Chapter 8 Formal fallacies and fallacies of language.

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Chapter 8 Formal fallacies and fallacies of language

Transcript of Chapter 8 Formal fallacies and fallacies of language.

Page 1: Chapter 8 Formal fallacies and fallacies of language.

Chapter 8Formal fallacies and fallacies of language

Page 2: Chapter 8 Formal fallacies and fallacies of language.

Three Formal Fallacies

Affirming the Consequent Denying the AntecedentUndistributed Middle

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Page 3: Chapter 8 Formal fallacies and fallacies of language.

AFFIRMING THE CONSEQUENTWhenever an argument is in this form:

If P, then Q.Q.Therefore, P.

It is an invalid argument.

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Page 4: Chapter 8 Formal fallacies and fallacies of language.

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!

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Page 5: Chapter 8 Formal fallacies and fallacies of language.

DENYING THE ANTECEDENTWhenever an argument is in this form:

If P, then Q.Not-PTherefore, Not-Q

It is an invalid argument.

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Page 6: Chapter 8 Formal fallacies and fallacies of language.

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!

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Page 7: Chapter 8 Formal fallacies and fallacies of language.

THE UNDISTRIBUTED MIDDLEWhen 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.

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Page 8: Chapter 8 Formal fallacies and fallacies of language.

THE UNDISTRIBUTED MIDDLETakes 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.]

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Page 9: Chapter 8 Formal fallacies and fallacies of language.

THE UNDISTRIBUTED MIDDLEAnother 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.

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Page 10: Chapter 8 Formal fallacies and fallacies of language.

THE UNDISTRIBUTED MIDDLEHere 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.

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Page 11: Chapter 8 Formal fallacies and fallacies of language.

FALLACIES OF LANGUAGESome fallacies related to discussions in Chapter 3 on ambiguity are up next:EquivocationAmphibolyCompositionDivision

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Page 12: Chapter 8 Formal fallacies and fallacies of language.

The Fallacies of Equivocation and Amphiboly

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Page 13: Chapter 8 Formal fallacies and fallacies of language.

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.

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Page 14: Chapter 8 Formal fallacies and fallacies of language.

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.

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The Fallacies of Composition and Division

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Page 16: Chapter 8 Formal fallacies and fallacies of language.

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.”

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Confusing Fallacies: Composition versus Hasty Generalization

Composition

Jumping from a fact about individual members of a collection to a fact about the collection.

Hasty Generalization

Jumping from a fact about an individual member of a collection to a conclusion about every individual member of the collection.

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Page 18: Chapter 8 Formal fallacies and fallacies of language.

Confusing Fallacies: Composition versus Hasty Generalization

Composition

The Senators are all large. Therefore, the senate is large.

Hasty Generalization

Senator Brown is overweight. Therefore, all the senators are overweight.

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Page 19: Chapter 8 Formal fallacies and fallacies of language.

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.

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Page 20: Chapter 8 Formal fallacies and fallacies of language.

Confusing Fallacies: Division versus Accident

Division

Jumping from a fact about the members of a collection taken collectively to a conclusion about the members taken individually.

Accident

Jumping from a generalization about every individual member of a collection to a conclusion about this or that member of the collection.

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Page 21: Chapter 8 Formal fallacies and fallacies of language.

Confusing Fallacies: Division versus Accident

Division

This is a large senate. Therefore, each senator is large.

Accident

Senators are wealthy. Therefore, Senator Brown is wealthy.

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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?”

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Page 23: Chapter 8 Formal fallacies and fallacies of language.

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.

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VISITOR: I understand that all the fish in this pond are carp.CURATOR: No, quite the opposite, in fact.VISITOR: What? No carp?

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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.

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“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.

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CONSISTENCY AND INCONSISTENCY

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Miscalculating probabilities

Independent EventsGambler’s FallacyOverlooking Prior Probabilities Overlooking False Positives

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Page 27: Chapter 8 Formal fallacies and fallacies of language.

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.

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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.

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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.

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Page 30: Chapter 8 Formal fallacies and fallacies of language.

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’.

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Page 31: Chapter 8 Formal fallacies and fallacies of language.

OVERLOOKING PRIOR PROBABILITIESThe 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.

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OVERLOOKING PRIOR PROBABILITIESThis 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.”

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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.

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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.”

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