IGE104: LOGIC AND MATHEMATICS FOR DAILY LIVING

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1 1 IGE104: LOGIC AND MATHEMATICS FOR DAILY LIVING Lecture 3: Recognizing Fallacies

2 LOGIC Definition: The study of the methods and principles of reasoning. When do we use reasoning? Debating with friends Making decisions Interpreting newspaper articles 2

3 EXAMPLE OF AN ARGUMENT Bob: Global warming is causing an unusually hot summer Mary: No it isn t. Bob: Yes it is! We should all start bicycling to school! Mary: You don t even know how global warming works. Bob: I know more than you do! Mary: I can t talk to you; you re an idiot. Common type of conversation that accomplishes very little 3

4 ARGUMENTS An argument is a reasoned or thoughtful process in which premises support a conclusion Premises: a set of facts or assumptions Conclusion: a closing or final statement Example: This summer is unusually hot. Global warming has been shown to cause more extreme temperatures in tropical regions. Global warming is causing an unusually hot summer 4

5 FALLACY When there is an error in reasoning an argument fails to make a case for its conclusion, this error is called a fallacy. There are many different types of fallacies Most are easily hidden, unless you pay close attention You have likely seen many fallacies without knowing in: Advertisements Political campaigns Editorial commentaries In news reports 5

6 FALLACIES: TYPES AND EXAMPLES We will discuss 10 types of fallacies Each time we will separate the argument into premises and a conclusion The name of the fallacy is less important than understanding where the fault in reasoning lies The examples come from the exercises in the book, there are additional examples in the book 6

7 FALLACY 1: APPEAL TO POPULARITY Apple s iphone outsells all other smart phones, so Apple s iphone is the best smart phone on the market Premise: Apple s iphone outsells all other smart phones Conclusion: Apple s iphone is the best smart phone on the market Fallacy: many people purchasing iphones doesn t make iphone the best 7

8 FALLACY 1: APPEAL TO POPULARITY Just because a lot of people believe or act some way, does not provide evidence that this belief or action is correct Many people believe P is true therefore P is true Example: many people used to think that Sun revolved around the earth, but now we know that it doesn t 8

9 FALLACY 2: FALSE CAUSE Tax cuts must cause recessions, because the current recession began just a few years after large tax cuts Premise: the current recession began just a few years after large tax cuts Conclusion: Tax cuts must cause recessions Fallacy: the premise states that the recession began after tax cuts, but it does not prove that one caused the other. 9

10 FALLACY 2: FALSE CAUSE Just because something happens right before something else, doesn t mean there is a connection between the two A came before B therefore A caused B 10

11 FALLACY 3: APPEAL TO IGNORANCE Fifty years of searching has not revealed life on other planets, so life in the universe must be confined to Earth. Premise: Fifty years of searching has not revealed life on other planets Conclusion: Life in the universe must be confined to Earth Fallacy: Lack of proof of life on other planets does not mean that life does not exist on other planets 11

12 FALLACY 3: APPEAL TO IGNORANCE Just because you don t know whether or not something is true, doesn t make it false There is no proof that P is true therefore P is false 12

13 FALLACY 4: HASTY GENERALIZATION Both Drew Barrymore and Lindsay Lohan struggled with drug abuse as child actresses. Therefore all child actresses become addicted to drugs. Premise: Both Drew Barrymore and Lindsay Lohan struggled with drug abuse as child actresses. Conclusion: all child actresses become addicted to drugs. Fallacy: two cases of a child actress becoming addicted to drugs do not merit an overarching statement that all child actresses become addicted to drugs. 13

14 FALLACY 4: HASTY GENERALIZATION Just because we have a few cases where two things are linked, doesn t mean one causes the other. More examples &further study are necessary for proof of cause. A and B are linked one or a few times therefore A causes B 14

15 FALLACY 5: LIMITED CHOICE You don t like taking math classes, so you must be bad at math. Premise: You don t like taking math classes Conclusion: you must be bad at math Fallacy: This arguments suggests that there are only two types of people, those who like taking math classes and are good at math, and those who don t. However, it is possible to not enjoy math, and still be good at it 15

16 FALLACY 5: LIMITED CHOICE Just because something is false doesn t mean something else is true. It is possible for both choices to be false. P is false therefore Q is true 16

17 FALLACY 6: APPEAL TO EMOTION Premise: You love your baby Conclusion: You should buy Michelin tires Fallacy: There is no logic to using an emotional response as a tool for persuasion 17

18 FALLACY 6: APPEAL TO EMOTION Just because something is associated with a positive emotional response doesn t mean it is true. P is associated with a positive emotional response therefore P is true 18

19 FALLACY 7: PERSONAL ATTACK If the Senator doesn t have any religious affiliation, then he can t have the personal values required to represent me. Premise: the Senator doesn t have any religious affiliation Conclusion: he can t have the personal values required to represent me Fallacy: disliking the senator s religious views should not have sway on your judgment on his ability to represent your needs in the Senate 19

20 FALLACY 7: PERSONAL ATTACK Just because you dislike some characteristic of a person or group doesn t mean that what they are saying is false. I have a problem with the person or group claiming P therefore P is not true 20

21 FALLACY 8: CIRCULAR REASONING Illegal immigration is against the law, so illegal immigrants are criminals Premise: Illegal immigration is against the law Conclusion: illegal immigrants are criminals Fallacy: Saying that illegal immigrants are criminals is just a different way of saying that illegal immigration is against the law. The conclusion and the premise are the same statement, and therefore one cannot support the other. 21

22 FALLACY 8: CIRCULAR REASONING Using the premise to support itself is not a valid argument. P is true P is restated in different words 22

23 FALLACY 9: DIVERSION Good grades are needed to get into college, and a college diploma is necessary for a good career. Therefore, attendance should count in high school grades Premise: Good grades are needed to get into college, and a college diploma is necessary for a good career Conclusion: attendance should count in high school grades Fallacy: 23

24 FALLACY 9: DIVERSION Using an argument about a different proposition does not make your conclusion true, even if the two are associated with each other P is related to Q and I have an argument concerning Q therefore P is true 24

25 FALLACY 10: STRAW MAN The mayor wants to raise taxes to fund social programs, so she must not believe in the value of hard work. Premise: The mayor wants to raise taxes to fund social programs Conclusion: she must not believe in the value of hard work Fallacy: The mayor did not say that she does not believe in the value of hard work. Her desire to raise taxes to fund social programs is designed to reduce crime rates and improve quality of life. The conclusion is a distortion of the premise. 25

26 FALLACY 10: STRAW MAN Distorting someone s words or beliefs I have an argument concerning a distorted version of P therefore I hope you are fooled into concluding I have an argument concerning the real version of P 26

27 CLASS ACTIVITY 27 Newspaper article

28 BIBLIOGRAPHY (1) Bennett, J. O., and W. L. Briggs. General Education Mathematics: New Approaches for a New Millennium. AMATYC Review, vol. 21, no. 1, Fall 1999, pp (2) Michelin Tire Ad 28

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