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1. Consider the following argument: All states in the United States have capital cities. Paris, France, is a capital city. Therefore, Paris, France, is a state in the United States. Explain why this argument is invalid. In your response, make sure to explain why the argument is not truth-preserving. Your response must be at least 100 words in length. 2. All countries have cities. Canada is a country. Therefore, Canada has cities. This is an example of a valid argument. Write your own valid argument. Explain why your argument is valid. In your explanation, make sure you appeal to the idea of truth-preserving arguments. Your response must be at least 100 words in l ength. PHI 1301, Critical Thinking 1 Course Learning Outcomes for Unit III Upon completion of this unit, students should be able to: 3. Recognize well-reasoned, logical arguments. 3.1 Identify concepts related to deductive reasoning. 4. Relate good reasoning to effective thinking. 4.1 Determine whether an argument is valid, invalid, or sound. 4.2 Explain what makes an argument truth-preserving. Course/Unit Learning Outcomes Learning Activity 3.1 Unit Lesson Chapter 3 Unit III Video Unit III Assessment 4.1 Unit Lesson Chapter 3 Unit III Video Unit III Assessment 4.2 Unit Lesson Chapter 3 Unit III Video Unit III Assessment Required Unit Resources Chapter 3: Reasoning With Logic and Certainty In order to access the following resource, click the link below. Unit III Video A transcript and closed captioning are available once you access the video. Unit Lesson There are two major types of reasoning, deductive and inductive. Unit IV will address inductive reasoning. In this unit, we will focus on deductive reasoning. Different types of reasoning mean different types of arguments. The difference between induction and deduction is based on the fact that we arrive at the conclusion in a different way. Since not all reasoning is the same, we do not always arrive at the conclusion in the same way. Consider the following argument: All big cities in the United States have a mayor. Chicago is a big city in the United States. Therefore, Chicago has a mayor. We arrive at the conclusion Chicago has a mayor by a process of reasoning and by reasoning in a certain way. In order to understand how we arrive at this conclusion, we must always assume the premises are true. In the argument above, we do not have to assume this since the premises are, in fact, true. Since it is true all big cities in the United States have a mayor, and since it is also true Chicago is a big city in the United States, UNIT III STUDY GUIDE Deductive Reasoning https://c24.page/r9y9arnknuspkwv6399jdq5mdv PHI 1301, Critical Thinking 2 UNIT x STUDY GUIDE Title does it not necessarily follow that Chicago must have a mayor? If you are not convinced this is a matter of necessity (that is, that Chicago must have a mayor), consider an argument from a fictional city in the The Wonderful Wizard of Oz: All cities in the land of Oz have a mayor. Emerald City is a city in the land of Oz. Therefore, Emerald City must have a mayor. Just like in our first argument, if we are to decide whether the conclusion follows and whether it follows necessarily (that is, whether it must follow), we have to assume the premises are true. In this case, we know the premises are false, but in order to determine if the conclusion follows from the given premises, we have to take the premises to be true. Since we take it to be true all cities in the land of Oz have a mayor, and since we take it to be true Emerald City is a city in the land of Oz—must it not necessarily follow that Emerald City must have a mayor? Once again, just like with our first argument, the conclusion is logically inescapable. In other words, given the truth of the premises, the conclusion must necessarily follow. This conclusion is not a matter of chance, contingency, or luck. If the premises are true, the conclusion must be true. This is deductive reasoning. In order to better understand this, consider a very different type of reasoning. Consider the type of reasoning in which the conclusion is not a must—that is, a type of reasoning where the conclusion is not a matter of necessity but rather a matter of chance or contingency. Consider the following argument: I drive to the supermarket on a daily basis, and the supermarket is always open. I will drive to the supermarket tomorrow. Thus, the supermarket will be open tomorrow. Once again, if we are to understand the reasoning behind this argument, we have to take the premises to be true even though the premises may or may not be true. If it is true I drive to the supermarket on a daily basis and it is always open, and if it is also true I will drive to the supermarket tomorrow, will it necessarily follow that the supermarket will be open tomorrow? In other words, must it be the case the supermarket will be open tomorrow? It is easy to see the conclusion does not necessarily follow. In this case, the conclusion is a matter of chance or contingency. Why? Because, it is easy to see the supermarket can close down because of an emergency. Whether the supermarket is open or not is a matter of chance or luck. If I really want to go to the supermarket and the supermarket is open, then I am, in some sense, lucky it is open. Since, in this case, the conclusion does not necessarily follow (given the premises are true), this argument is inductive. Because an argument is deductive does not mean it is automatically well reasoned. We humans make mistakes all the time, and we can make mistakes in our reasoning even if that reasoning is deductive. This raises the question what is the criterion or criteria for a deductive argument to be well reasoned? The answer is simple; a deductive argument is well reasoned in cases where the conclusion does necessarily follow from the premises. Another way to express this is to say whenever the premises are true and the conclusion is also true, the given deductive argument is well reasoned. Logicians call such arguments valid arguments. Hence, only deductive arguments can be valid or invalid. An invalid argument is one in which the conclusion does not necessarily follow even if the premises are true or taken to be true. Consider the following argument: All high schools in Los Angeles are educational institutions. The University of California, Los Angeles (UCLA) is an educational institution. Therefore, the University of California, Los Angeles (UCLA) is a high school in Los Angeles. Remember that to determine how the conclusion follows or whether it follows necessarily, we must take the premises to be true. In this case, it is easy to take the premises to be true because they are, in fact, true. Notice, however, the conclusion is false. The University of California, Los Angeles (UCLA) is not a high school in Los Angeles. It is a university. Since the conclusion does not necessarily follow—even though the premises are true—this argument is not well reasoned, and hence it is invalid. It is easy to see the person who has made this argument has gotten things confused and has drawn a false conclusion from true premises. The first two arguments presented at the beginning of this lesson are both valid. Recall these arguments: PHI 1301, Critical Thinking 3 UNIT x STUDY GUIDE Title • All big cities in the United States have a mayor. Chicago is a big city in the United States. Therefore, Chicago has a mayor. • All cities in the land of Oz have a mayor. Emerald City is a city in the land of Oz. Therefore, Emerald City must have a mayor. Why are these arguments both valid? They are valid arguments because in both of them, the conclusion follows necessarily given the premises are true. You might object and say “But the premises in the second argument (the argument about the land of Oz) are false and so is the conclusion!” This is correct. The premises in the argument about Oz are false since the premises are about a fictional place. However, the premises in the first argument (about big cities having mayors) are true because it is true that there are big cities in the United States, and it is true Chicago is a big city in the United States. Nevertheless, remember it does not matter if the premises are, in fact, false. What matters is the conclusion would follow if the premises were true. In other words, if we take the premises to be true even when we know they are false, and if the conclusion does necessarily follow, then we have a valid argument. Notice what matters in these two valid arguments is the truth of the premises is preserved in the conclusion. This is because valid arguments are truth-preserving. This has an important implication: it means we can have valid and truth-preserving arguments even if the premises are blatantly false. Consider the following argument: All people who live in California are people who live in Germany. All people who live in Germany are people who live in Asia. Therefore, all people who live in California are people who live in Asia. This argument is valid and truth preserving because if the premises were true, the conclusion would necessarily follow. In order to understand why the conclusion would necessarily follow, let us represent the argument in abstract terms as shown in the oval diagram. Based on this diagram, we can see the category of people who live in California is inside the category (or group) of people who live in Asia. This means the truth of the premises has been preserved in the conclusion that all people who live in California are people who live in Asia even though we know the premises are, in fact, blatantly false. Also, notice it is only necessary to diagram the premises. In the diagram above, only the premises were intentionally diagrammed, but we see (with our mind’s eye) that the conclusion is also represented—the category of people who live in California is inside the category (or group) of people who live in Asia. This visually shows us that the truth of the premises has been preserved in the conclusion. This type of truth preservation is what validity is all about. At this point, you may ask—if premises can be false and we can still have a valid argument, why does validity matter? In other words, who cares if arguments are valid? This is a good question. This implies we need another criterion for deductive arguments. We need an additional criterion that also guarantees we are dealing with facts and not just make believe. There is such a criterion, and it is called soundness. An argument is sound when it is both valid and the premises are true. In other words, two conditions are needed in order for an argument to be sound: it needs to be valid, and the premises need to be true. This means only deductive arguments can be valid, and only deductive arguments can be sound. We need this criterion because we want logical arguments not just to be well reasoned. We also want them to tell us something about the world. We want them to be about facts. Good arguments are much more significant if they are well reasoned (valid), and they tell us something about the world we live in. PHI 1301, Critical Thinking 4 UNIT x STUDY GUIDE Title Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information. The Unit III Practice Questions are a fantastic resource for practicing the material in this unit. It is recommended that you complete these before attempting the unit assessment. An answer key is provided at the end of the questions. https://online.columbiasouthern.edu/bbcswebdav/xid-128512529_1 Course Learning Outcomes for Unit III Required Unit Resources Unit Lesson Learning Activities (Nongraded)