Formal fallacies and fallacies of language Chapter 8 Formal fallacies and fallacies of language

Three Formal Fallacies Affirming the Consequent Denying the Antecedent Undistributed Middle © 2015 McGraw-Hill Higher Education. All rights reserved.

Affirming the Consequent Whenever an argument is in this form: If P, then Q. Q. Therefore, P. It is an invalid argument. © 2015 McGraw-Hill Higher Education. All rights reserved.

Affirming the Consequent If Jane is a member of a sorority, then she is female. Jane is female. Therefore, Jane is a member of a sorority. An Invalid Argument! © 2015 McGraw-Hill Higher Education. All rights reserved.

Denying the antecedent Whenever an argument is in this form: If P, then Q. Not-P Therefore, Not-Q It is an invalid argument. © 2015 McGraw-Hill Higher Education. All rights reserved.

Denying the antecedent If Howard passed the final, then he passed the course. Howard did not pass the final. Therefore, Howard did not pass the course. An Invalid Argument! © 2015 McGraw-Hill Higher Education. All rights reserved.

The undistributed middle When someone assumes that two things related to a third thing are related to each other, as in: All cats are mammals. All dogs are mammals. Therefore, all cats are dogs. © 2015 McGraw-Hill Higher Education. All rights reserved.

The undistributed middle Takes several forms: X has features a, b, c, etc. Y has features a, b, c, etc. Therefore X is Y. Another form is: All X’s are Y’s. This thing is Y Therefore, this thing is X. [We saw this form in the previous slide.] © 2015 McGraw-Hill Higher Education. All rights reserved.

The undistributed middle Another form: X is a Z. Y is a Z. Therefore, X is a Y. One other form is: If P is true, then Q is true. If R is true, then Q is true. Therefore if P is true, then R is true. © 2015 McGraw-Hill Higher Education. All rights reserved.

The undistributed middle Here is an example of that last form. If Bill wins the lottery, then he’ll be happy. If Bill buys a new car, then he’ll be happy. Therefore, if Bill wins the lottery, then he’ll buy a new car. If P is true, then Q is true. If R is true, then Q is true. Therefore if P is true, then R is true. © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. Fallacies of LANGUAGE Some fallacies related to discussions in Chapter 3 on ambiguity are up next: Equivocation Amphiboly Composition Division © 2015 McGraw-Hill Higher Education. All rights reserved.

The Fallacies of Equivocation and Amphiboly © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. equivocation Equivocation occurs in this argument because the word ‘bank’ is ambiguous and used in two different senses: All banks are alongside rivers, and the place where I keep my money is a bank. Therefore the place where I keep my money is alongside a river. © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. AMphiboly This occurs when the structure of a sentence makes the sentence ambiguous. If you want to take the motor out of the car, I’ll sell it to you cheap. The pronoun ‘it’ may refer to the car or to the motor. It isn’t clear which. It would be a fallacy to conclude one way or the other, without more information. © 2015 McGraw-Hill Higher Education. All rights reserved.

The Fallacies of Composition and Division © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. composition A fallacy that happens when a speaker or writer assumes that what is true of a group of things taken individually must also be true of those same things taken collectively; or assumes that what is true of the parts of a thing must be true of the thing itself. “This building is made from rectangular bricks; therefore, it must be rectangular.” © 2015 McGraw-Hill Higher Education. All rights reserved.

Confusing Fallacies: Composition versus Hasty Generalization Jumping from a fact about individual members of a collection to a fact about the collection. Jumping from a fact about an individual member of a collection to a conclusion about every individual member of the collection. © 2015 McGraw-Hill Higher Education. All rights reserved.

Confusing Fallacies: Composition versus Hasty Generalization The Senators are all large. Therefore, the senate is large. Senator Brown is overweight. Therefore, all the senators are overweight. © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. division A fallacy that happens when a speaker or writer assumes that what is true of a group of things taken individually must also be true of those same things taken collectively; or assumes that what is true of the parts of a thing must be true of the thing itself. This building is circular; therefore, it must be made from circular bricks. © 2015 McGraw-Hill Higher Education. All rights reserved.

Confusing Fallacies: Division versus Accident Jumping from a fact about the members of a collection taken collectively to a conclusion about the members taken individually. Jumping from a generalization about every individual member of a collection to a conclusion about this or that member of the collection. © 2015 McGraw-Hill Higher Education. All rights reserved.

Confusing Fallacies: Division versus Accident This is a large senate. Therefore, each senator is large. Senators are wealthy. Therefore, Senator Brown is wealthy. © 2015 McGraw-Hill Higher Education. All rights reserved.

Confusing explanations with excuses The fallacy of presuming that when someone explains how or why something happened, he or she is either excusing or justifying what happened. “I heard on the History Channel about how the weak German economy after World War I contributed to the rise of Adolf Hitler. What’s that about? Why would the History Channel try to excuse the Germans?” © 2015 McGraw-Hill Higher Education. All rights reserved.

Confusing contraries and contradictories Contradictory claims are claims that cannot have the same truth value. Contrary claims are claims that cannot both be true but can both be false. VISITOR: I understand that all the fish in this pond are carp. CURATOR: No, quite the opposite, in fact. VISITOR: What? No carp? © 2015 McGraw-Hill Higher Education. All rights reserved.

Consistency and inconsistency An individual is inconsistent if he/she says two things that can’t both be true. “I think taxes should not be raised.” [One year later]: “I think taxes should be raised.” The fact that an individual has been inconsistent doesn’t mean that his/her present belief is false. © 2015 McGraw-Hill Higher Education. All rights reserved.

Consistency and inconsistency “Flip-flopping” is no reason for thinking that the person’s current belief is defective. An inconsistent position cannot of course be accepted, but one of the beliefs of an inconsistent person may well be, depending on its merits. And don’t forget, if both beliefs are contraries, they might both be false. © 2015 McGraw-Hill Higher Education. All rights reserved.

Miscalculating probabilities Independent Events Gambler’s Fallacy Overlooking Prior Probabilities Overlooking False Positives © 2015 McGraw-Hill Higher Education. All rights reserved.

Miscalculating probabilities Bill’s chances of becoming a professional football player are about 1 in 1,000, and Hal’s chances of becoming a professional hockey player are about 1 in 5,000. So the chance of both of them becoming professionals in their respective sports is 1 in 6,000. NOPE. The two events, Hal becoming a hockey player and Bill becoming a football player, are independent. © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. Independent events One independent event cannot affect the outcome of another independent event. To calculate the probability that independent events both occur, we multiply their individual probabilities. The probability of both Hal and Bill becoming pro is 1/1000 times 1/5000 which is 1/5,000,000. © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. The Gambler’s fallacy When we don’t realize that independent events really are independent, that past performance of an independent event will not influence a subsequent performance of that kind of event, Then we are at risk of committing the Gambler’ Fallacy. © 2015 McGraw-Hill Higher Education. All rights reserved.

© 2015 McGraw-Hill Higher Education. All rights reserved. The Gambler’s fallacy Remember, independent events do not affect one another’s outcome. Example: No matter how many times a fair coin is flipped, no matter how many times ‘Tails’ has been the outcome of those flips, the probability that the next flip will show ‘Heads’ is still exactly ½. And, for that matter, there is the same probability that it will come up ‘Tails’. © 2015 McGraw-Hill Higher Education. All rights reserved.

Overlooking prior probabilities The prior probability of something is its true or actual proportion. The prior probability of a fair coin coming up ‘Heads’ when it is flipped is one in two, or ½. The prior probability of an unfair coin coming up ‘Heads’ when it is flipped is a proportion different than ½. © 2015 McGraw-Hill Higher Education. All rights reserved.

Overlooking prior probabilities This fallacy occurs when failing to take into consideration the likelihood of an event all other things being equal; that is, its likelihood apart from any outside influences. “Bill is the best football player in our high school, and Hal is the best hockey player in our high school. So it appears that Bill’s chances of becoming a professional football player and Hal’s chances of becoming a professional football player are equally good.” © 2015 McGraw-Hill Higher Education. All rights reserved.

Overlooking false positives False positives are false alarms. The fallacy of Overlooking False Positives occurs when probabilities are calculated. That is, When deriving the proportion of Xs that are Ys from the proportion of Ys that are Xs, and failing to take into consideration the proportion of non- Ys that are Xs. © 2015 McGraw-Hill Higher Education. All rights reserved.

Overlooking false positives 66% of the people who flunked the midterm ate carrots prior to the test. Therefore, avoid carrots before taking a test. You must take into account the proportion of carrot- eaters who did not flunk the midterm. Eating carrots might be a “false alarm.” © 2015 McGraw-Hill Higher Education. All rights reserved.