{"id":2658,"date":"2022-03-29T22:07:13","date_gmt":"2022-03-29T22:07:13","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/chapter\/2-6-validity-2\/"},"modified":"2024-01-15T16:50:31","modified_gmt":"2024-01-15T16:50:31","slug":"2-6-validity-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/chapter\/2-6-validity-2\/","title":{"raw":"2.6 Validity","rendered":"2.6 Validity"},"content":{"raw":"<div class=\"textbox shaded\">\r\n\r\n<strong>LEARNING OBJECTIVES<\/strong>\r\n\r\n<hr \/>\r\n\r\nBy the end of this section you will discover:\r\n<ul>\r\n \t<li>The meaning of a valid argument.<\/li>\r\n \t<li>Means of recognizing validity or invalidity in an argument.<\/li>\r\n<\/ul>\r\n<\/div>\r\nSo far, we have discussed what arguments are and how to determine their structure, including how to reconstruct arguments in standard form. But we have not yet discussed what makes an argument good or bad.\r\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline;\"><strong>How to Argue - Philosophical Reasoning: Crash Course Philosophy #2<\/strong><\/span><\/p>\r\n[embed]https:\/\/www.youtube.com\/embed\/NKEhdsnKKHs[\/embed]\r\n<p style=\"text-align: center;\"><a href=\"https:\/\/youtu.be\/NKEhdsnKKHs\" target=\"_blank\" rel=\"noopener noreferrer\">Or watch the video here<\/a><\/p>\r\nThe central concept that you will learn in logic is the concept of <strong>validity<\/strong>. Validity relates to how well the premises support the conclusion, and it is the golden standard that every argument should aim for.\r\n<div class=\"textbox shaded\"><strong>Valid Argument<\/strong>: an argument in which if the premises are true, the conclusion must be true<\/div>\r\nA valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are true. Another way of putting this is as a conditional statement: <strong>A valid argument is an<\/strong> <strong>argument in which <\/strong><strong><em>if<\/em><\/strong><strong> the premises are true, the conclusion <\/strong><strong><em>must<\/em><\/strong><strong> be true.<\/strong> Here is an example of a valid argument:\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>Violet is a dog<\/li>\r\n \t<li>Therefore, Violet is a mammal (from 1)<\/li>\r\n<\/ol>\r\n<\/div>\r\nYou might wonder whether it <em>is<\/em> true that Violet is a dog (maybe she is a lizard or a buffalo\u2014we have no way of knowing from the information given). But, for the purposes of validity, it does not matter whether premise 1 is <em>actually<\/em> true or false. All that matters for validity is whether the conclusion follows from the premise. And we can see that the conclusion, Violet is a mammal, does seem to follow from the premise, Violet is a dog. That is, given the truth of the premise, the conclusion has to be true. This argument is clearly valid since if we assume that \u201cViolet is a dog\u201d is true, then, since all dogs are mammals, it follows that \u201cViolet is a mammal\u201d must also be true. As we have just seen, whether or not an argument is valid has nothing to do with whether the premises of the argument are actually true or not. We can illustrate this with another example, where the premises are clearly false:\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>Everyone born in France can speak French<\/li>\r\n \t<li>Barack Obama was born in France<\/li>\r\n \t<li>Therefore, Barak Obama can speak French (from 1-2)<\/li>\r\n<\/ol>\r\n<\/div>\r\nThis is a valid argument. Why? Because when we <em>assume<\/em> the truth of the premises (everyone born in France can speak French, Barack Obama was born in France) the conclusion (Barack Obama can speak French) <em>must<\/em> be true. Notice that this is so even though none of these statements is <em>actually<\/em> true. Not everyone born in France can speak French (think about people who were born there but then moved somewhere else where they did not speak French and never learned it) and Obama was not born in France, but it is also false that Obama can speak French. So, we have a valid argument even though neither the premises nor the conclusion is actually true. That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember: validity describes the <em>relationship<\/em> between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true. In order to better understand the concept of validity, let us look at an example of an <strong><em>invalid<\/em><\/strong> argument:\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>George was President of the United States<\/li>\r\n \t<li>Therefore, George was elected President of the United States (from 1)<\/li>\r\n<\/ol>\r\n&nbsp;\r\n\r\n<\/div>\r\n<span style=\"text-align: initial; font-size: 1em;\">This argument is invalid because it is possible for the premise to be true and yet the conclusion false. Here is a counterexample to the argument. Gerald Ford was President of the United States, but he was never elected president, since Ford Replaced Richard Nixon when Nixon resigned in the wake of the <\/span>\r\n<div class=\"textbox shaded\"><strong>Counterexample<\/strong>: a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false<\/div>\r\nWatergate scandal. So, it does not follow that just because someone is President of the United States that they were <em>elected<\/em> President of the United States. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. And this means that the argument is invalid. If an argument is invalid it will always be possible to construct a counterexample to show that it is invalid (as I have done with the Gerald Ford scenario). A <strong>counterexample<\/strong> is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.\r\n\r\nIn order to determine whether an argument is valid or invalid we can use what I will call the informal test of validity. To apply the informal test of validity ask yourself whether you can <em>imagine<\/em> a world in which all the premises are true and yet the conclusion is false. If you <em>can<\/em> imagine such a world, then the argument is invalid. If you <em>cannot<\/em> imagine such a world, then the argument is valid.\r\n\r\nNotice: it is possible to imagine a world where the premises are true even if the premises are not, as a matter of actual fact, true. This is why it does not matter for validity whether the premises (or conclusion) of the argument are actually true. It will help to better understand the concept of validity by applying the informal test of validity to some sample arguments.\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>Joan jumped out of an airplane without a parachute<\/li>\r\n \t<li>Therefore, Joan fell to her death (from 1)<\/li>\r\n<\/ol>\r\n<\/div>\r\nTo apply the informal test of validity we have to ask whether it is possible to imagine a scenario in which the premise is true and yet the conclusion is false (if so, the argument is invalid). So, can we imagine a world in which someone jumped out of an airplane without a parachute and yet did not fall to her death? (Think about it carefully before reading on.) As we will see, applying the informal test of validity takes some creativity, but it seems clearly possible that Joan could jump out of an airplane without a parachute and not die\u2014she could be perfectly fine, in fact. All we have to imagine is that the airplane was not operating and in fact was on the ground when Joan jumped out of it. If that were the case, it would be a) true that Joan jumped out of an airplane without a parachute and yet b) false that Joan fell to her death. Thus, since it is possible to imagine a scenario in which the premise is true and yet the conclusion is false, the argument is invalid. Let us slightly change the argument, this time making it clear that the plane is flying:\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>Joan jumped out of an airplane travelling 300 mph at a height of 10,000 ft without a parachute<\/li>\r\n \t<li>Joan fell to her death (from 1)<\/li>\r\n<\/ol>\r\n<\/div>\r\nIs this argument valid? You might think so since you might think that anyone who did such a thing would surely die. But is it possible to not die in the scenario described by the premise? If you think about it, you will realize that there are lots of ways someone could survive. For example, maybe someone <em>else<\/em> who was wearing a parachute jumped out of the plane after them, caught them and attached the parachute-less person to them, and then pulled the ripcord and they both landed on the ground safe and sound. Or maybe Joan was performing a stunt and landed in a giant net that had been set up for that purpose. Or maybe she was just one of those people who, although they did fall to the ground, happened to survive (it has happened before). All of these scenarios are consistent with the information in the first premise being true and also consistent with the conclusion being false. Thus, again, any of these counterexamples show that this argument is invalid. Notice that it is also possible that the scenario described in the premises ends with Joan falling to her death. But that does not matter because all we want to know is whether it is possible that she does not. And if it is possible, what we have shown is that the conclusion does not logically follow from the premise alone. That is, the conclusion does not have to be true, even if we grant that the premise is. And that means that the argument is not valid (i.e., it is invalid).\r\n\r\nLet us switch examples and consider a different argument.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"245\"]<img src=\"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-content\/uploads\/sites\/65\/2022\/03\/image14-2-scaled-1.jpeg\" alt=\"Official photographic portrait of US President Barack Obama (born 4 August 1961; assumed office 20 January 2009)\" width=\"245\" height=\"333\" \/> Official photographic portrait of US President Barack Obama[\/caption]\r\n\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>A person can be President of the United States only if they were born in the United States.<\/li>\r\n \t<li>Obama is President of the United States.<\/li>\r\n \t<li>Kenya is not in the United States.<\/li>\r\n \t<li>Therefore, Obama was not born in Kenya (from 1-3)<\/li>\r\n<\/ol>\r\n<\/div>\r\nIn order to apply the informal test of validity, we have to ask whether we can imagine a scenario in which the premises are both true and yet the conclusion is false. So, we have to imagine a scenario in which premises 1, 2, and 3 are true and yet the conclusion (\u201cObama was not born in Kenya\u201d) is false. Can you imagine such a scenario? You cannot. The reason is that if you are imagining that it is a) true that a person can be President of the United States only if they were born in the United States, b) true that Obama is president and c) true that Kenya is not in the U.S., then it <em>must<\/em> be true that Obama was not born in Kenya. Thus, we know that on the assumption of the truth of the premises, the Conclusion <em>must<\/em> be true. And that means the argument is valid. In this example, however, premises 1, 2, and 3 are not only assumed to be true but are actually true. However, as we have already seen, the validity of an argument does not depend on its premises <em>actually<\/em> being true. Here is another example of a valid argument to illustrate that point.\r\n<div class=\"textbox shaded\">\r\n<ol>\r\n \t<li>A person can be President of the United States only if they were born in Kenya<\/li>\r\n \t<li>Obama is President of the United States<\/li>\r\n \t<li>Therefore, Obama was born in Kenya (from 1-2)<\/li>\r\n<\/ol>\r\n<\/div>\r\nClearly, the first premise of this argument is false. But if we were to imagine a scenario in which it is true and in which premise 2 is also true, then the conclusion (\u201cObama was born in Kenya\u201d) must be true. And this means that the argument is valid. We cannot imagine a scenario in which the premises of the argument are true and yet the conclusion is false. The important point to recognize here\u2014a point I have been trying to reiterate throughout this section\u2014is that the validity of the argument does not depend on whether or not the premises (or conclusion) are <em>actually<\/em> true. Rather, validity depends only on the logical relationship between the premises and the conclusion. The actual truth of the premises is, of course, important to the quality of the argument, since if the premises of the argument are false, then the argument does not provide any reason for accepting the conclusion. In the next section we will address this topic.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<h2 class=\"textbox__title\"><strong>Exercise 5:<\/strong> Determine whether or not the following arguments are valid by using the informal test of validity. If the argument is invalid, provide a counterexample.<\/h2>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol>\r\n \t<li>Katie is a human being. Therefore, Katie is smarter than a chimpanzee.<\/li>\r\n \t<li>Bob is a fireman. Therefore, Bob has put out fires.<\/li>\r\n \t<li>Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.<\/li>\r\n \t<li>Monica is a French teacher. Therefore, Monica knows how to teach French.<\/li>\r\n \t<li>Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie.<\/li>\r\n \t<li>Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique.<\/li>\r\n \t<li>Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God.<\/li>\r\n \t<li>All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.<\/li>\r\n \t<li>Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.<\/li>\r\n \t<li>Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong>Works Cited<\/strong><\/p>\r\n<p class=\"hanging-indent\">CrashCourse, director. <i>How to Argue - Philosophical Reasoning: Crash Course Philosophy #2<\/i>. <i>YouTube<\/i>, YouTube, 16 Feb. 2016, https:\/\/youtu.be\/NKEhdsnKKHs. Accessed 29 Mar. 2022.<\/p>\r\n<p class=\"hanging-indent\">Souza, Pete. \u201cOfficial Portrait of Barack Obama.\u201d <em>Wikimedia Commons,<\/em> Wikimedia Commons, 13 Jan. 2009, https:\/\/commons.wikimedia.org\/wiki\/File:Official_portrait_of_Barack_Obama.jpg. Accessed 29 Mar. 2022.<\/p>","rendered":"<div class=\"textbox shaded\">\n<p><strong>LEARNING OBJECTIVES<\/strong><\/p>\n<hr \/>\n<p>By the end of this section you will discover:<\/p>\n<ul>\n<li>The meaning of a valid argument.<\/li>\n<li>Means of recognizing validity or invalidity in an argument.<\/li>\n<\/ul>\n<\/div>\n<p>So far, we have discussed what arguments are and how to determine their structure, including how to reconstruct arguments in standard form. But we have not yet discussed what makes an argument good or bad.<\/p>\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline;\"><strong>How to Argue &#8211; Philosophical Reasoning: Crash Course Philosophy #2<\/strong><\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"How to Argue - Philosophical Reasoning: Crash Course Philosophy #2\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/NKEhdsnKKHs?feature=oembed&#38;rel=0&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/youtu.be\/NKEhdsnKKHs\" target=\"_blank\" rel=\"noopener noreferrer\">Or watch the video here<\/a><\/p>\n<p>The central concept that you will learn in logic is the concept of <strong>validity<\/strong>. Validity relates to how well the premises support the conclusion, and it is the golden standard that every argument should aim for.<\/p>\n<div class=\"textbox shaded\"><strong>Valid Argument<\/strong>: an argument in which if the premises are true, the conclusion must be true<\/div>\n<p>A valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are true. Another way of putting this is as a conditional statement: <strong>A valid argument is an<\/strong> <strong>argument in which <\/strong><strong><em>if<\/em><\/strong><strong> the premises are true, the conclusion <\/strong><strong><em>must<\/em><\/strong><strong> be true.<\/strong> Here is an example of a valid argument:<\/p>\n<div class=\"textbox shaded\">\n<ol>\n<li>Violet is a dog<\/li>\n<li>Therefore, Violet is a mammal (from 1)<\/li>\n<\/ol>\n<\/div>\n<p>You might wonder whether it <em>is<\/em> true that Violet is a dog (maybe she is a lizard or a buffalo\u2014we have no way of knowing from the information given). But, for the purposes of validity, it does not matter whether premise 1 is <em>actually<\/em> true or false. All that matters for validity is whether the conclusion follows from the premise. And we can see that the conclusion, Violet is a mammal, does seem to follow from the premise, Violet is a dog. That is, given the truth of the premise, the conclusion has to be true. This argument is clearly valid since if we assume that \u201cViolet is a dog\u201d is true, then, since all dogs are mammals, it follows that \u201cViolet is a mammal\u201d must also be true. As we have just seen, whether or not an argument is valid has nothing to do with whether the premises of the argument are actually true or not. We can illustrate this with another example, where the premises are clearly false:<\/p>\n<div class=\"textbox shaded\">\n<ol>\n<li>Everyone born in France can speak French<\/li>\n<li>Barack Obama was born in France<\/li>\n<li>Therefore, Barak Obama can speak French (from 1-2)<\/li>\n<\/ol>\n<\/div>\n<p>This is a valid argument. Why? Because when we <em>assume<\/em> the truth of the premises (everyone born in France can speak French, Barack Obama was born in France) the conclusion (Barack Obama can speak French) <em>must<\/em> be true. Notice that this is so even though none of these statements is <em>actually<\/em> true. Not everyone born in France can speak French (think about people who were born there but then moved somewhere else where they did not speak French and never learned it) and Obama was not born in France, but it is also false that Obama can speak French. So, we have a valid argument even though neither the premises nor the conclusion is actually true. That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember: validity describes the <em>relationship<\/em> between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true. In order to better understand the concept of validity, let us look at an example of an <strong><em>invalid<\/em><\/strong> argument:<\/p>\n<div class=\"textbox shaded\">\n<ol>\n<li>George was President of the United States<\/li>\n<li>Therefore, George was elected President of the United States (from 1)<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<\/div>\n<p><span style=\"text-align: initial; font-size: 1em;\">This argument is invalid because it is possible for the premise to be true and yet the conclusion false. Here is a counterexample to the argument. Gerald Ford was President of the United States, but he was never elected president, since Ford Replaced Richard Nixon when Nixon resigned in the wake of the <\/span><\/p>\n<div class=\"textbox shaded\"><strong>Counterexample<\/strong>: a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false<\/div>\n<p>Watergate scandal. So, it does not follow that just because someone is President of the United States that they were <em>elected<\/em> President of the United States. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. And this means that the argument is invalid. If an argument is invalid it will always be possible to construct a counterexample to show that it is invalid (as I have done with the Gerald Ford scenario). A <strong>counterexample<\/strong> is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.<\/p>\n<p>In order to determine whether an argument is valid or invalid we can use what I will call the informal test of validity. To apply the informal test of validity ask yourself whether you can <em>imagine<\/em> a world in which all the premises are true and yet the conclusion is false. If you <em>can<\/em> imagine such a world, then the argument is invalid. If you <em>cannot<\/em> imagine such a world, then the argument is valid.<\/p>\n<p>Notice: it is possible to imagine a world where the premises are true even if the premises are not, as a matter of actual fact, true. This is why it does not matter for validity whether the premises (or conclusion) of the argument are actually true. It will help to better understand the concept of validity by applying the informal test of validity to some sample arguments.<\/p>\n<div class=\"textbox shaded\">\n<ol>\n<li>Joan jumped out of an airplane without a parachute<\/li>\n<li>Therefore, Joan fell to her death (from 1)<\/li>\n<\/ol>\n<\/div>\n<p>To apply the informal test of validity we have to ask whether it is possible to imagine a scenario in which the premise is true and yet the conclusion is false (if so, the argument is invalid). So, can we imagine a world in which someone jumped out of an airplane without a parachute and yet did not fall to her death? (Think about it carefully before reading on.) As we will see, applying the informal test of validity takes some creativity, but it seems clearly possible that Joan could jump out of an airplane without a parachute and not die\u2014she could be perfectly fine, in fact. All we have to imagine is that the airplane was not operating and in fact was on the ground when Joan jumped out of it. If that were the case, it would be a) true that Joan jumped out of an airplane without a parachute and yet b) false that Joan fell to her death. Thus, since it is possible to imagine a scenario in which the premise is true and yet the conclusion is false, the argument is invalid. Let us slightly change the argument, this time making it clear that the plane is flying:<\/p>\n<div class=\"textbox shaded\">\n<ol>\n<li>Joan jumped out of an airplane travelling 300 mph at a height of 10,000 ft without a parachute<\/li>\n<li>Joan fell to her death (from 1)<\/li>\n<\/ol>\n<\/div>\n<p>Is this argument valid? You might think so since you might think that anyone who did such a thing would surely die. But is it possible to not die in the scenario described by the premise? If you think about it, you will realize that there are lots of ways someone could survive. For example, maybe someone <em>else<\/em> who was wearing a parachute jumped out of the plane after them, caught them and attached the parachute-less person to them, and then pulled the ripcord and they both landed on the ground safe and sound. Or maybe Joan was performing a stunt and landed in a giant net that had been set up for that purpose. Or maybe she was just one of those people who, although they did fall to the ground, happened to survive (it has happened before). All of these scenarios are consistent with the information in the first premise being true and also consistent with the conclusion being false. Thus, again, any of these counterexamples show that this argument is invalid. Notice that it is also possible that the scenario described in the premises ends with Joan falling to her death. But that does not matter because all we want to know is whether it is possible that she does not. And if it is possible, what we have shown is that the conclusion does not logically follow from the premise alone. That is, the conclusion does not have to be true, even if we grant that the premise is. And that means that the argument is not valid (i.e., it is invalid).<\/p>\n<p>Let us switch examples and consider a different argument.<\/p>\n<p>&nbsp;<\/p>\n<figure style=\"width: 245px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-content\/uploads\/sites\/65\/2022\/03\/image14-2-scaled-1.jpeg\" alt=\"Official photographic portrait of US President Barack Obama (born 4 August 1961; assumed office 20 January 2009)\" width=\"245\" height=\"333\" \/><figcaption class=\"wp-caption-text\">Official photographic portrait of US President Barack Obama<\/figcaption><\/figure>\n<div class=\"textbox shaded\">\n<ol>\n<li>A person can be President of the United States only if they were born in the United States.<\/li>\n<li>Obama is President of the United States.<\/li>\n<li>Kenya is not in the United States.<\/li>\n<li>Therefore, Obama was not born in Kenya (from 1-3)<\/li>\n<\/ol>\n<\/div>\n<p>In order to apply the informal test of validity, we have to ask whether we can imagine a scenario in which the premises are both true and yet the conclusion is false. So, we have to imagine a scenario in which premises 1, 2, and 3 are true and yet the conclusion (\u201cObama was not born in Kenya\u201d) is false. Can you imagine such a scenario? You cannot. The reason is that if you are imagining that it is a) true that a person can be President of the United States only if they were born in the United States, b) true that Obama is president and c) true that Kenya is not in the U.S., then it <em>must<\/em> be true that Obama was not born in Kenya. Thus, we know that on the assumption of the truth of the premises, the Conclusion <em>must<\/em> be true. And that means the argument is valid. In this example, however, premises 1, 2, and 3 are not only assumed to be true but are actually true. However, as we have already seen, the validity of an argument does not depend on its premises <em>actually<\/em> being true. Here is another example of a valid argument to illustrate that point.<\/p>\n<div class=\"textbox shaded\">\n<ol>\n<li>A person can be President of the United States only if they were born in Kenya<\/li>\n<li>Obama is President of the United States<\/li>\n<li>Therefore, Obama was born in Kenya (from 1-2)<\/li>\n<\/ol>\n<\/div>\n<p>Clearly, the first premise of this argument is false. But if we were to imagine a scenario in which it is true and in which premise 2 is also true, then the conclusion (\u201cObama was born in Kenya\u201d) must be true. And this means that the argument is valid. We cannot imagine a scenario in which the premises of the argument are true and yet the conclusion is false. The important point to recognize here\u2014a point I have been trying to reiterate throughout this section\u2014is that the validity of the argument does not depend on whether or not the premises (or conclusion) are <em>actually<\/em> true. Rather, validity depends only on the logical relationship between the premises and the conclusion. The actual truth of the premises is, of course, important to the quality of the argument, since if the premises of the argument are false, then the argument does not provide any reason for accepting the conclusion. In the next section we will address this topic.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<h2 class=\"textbox__title\"><strong>Exercise 5:<\/strong> Determine whether or not the following arguments are valid by using the informal test of validity. If the argument is invalid, provide a counterexample.<\/h2>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>Katie is a human being. Therefore, Katie is smarter than a chimpanzee.<\/li>\n<li>Bob is a fireman. Therefore, Bob has put out fires.<\/li>\n<li>Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.<\/li>\n<li>Monica is a French teacher. Therefore, Monica knows how to teach French.<\/li>\n<li>Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie.<\/li>\n<li>Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique.<\/li>\n<li>Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God.<\/li>\n<li>All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.<\/li>\n<li>Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.<\/li>\n<li>Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Works Cited<\/strong><\/p>\n<p class=\"hanging-indent\">CrashCourse, director. <i>How to Argue &#8211; Philosophical Reasoning: Crash Course Philosophy #2<\/i>. <i>YouTube<\/i>, YouTube, 16 Feb. 2016, https:\/\/youtu.be\/NKEhdsnKKHs. Accessed 29 Mar. 2022.<\/p>\n<p class=\"hanging-indent\">Souza, Pete. \u201cOfficial Portrait of Barack Obama.\u201d <em>Wikimedia Commons,<\/em> Wikimedia Commons, 13 Jan. 2009, https:\/\/commons.wikimedia.org\/wiki\/File:Official_portrait_of_Barack_Obama.jpg. Accessed 29 Mar. 2022.<\/p>\n","protected":false},"author":101,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc"},"chapter-type":[48],"contributor":[62,63],"license":[55],"class_list":["post-2658","chapter","type-chapter","status-publish","hentry","chapter-type-numberless","contributor-daniel-g-shaw","contributor-ph-d","license-cc-by-nc"],"part":2643,"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/chapters\/2658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/wp\/v2\/users\/101"}],"version-history":[{"count":2,"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/chapters\/2658\/revisions"}],"predecessor-version":[{"id":2900,"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/chapters\/2658\/revisions\/2900"}],"part":[{"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/parts\/2643"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/chapters\/2658\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/wp\/v2\/media?parent=2658"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/pressbooks\/v2\/chapter-type?post=2658"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/wp\/v2\/contributor?post=2658"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/introtophilosophy\/wp-json\/wp\/v2\/license?post=2658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}