your answer should be direct to the question, and the answer should say “yes, I am a thief” or “no, I am not a thief.” Do not, for example, say, “no, I am not a thief but I know that Yaw and Becky are thieves. Last time, they stole money from a neighbour’s house. The other time, they stole money from a business man at a guy point.” Such superfluous information to the question can put Yaw 38  and Becky in trouble. You can only give such superfluous information if, for example, you are providing the police with information about the criminal activities of Yaw and Becky. 4. Do not rush to answer a question if you have not understood it. It is important you understand the import of the question or the key word in the question before answering the question. Even if you understood it, pause for a while to think through your answer critically before answering the question. This is particularly the case where you do not understand a key word in the question. Take a look at the following question: Are you a nitwit? The key word in the question is nitwit. If, for instance, you do not know the meaning of the word nitwit, do not answer it. Ask the person who posed the question to tell you the meaning of the word nitwit before you decide to answer the question or not. Do not just assume or speculate about the meaning of the key word to give a wrong answer to the question. Speculations to questions have put many people in trouble in the hands of the police. A police officer may ask you the question, “do you know why I stopped you?” Pause to think carefully about the question before you answer it. Do not rush to say, “yes, you stopped me because I jumped the traffic light” or “yes, because I was over-speeding” or “yes, because I was making a call on phone while driving”, etc. You are not in the mind of the police; therefore, you cannot know what he/she has in mind for stopping you. It could be that the police had nothing in mind, but only posed the question as a psychological means to get you admit to an offense which he/she will use against you in court. By so doing, you have admitted to an offense. Even granted that the police had an offence in mind, it could be that your answer would talk about a different offence. By so doing, you unwittingly admitted to a commission of an offence, which the police officer can use against you in court. The appropriate response to such a question is to say “no, I do not know unless you tell me.” In this way, you prevent yourself from delving into speculations which may give an answer that can put you into trouble. 5. There are some complex questions. You are likely to put yourself in trouble if you answer a complex question. For instance, someone may ask you the question, “have you stopped cheating on your partner?” This is a complex question but it looks simple on the face value. The question is asked in such a way that, whichever way you answer it, you commit yourself. If you answer “yes” to the question, it implies that you used to cheat on you partner but you have stopped now. If you answer “no”, it implies that you cheated on your partner in the past, you are still cheating and you would probably continue to cheat on your partner in the future. 6. You are not bound to answer questions. You may elect to answer a question or not to answer a question at your volition. Electing/choosing not to answer a question does not necessarily mean you are guilty or that you tacitly consented to it. Someone may ask you the question, “why are your parents poor?” You can elect to answer the question or not to answer the question. If, for instance, you elected not to answer the question, it does not necessarily mean that you explicitly or implicitly accepted or admitted that your parents are poor. 7. Persons are not liable for posing questions, neither are they liable for the answers people give to their questions. You cannot take a person to court for asking another person a 39  question about your supposedly bad character. Neither is the person who asked a question liable for the answers people give his/her question. Assuming that Dr. Cletus Mbowura posed the question to some people about Grace Anatu as: “Is Grace Anatu a prostitute?” Assuming that people answered the question saying “yes, Grace Anatu is a prostitute.” In this situation, Dr. Cletus Mbowura is not liable, and Grace Anatu cannot take him to court for defamation. Even if she does, the court would not accept the question as a declarative sentence (a statement of fact). Besides, Dr. Cletus Mbowura is not liable for the answers that people offered in response to his question. Activity 1.2 5. A lawyer asked a witness, “between you and the Attorney-General, who is telling this honourable court the truth?” All the following are the possible reactions with their respective implications that the witness can make to the question except: A. The witness can respond by saying he the witness is telling the court the truth, and his answer implies the Attorney-General is not telling the honourable court the truth. B. The witness can respond to the question by saying both he and the Attorney-General are telling the truth, and this i