{"id":874,"date":"2016-12-19T21:20:22","date_gmt":"2016-12-19T21:20:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=874"},"modified":"2021-02-05T23:51:33","modified_gmt":"2021-02-05T23:51:33","slug":"logical-fallacies-in-common-language","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/logical-fallacies-in-common-language\/","title":{"raw":"Logical Fallacies in Common Language","rendered":"Logical Fallacies in Common Language"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, false dilemma, circular reasoning, post hoc, correlation implies causation, and straw man arguments<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the previous discussion, we saw that logical arguments can be invalid when the premises are not true, when the premises are not sufficient to guarantee the conclusion, or when there are invalid chains in logic. There are a number of other ways in which arguments can be invalid, a sampling of which are given here.\r\n<div class=\"textbox examples\">\r\n<h3>a note about logical fallacies<\/h3>\r\nThe ideas sampled on this page are classic and are often found in irresponsible advertising, politics, and in social media. A good way to understand them is to see as many examples of them in the world as you can.\r\n\r\nLook at social media arguments that appeal to emotion and sentiment. Political candidates, too,\u00a0 sometimes employ one or more of these to favorably manipulate situation.\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Ad hominem<\/h3>\r\nAn ad hominem argument attacks the person making the argument, ignoring the argument itself.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cJane says that whales aren\u2019t fish, but she\u2019s only in the second grade, so she can\u2019t be right.\u201d\r\n[reveal-answer q=\"683444\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"683444\"]\r\n\r\nHere the argument is attacking Jane, not the validity of her claim, so this is an ad hominem argument.\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cJane says that whales aren\u2019t fish, but everyone knows that they\u2019re really mammals\u2014she\u2019s so stupid.\u201d\r\n[reveal-answer q=\"421872\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"421872\"]This certainly isn\u2019t very nice, but it is <em>not<\/em> ad hominem since a valid counterargument is made along with the personal insult.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25481[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Appeal to ignorance<\/h3>\r\nThis type of argument assumes something it true because it hasn\u2019t been proven false.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cNobody has proven that photo isn\u2019t Bigfoot, so it must be Bigfoot.\u201d\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Appeal to authority<\/h3>\r\nThese arguments attempt to use the authority of a person to prove a claim. While often authority can provide strength to an argument, problems can occur when the person\u2019s opinion is not shared by other experts, or when the authority is irrelevant to the claim.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25600[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cA diet high in bacon can be healthy \u2013 Doctor Atkins said so.\u201d\r\n[reveal-answer q=\"536253\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"536253\"]Here, an appeal to the authority of a doctor is used for the argument. This generally would provide strength to the argument, except that the opinion that eating a diet high in saturated fat runs counter to general medical opinion. More supporting evidence would be needed to justify this claim.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cJennifer Hudson lost weight with Weight Watchers, so their program must work.\u201d\r\n\r\n[reveal-answer q=\"764781\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"764781\"]\r\n\r\nHere, there is an appeal to the authority of a celebrity. While her experience does provide evidence, it provides no more than any other person\u2019s experience would.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Appeal to Consequence<\/h3>\r\nAn appeal to consequence concludes that a premise is true or false based on whether the consequences are desirable or not.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cHumans will travel faster than light: faster-than-light travel would be beneficial for space travel.\u201d\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25602[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>False dilemma<\/h3>\r\nA false dilemma argument falsely frames an argument as an \u201ceither or\u201d choice, without allowing for additional options.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cEither those lights in the sky were an airplane or aliens. There are no airplanes scheduled for tonight, so it must be aliens.\u201d\r\n\r\nThis argument ignores the possibility that the lights could be something other than an airplane or aliens.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25484[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Circular reasoning<\/h3>\r\nCircular reasoning is an argument that relies on the conclusion being true for the premise to be true.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cI shouldn\u2019t have gotten a C in that class; I\u2019m an A student!\u201d\r\n\r\nIn this argument, the student is claiming that because they\u2019re an A student, though shouldn\u2019t have gotten a C. But because they got a C, they\u2019re not an A student.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25603[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Straw man<\/h3>\r\nA straw man argument involves misrepresenting the argument in a less favorable way to make it easier to attack.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cSenator Jones has proposed reducing military funding by 10%. Apparently he wants to leave us defenseless against attacks by terrorists\u201d\r\n\r\nHere the arguer has represented a 10% funding cut as equivalent to leaving us defenseless, making it easier to attack.\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Post hoc (post hoc ergo propter hoc)<\/h3>\r\nA post hoc argument claims that because two things happened sequentially, then the first must have caused the second.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cToday I wore a red shirt, and my football team won! I need to wear a red shirt everytime they play to make sure they keep winning.\u201d\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25604[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Correlation implies causation<\/h3>\r\nSimilar to post hoc, but without the requirement of sequence, this fallacy assumes that just because two things are related one must have caused the other. Often there is a third variable not considered.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n\u201cMonths with high ice cream sales also have a high rate of deaths by drowning. Therefore ice cream must be causing people to drown.\u201d\r\n\r\nThis argument is implying a causal relation, when really both are more likely dependent on the weather; that ice cream and drowning are both more likely during warm summer months.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25482[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nIdentify the logical fallacy in each of the arguments\r\n<ol>\r\n \t<li>Only an untrustworthy person would run for office. The fact that politicians are untrustworthy is proof of this.<\/li>\r\n \t<li>Since the 1950s, both the atmospheric carbon dioxide level and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Obesity\">obesity<\/a> levels have increased sharply. Hence, atmospheric carbon dioxide causes obesity.<\/li>\r\n \t<li>The oven was working fine until you started using it, so you must have broken it.<\/li>\r\n \t<li>You can\u2019t give me a D in the class\u2014I can\u2019t afford to retake it.<\/li>\r\n \t<li>The senator wants to increase support for food stamps. He wants to take the taxpayers\u2019 hard-earned money and give it away to lazy people. This isn\u2019t fair so we shouldn\u2019t do it.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"912175\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"912175\"]\r\n\r\n1.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]A[\/latex]<\/td>\r\n<td>[latex]B[\/latex]<\/td>\r\n<td>[latex]{\\sim}A[\/latex]<\/td>\r\n<td>[latex]{\\sim}A{\\wedge}B[\/latex]<\/td>\r\n<td>[latex]{\\sim}B[\/latex]<\/td>\r\n<td>[latex]\\left({\\sim}A{\\wedge}B\\right){\\vee}{\\sim}B[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. Since no cows are purple, we know there is no overlap between the set of cows and the set of purple things. We know Fido is not in the cow set, but that is not enough to conclude that Fido is in the purple things set.\r\n\r\n<img class=\"aligncenter wp-image-1939 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/20214932\/Screen-Shot-2017-03-20-at-2.48.21-PM.png\" alt=\"A blue circle labeled Cows. A yellow circle labeled Purple things, with an x followed by a question mark. Apart from both circles is a note asking Fido x?\" width=\"366\" height=\"215\" \/>\r\n\r\n3. Let S: have a shovel, D: dig a hole. The first premise is equivalent to [latex]S{\\rightarrow}D[\/latex]. The second premise is D. The conclusion is S.\r\n\r\nWe are testing [latex]\\left[\\left(S{\\rightarrow}D\\right){\\wedge}D\\right]{\\rightarrow}S[\/latex]\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]S[\/latex]<\/td>\r\n<td>[latex]D[\/latex]<\/td>\r\n<td>[latex]S{\\rightarrow}D[\/latex]<\/td>\r\n<td>[latex]\\left(S{\\rightarrow}D\\right){\\wedge}D[\/latex]<\/td>\r\n<td>[latex]\\left[\\left(S{\\rightarrow}D\\right){\\wedge}D\\right]{\\rightarrow}S[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis is not a tautology, so this is an invalid argument.\r\n\r\n4.\u00a0Letting P = go to the party, T = being tired, and F = seeing friends, then we can represent this argument as P:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Premise:<\/td>\r\n<td>[latex]P{\\rightarrow}T[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Premise:<\/td>\r\n<td>[latex]P{\\rightarrow}F[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Conclusion:<\/td>\r\n<td>[latex]{\\sim}F{\\rightarrow}{\\sim}T[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe could rewrite the second premise using the contrapositive to state [latex]{\\sim}F{\\rightarrow}{\\sim}P[\/latex], but that does not allow us to form a syllogism. If we don\u2019t see friends, then we didn\u2019t go the party, but that is not sufficient to claim I won\u2019t be tired tomorrow. Maybe I stayed up all night watching movies.\r\n\r\n5.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Circular<\/li>\r\n \t<li>Correlation does not imply causation<\/li>\r\n \t<li>Post hoc<\/li>\r\n \t<li>Appeal to consequence<\/li>\r\n \t<li>Straw man<\/li>\r\n<\/ol>\r\n[\/hidden-answer][ohm_question]25604[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, false dilemma, circular reasoning, post hoc, correlation implies causation, and straw man arguments<\/li>\n<\/ul>\n<\/div>\n<p>In the previous discussion, we saw that logical arguments can be invalid when the premises are not true, when the premises are not sufficient to guarantee the conclusion, or when there are invalid chains in logic. There are a number of other ways in which arguments can be invalid, a sampling of which are given here.<\/p>\n<div class=\"textbox examples\">\n<h3>a note about logical fallacies<\/h3>\n<p>The ideas sampled on this page are classic and are often found in irresponsible advertising, politics, and in social media. A good way to understand them is to see as many examples of them in the world as you can.<\/p>\n<p>Look at social media arguments that appeal to emotion and sentiment. Political candidates, too,\u00a0 sometimes employ one or more of these to favorably manipulate situation.<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Ad hominem<\/h3>\n<p>An ad hominem argument attacks the person making the argument, ignoring the argument itself.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cJane says that whales aren\u2019t fish, but she\u2019s only in the second grade, so she can\u2019t be right.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q683444\">Show Solution<\/span><\/p>\n<div id=\"q683444\" class=\"hidden-answer\" style=\"display: none\">\n<p>Here the argument is attacking Jane, not the validity of her claim, so this is an ad hominem argument.\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cJane says that whales aren\u2019t fish, but everyone knows that they\u2019re really mammals\u2014she\u2019s so stupid.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q421872\">Show Solution<\/span><\/p>\n<div id=\"q421872\" class=\"hidden-answer\" style=\"display: none\">This certainly isn\u2019t very nice, but it is <em>not<\/em> ad hominem since a valid counterargument is made along with the personal insult.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25481\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25481&theme=oea&iframe_resize_id=ohm25481&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Appeal to ignorance<\/h3>\n<p>This type of argument assumes something it true because it hasn\u2019t been proven false.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cNobody has proven that photo isn\u2019t Bigfoot, so it must be Bigfoot.\u201d<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Appeal to authority<\/h3>\n<p>These arguments attempt to use the authority of a person to prove a claim. While often authority can provide strength to an argument, problems can occur when the person\u2019s opinion is not shared by other experts, or when the authority is irrelevant to the claim.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25600\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25600&theme=oea&iframe_resize_id=ohm25600&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cA diet high in bacon can be healthy \u2013 Doctor Atkins said so.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q536253\">Show Solution<\/span><\/p>\n<div id=\"q536253\" class=\"hidden-answer\" style=\"display: none\">Here, an appeal to the authority of a doctor is used for the argument. This generally would provide strength to the argument, except that the opinion that eating a diet high in saturated fat runs counter to general medical opinion. More supporting evidence would be needed to justify this claim.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cJennifer Hudson lost weight with Weight Watchers, so their program must work.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q764781\">Show Solution<\/span><\/p>\n<div id=\"q764781\" class=\"hidden-answer\" style=\"display: none\">\n<p>Here, there is an appeal to the authority of a celebrity. While her experience does provide evidence, it provides no more than any other person\u2019s experience would.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<h3>Appeal to Consequence<\/h3>\n<p>An appeal to consequence concludes that a premise is true or false based on whether the consequences are desirable or not.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cHumans will travel faster than light: faster-than-light travel would be beneficial for space travel.\u201d<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25602\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25602&theme=oea&iframe_resize_id=ohm25602&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>False dilemma<\/h3>\n<p>A false dilemma argument falsely frames an argument as an \u201ceither or\u201d choice, without allowing for additional options.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cEither those lights in the sky were an airplane or aliens. There are no airplanes scheduled for tonight, so it must be aliens.\u201d<\/p>\n<p>This argument ignores the possibility that the lights could be something other than an airplane or aliens.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25484\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25484&theme=oea&iframe_resize_id=ohm25484&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Circular reasoning<\/h3>\n<p>Circular reasoning is an argument that relies on the conclusion being true for the premise to be true.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cI shouldn\u2019t have gotten a C in that class; I\u2019m an A student!\u201d<\/p>\n<p>In this argument, the student is claiming that because they\u2019re an A student, though shouldn\u2019t have gotten a C. But because they got a C, they\u2019re not an A student.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25603\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25603&theme=oea&iframe_resize_id=ohm25603&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Straw man<\/h3>\n<p>A straw man argument involves misrepresenting the argument in a less favorable way to make it easier to attack.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cSenator Jones has proposed reducing military funding by 10%. Apparently he wants to leave us defenseless against attacks by terrorists\u201d<\/p>\n<p>Here the arguer has represented a 10% funding cut as equivalent to leaving us defenseless, making it easier to attack.<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Post hoc (post hoc ergo propter hoc)<\/h3>\n<p>A post hoc argument claims that because two things happened sequentially, then the first must have caused the second.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cToday I wore a red shirt, and my football team won! I need to wear a red shirt everytime they play to make sure they keep winning.\u201d<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25604\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25604&theme=oea&iframe_resize_id=ohm25604&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Correlation implies causation<\/h3>\n<p>Similar to post hoc, but without the requirement of sequence, this fallacy assumes that just because two things are related one must have caused the other. Often there is a third variable not considered.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>\u201cMonths with high ice cream sales also have a high rate of deaths by drowning. Therefore ice cream must be causing people to drown.\u201d<\/p>\n<p>This argument is implying a causal relation, when really both are more likely dependent on the weather; that ice cream and drowning are both more likely during warm summer months.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25482\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25482&theme=oea&iframe_resize_id=ohm25482&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Identify the logical fallacy in each of the arguments<\/p>\n<ol>\n<li>Only an untrustworthy person would run for office. The fact that politicians are untrustworthy is proof of this.<\/li>\n<li>Since the 1950s, both the atmospheric carbon dioxide level and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Obesity\">obesity<\/a> levels have increased sharply. Hence, atmospheric carbon dioxide causes obesity.<\/li>\n<li>The oven was working fine until you started using it, so you must have broken it.<\/li>\n<li>You can\u2019t give me a D in the class\u2014I can\u2019t afford to retake it.<\/li>\n<li>The senator wants to increase support for food stamps. He wants to take the taxpayers\u2019 hard-earned money and give it away to lazy people. This isn\u2019t fair so we shouldn\u2019t do it.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q912175\">Show Solution<\/span><\/p>\n<div id=\"q912175\" class=\"hidden-answer\" style=\"display: none\">\n<p>1.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]A[\/latex]<\/td>\n<td>[latex]B[\/latex]<\/td>\n<td>[latex]{\\sim}A[\/latex]<\/td>\n<td>[latex]{\\sim}A{\\wedge}B[\/latex]<\/td>\n<td>[latex]{\\sim}B[\/latex]<\/td>\n<td>[latex]\\left({\\sim}A{\\wedge}B\\right){\\vee}{\\sim}B[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. Since no cows are purple, we know there is no overlap between the set of cows and the set of purple things. We know Fido is not in the cow set, but that is not enough to conclude that Fido is in the purple things set.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1939 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/20214932\/Screen-Shot-2017-03-20-at-2.48.21-PM.png\" alt=\"A blue circle labeled Cows. A yellow circle labeled Purple things, with an x followed by a question mark. Apart from both circles is a note asking Fido x?\" width=\"366\" height=\"215\" \/><\/p>\n<p>3. Let S: have a shovel, D: dig a hole. The first premise is equivalent to [latex]S{\\rightarrow}D[\/latex]. The second premise is D. The conclusion is S.<\/p>\n<p>We are testing [latex]\\left[\\left(S{\\rightarrow}D\\right){\\wedge}D\\right]{\\rightarrow}S[\/latex]<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]S[\/latex]<\/td>\n<td>[latex]D[\/latex]<\/td>\n<td>[latex]S{\\rightarrow}D[\/latex]<\/td>\n<td>[latex]\\left(S{\\rightarrow}D\\right){\\wedge}D[\/latex]<\/td>\n<td>[latex]\\left[\\left(S{\\rightarrow}D\\right){\\wedge}D\\right]{\\rightarrow}S[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This is not a tautology, so this is an invalid argument.<\/p>\n<p>4.\u00a0Letting P = go to the party, T = being tired, and F = seeing friends, then we can represent this argument as P:<\/p>\n<table>\n<tbody>\n<tr>\n<td>Premise:<\/td>\n<td>[latex]P{\\rightarrow}T[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Premise:<\/td>\n<td>[latex]P{\\rightarrow}F[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Conclusion:<\/td>\n<td>[latex]{\\sim}F{\\rightarrow}{\\sim}T[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We could rewrite the second premise using the contrapositive to state [latex]{\\sim}F{\\rightarrow}{\\sim}P[\/latex], but that does not allow us to form a syllogism. If we don\u2019t see friends, then we didn\u2019t go the party, but that is not sufficient to claim I won\u2019t be tired tomorrow. Maybe I stayed up all night watching movies.<\/p>\n<p>5.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Circular<\/li>\n<li>Correlation does not imply causation<\/li>\n<li>Post hoc<\/li>\n<li>Appeal to consequence<\/li>\n<li>Straw man<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm25604\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25604&theme=oea&iframe_resize_id=ohm25604&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-874\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Math in society. <strong>Authored by<\/strong>: Lippman, David. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Question ID 25481, 25482, 25483. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t 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