1 nondeductive logic induction & informal fallacies

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1 NONDEDUCTIVE LOGIC INDUCTION & INFORMAL FALLACIES

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Page 1: 1 NONDEDUCTIVE LOGIC INDUCTION & INFORMAL FALLACIES

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NONDEDUCTIVE LOGIC

INDUCTION

&

INFORMAL FALLACIES

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Reasoning

• To give an argument is to give reasons for a conclusion. It’s more than offering an opinion or making an assertion.

• Reasoning is about what people should believe based on EVIDENCE. Rational inquiry depends on logic. Good arguments should persuade but they may not. That a good (sound) deductive argument does not persuade is a rhetorical issue, or a case of stubbornness on the part of the listener. Bad or fallacious arguments are often highly persuasive.

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Inductive Reasoning-1

• While a valid deductive argument is risk free since its conclusion follows necessarily from its premises, an inductive argument is risky. Its conclusion can be denied without contradiction because the conclusion is not entailed by its premises but the premises provide strong evidence for it.

• Most horses are friendly. Mr. Ed is a horse. Therefore, Mr. Ed is friendly.

• A deductive argument has ‘All’ instead of ‘most’.

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Inductive Reasoning-2• Induction is the process of drawing generalizations

from known facts or research to give strength and support to conclusions.

• Inductive reasoning is the process of finding truth by making observations; inferring general laws and truths from specific instances.

• Inductive generalizations are possible, but some are much more probable than others.

• Statistical evidence—data collected by polling and research studies—leads to statistical generalizations, which are inferences drawn from statistical evidence used to give strength to inductive arguments.

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Statistical Reports• Characteristic of interest—the specific question the

researcher seeks to answer concerning a given population.

• Target population—the group about which a researcher wishes to generalize.

• Sample—members of the target population studied by the researcher.

• The sample must be representative [not biased] of the target population and must be random.

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Inductive Reasoning: Types

• Enumerative induction—one or more premises state that some things of a certain kind have a certain feature, and this is offered as evidence that all things of the same kind have that same feature. Inductive generalization. (universal)– Every raven so far observed has been black.– Ravens are black– Many roses have been observed to bloom in the summer.– All roses blossom in the summer.– Counterexample proves the conclusion false.– In the past, most animal species have survived by adapting.– Animal species will continue to survive by adapting?

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Inductive Reasoning: Types

• Statistical syllogism—an inductive argument whereby a certain feature is ascribed to some case or cases on the basis of their being a part of a larger class, some of which, perhaps many have the ascribed feature. – Most surgeons carry malpractice insurance.– Dr. Marreno is a surgeon.– Dr. Marreno carries malpractice insurance.– Most A’s are B’s compare All A’s are B’s– h is an A h is an A– h is a B h is a B– Inductive deductive

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Inductive Reasoning: Types

• Statistical syllogisms share a common pattern which can be used for explaining the past and the future. – Most famous battles involved careful strategy.– Trafalgar was a famous battle.– Trafalgar involved careful strategy.– 80% of police officers have terrorism training.– David will be a police officer.– David will have terrorism training.– n% of A’s are B’s– m is an A– m is a B n<100

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Inductive Reasoning: Types• In a causal argument, one or more premises are offered to

support that the hypothesis that a certain event is causally related to another event. A cause regularly precedes an effect, but a cause must do more. Whenever something occurs, it is often possible to narrow the range of hypotheses about its likely cause. Mill identified two such methods: the method of agreement and difference and the method of concomitant variation.

• Agreement and Difference: What different occurrences of a certain phenomenon have in common is probably its cause. And factors that are present only when some observed phenomenon occurs are probably its cause.

• Concomitant Variation: When variations of one sort are highly correlated with variations of another, one is likely to be the cause of the other, or they may both be caused by something else.

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Inductive Reasoning: Types• The Method of Agreement and Difference: An example:

Coach wants to find out why three of his best players perform poorly on Friday afternoons.

• 1—David, Jim, and Bob have been performing poorly on Friday afternoons.

• 2—Going to late parties on Thursday is the one and only thing that all three do when and only when they perform poorly.

• 3—Going to late parties on Thursday likely causes their poor game performance.

• X has occurred several times.• Y is the one and only other thing that precedes all

occurrences of X.• Y causes X.• Coach must compare both agreement and difference—

employ jointly.

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Inductive Reasoning: Types• Analogy—a type of inductive argument whereby a

certain conclusion about an individual or a class of individuals is drawn on the basis of some similarities that an individual or class has with other individuals or classes: – David’s vehicle, a 2007 Hummer, is expensive to run.– Jane’s vehicle , a 2007 Hummer, is expensive to run.– Mark’s vehicle, a 2007 Hummer, is expensive to run.– Jack’s vehicle is a 2007 Hummer.– Jack’s vehicle is expensive to run.

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Inductive Reasoning: Types• Factors that effect the success of an analogy:

– the number of things and features held to be analogous.– the degree of similarities and differences among those things.– the relevance of ascribed features to the hypothesis.– the boldness of the hypothesis with respect to the evidence.

• Extensive research on polar bears and hippos has shown that they have a great number of relevant features in common with other species listed as threatened species. These threatened species might disappear. So polar bears and hippos might disappear.

• The pattern of reasoning underlying this analogy is:– Things a and b have n relevant features in common with x, y, and z.– x, y, and z also have feature n+1– a and b probably have feature n+1.

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Inductive Reasoning: Types• 1--Anyone wishing to be a space tourist will have to pay

$100 million. For, according to my records, each space tourist has recently paid $100 million for traveling in space.

• 2-- Smaller, more fuel-efficient vehicles are now quite popular among many college students. My roommate is about to buy a vehicle. I predict that he’ll buy a small, fuel-efficient car.

• 3--People who have a high percentage of folic acid in their diets also have a lower incidence of Alzheimer’s disease. But these people generally have more healthy habits. Thus either a high percentage of dietary folic acid causes a lower incidence of Alzheimer’s disease or having healthy habits causes both.

• 4--The earth is a planet with carbon based life. The required elements—Carbon, water, and energy—appear to be, or to have been, present on Mars, which is also a planet. This suggests that Mars could have had carbon based life.

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Inductive Reasoning: Characteristics

• Inductive reliability—an inductive argument is reliable if and only if its form is such that, if its premises were true, it would be reasonable to accept its conclusion as true. (cogency)– 99% of A’s are B’s– h is an A highly reliable– h is a B– 39% of A’s are B’s– h is an A less reliable (a matter of degree)

– H is a B– Compare to validity of deductive arguments—not

necessarily truth preserving.

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Inductive Reasoning: Characteristics

• Inductive strength—when an inductive argument is strong, it has a reliable form and its premises are true. It is then reasonable to accept its conclusion as true.– 80% of students in Biology 100 are women.– Robin is a student in Biology 100.– Robin is a women. – An inductive argument is strong if and only if its

hypothesis is the one that has the greatest probability of being true on the basis of the evidence.

– Compare inductive strength and deductive soundness—not necessarily true but probably true.

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Definition of Informal fallacy• A fallacy is a mistake in reasoning. A fallacious argument

is one that contains such an error. To identify errors in reasoning is a necessary condition for reasoning soundly.

• In formal logic arguments are valid or invalid. We have discussed, for example, certain formal fallacies that arguments may have that make them invalid.

• An informal fallacy is a type of argument which, although incorrect, may nevertheless be psychologically persuasive either because we are deceived by some ambiguity in the language or we are misled by some technique designed to cause us to accept a particular conclusion, even though the truth of that conclusion is not established by the premises of the argument.

• Some fallacious patterns of reasoning are so common that they are given names. (20)

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Types of fallacies

• Fallacies of failed induction (5)

• Fallacies of presumption (4)

• Fallacies of relevance (6)

• Fallacies of ambiguity (5)

• Twenty discussed.

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Fallacies of failed induction (5 types)

• An argument can be classified as a fallacy of failed induction if its premises are irrelevant to its conclusion and therefore incapable of establishing the truth of its conclusion.

• Hasty generalization• false (weak) analogy• Post hoc ergo propter hoc• Appeal to ignorance (ad ignorantiam)• appeal to authority (ad verecundiam)

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Fallacies of failed induction (1)

• Hasty generalization (conclusion)—the fallacy of trying to draw a conclusion about all things of a certain kind on the basis of having observed only a few of them, or some unrepresentative sample of them. This fallacy is committed by any enumerative induction whose conclusion rests on a sample that either is too small or lacks comprehensiveness and randomness, or both.

• A Midwesterner visits California and observes that three people she meets all practice yoga All Californians practice yoga.

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Fallacies of failed induction (2)

• False (weak) analogy—Whether an analogy is strong or not depends chiefly on whether the things alleged to be alike really are alike in relevant ways. Any analogy where the things alleged to be alike may in fact not be very much alike in the relevant ways commits the fallacy of false analogy.

• Johnnie (5) and Suzy (13)• Parent says: Johnnie, it’s 9 o’clock: its time for bed.

Johnnie replies: You let Suzie stay up late! Johnnie’s argument:– Suzy and I are alike in a number of features.– Suzy is not supposed to go to bed at 9 o’clock.– I am not supposed to go to bed at 9 o’clock.

• The case are relevantly dissimilar—analogy is weak.

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Fallacies of failed induction (3)

• Post hoc ergo propter hoc (after this, therefore because of that)—The fallacy of concluding that some earlier event is the cause of some later event when the two are not in fact causally related. – Hector was born under the sign of Capricorn.– Barbara was born under the sign of Pisces.– They are not getting along because Capricorns

and Pisces are not compatible.

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Fallacies of failed induction (4)

• Appeal to ignorance— a fallacy committed by any argument whose conclusion rests on nothing more than the absence of evidence to the contrary.– No breath of scandal has ever touched the senator. Therefore he

must be incorruptibly honest.– In 1950 senator Joe McCarthy claimed to have 81 case histories of

State Department employees whom he could prove were Communists. Concerning case 40 he said: “I do not have much information on this except the general statement of the agency that there is nothing in the files to disprove his Communist connections.”

– No one has shown that P is false; therefore P is true.– No one has shown that P is true; Therefore P is false.

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Fallacies of failed induction(5)

• Appeal to authority—uncritically accepting the word of an authority when you should be suspicious. Know the authorities cited, be sure their expertise is relevant, and beware of conflicts of interest.– the fallacy of appeal to authority is committed by

acceptance of expert advice or information when it isn’t wise to do so because the authority’s competence is transferred from one field to another.

– The Bowery Savings Bank was a great bank because Joe DiMaggio said so. (authority in baseball, not banking).

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Fallacies of failed induction(5)• Appeal to authority—uncritically accepting the

word of an authority when you should be suspicious. Know the authorities cited, be sure their expertise is relevant, and beware of conflicts of interest.– the fallacy of appeal to authority is committed by

acceptance of expert advice or information when it isn’t wise to do so because the authority’s competence is transferred from one field to another.

– Example: Over heard in a laundry: “What makes me think that abortion is murder? When my pediatrician refused to perform an abortion for me, she said she wouldn’t be a party to murder. Babies and childbirth are her business, you know.”

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Fallacies of presumption (4 types)

• An argument can be classified as a fallacy of presumption if strong assumptions or background beliefs are taken for granted that are in fact debatable and only seem to be accurate or acceptable.

• Begging the Question• Complex question• Either /Or fallacy• Accident

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Fallacies of presumption (1)

• Begging the Question—this fallacy is committed when an argument assumes what it claims to prove. (viciously circular)– Ex. Professor Adams has established that depressions

come in cycles because severe economic slowdowns follow a more or less regular temporal sequence.

depression = severe economic slowdowncycle = a more or less regular temporal sequenceCalvin Coolidge: “We must keep people working—with

jobs—because when many people are out of work, unemployment results.”

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Fallacies of presumption (2)

• Complex question—an argument that commits this fallacy fails because it involves a loaded question: a question that has an unfair question built into it—so that one cannot give any answer to it without implicitly endorsing the questioner’s preferred claim (any answer will be the wrong answer).

• Have you stopped beating your child?

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Fallacies of presumption (3)

• Either /Or fallacy—an argument that commits this fallacy fails because it presents a disjunction as being exclusive, when in fact both disjuncts could be true, or as offering the only two alternatives, when in fact there are more than two.– Either you’re a Catholic or you’re a Baptist.– You are not a Baptist.– You are a Catholic.– 1960s bumper sticker: America—Love It or Leave It.

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Fallacies of presumption (4)

• Accident—an argument that commits this fallacy fails because it does not allow for an exception to a rule when an exception is warranted. Any such argument assumes that because some principle is generally true, therefore it must be true in this case (even though this case is an exception).– Dogs are friendly animals.– Otto (my Rottweiler—a biter of 10 people) is a dog.– Otto is a friendly animal.

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Fallacies of relevance (6 types)

• An argument can be classified as a fallacy of relevance if its premises are irrelevant to its conclusion and therefore incapable of establishing the truth of its conclusion.

• Appeal to pity• Appeal to force• Ad Hominem• Red herring• Straw man• Tu Quoque

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Fallacies of relevance (1)

• Appeal to pity—whenever a person tries to cause the acceptance of a particular conclusion by arousing an irrelevant feeling of pity.

• argumentum ad misericordiam (an argument addressed to our sense of mercy).

• The job of argument analysis is to judge when a given emotional appeal can be rightly criticized as an irrelevant or fallacious deception or distraction in the argument.

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Fallacies of relevance (1)

• Appeal to pity—whenever a person tries to cause the acceptance of a particular conclusion by provoking feelings of sympathy.– Example: I’ve been working hard in this course.– Any grade below an A would adversely affect my

chances to get into the nursing program.– I should get an A in this course.

• The job of argument analysis is to judge when a given emotional appeal can be rightly criticized as an irrelevant or fallacious deception or distraction in the argument.

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Fallacies of relevance (2)

• Appeal to force: use an irrelevant threat of force to cause acceptance of a proposition.– Examples:– If you do not convict this murderer, one of you

may be her next victim.– No, if you don’t mind losing a tire, going off the

road, and maybe killing yourself, you don’t need a new tire.

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Fallacies of relevance (3)• Ad Hominem Argument—attacks an

opponent’s person (often irrelevant) rather than the opponent’s evidence and arguments.

• Example: Smith is now saying big corporations shouldn’t pay more taxes. That’s what you’d expect from a Congressman who’s lived in Washington for a couple of years and has forgotten all about the people back home.

• Find evidence of corporate support

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Fallacies of relevance (4)

• Red herring—this fallacy is an attempt to hide the weakness of a position by drawing attention away from the real issue to an irrelevant side issue.– Example: I don’t see why you are so

concerned with the problem of drug abuse; the problem of alcoholism is in many respects no less an important national problem.

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Fallacies of relevance(5)

Straw man—this fallacy is committed when we misrepresent an opponent’s position, or a competitor’s product, or go after a weaker opponent or competitor while ignoring a stronger one. Employ the principle of charity where stating an opponents argument.– Ex.: As I understand it, communism proposes that we take all the

money and divide it equally among everyone. This is silly since in no time the smarter people would have the biggest share again.

– [communism—people should jointly own the tools, factories, and farms that are used to produce goods and food.]

– In attacking a proposed equal rights amendment to the state constitution of Iowa, Pat Robertson argued that the proposal was part of a “feminist agenda…a socialist, anti-family political movement that encourages women to leave their husbands, kill their children, practice witchcraft, destroy capitalism, and become lesbians.”

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Fallacies of relevance(6)

Tu Quoque (“you’re another”)—two wrongs make a right—justifying a wrong by pointing to a similar wrong perpetrated by others.

On Larry King Live 11/29/00—Republican Senator John McCain defended the acceptance of the Florida presidential election results by saying that the votes in disputed counties had been counted and recounted and that, although there were ways in which the 2000 election in Florida could have been better conducted, we should remember that many elections in the past have been less that perfect; for instance, in Illinois in 1960 (the year that John F. Kennedy was elected amidst claims of chicanery in Illinois and Texas).

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Fallacies of ambiguity (5)

• Arguer diverts attention by using words that shift their meaning in the course of the argument.

• Equivocation

• Amphiboly

• Slippery Slope

• Composition

• Division

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Fallacies of ambiguity (1)

• Equivocation—this fallacy consists in directing an opponent toward an unwarranted conclusion by making a word or phrase, employed in two different senses in the argument, appear to have the same meaning throughout.

• “I don’t see any reason why we should listen to the superintendent of schools on the textbook issue. We need to hear from someone who has authority in the field of education. Our superintendent doesn’t even have enough authority to keep the students or teachers in line. Nobody respects his orders.”

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Fallacies of ambiguity (1a)

• Equivocation—arises when some crucial expression is used with more than one meaning over the course of an argument.– All laws require a lawmaker.– Galileo’s principle of inertia is a law.– Galileo’s principle of inertia requires a lawmaker.– Law = statue– Law = scientific generalization based on

observed regularities in nature.

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Fallacies of ambiguity (2)

• Amphiboly—awkward sentence construction—the confusing way the words are arranged—renders them unclear and so invites drawing the wrong conclusion from them.– Patient: Doctor, doctor! My arm hurts in two places!

What should I do?– Doctor: Don’t go to those places! [there are two

places on my arm that hurt]– The minister delighted everyone with his brief sermon.

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Fallacies of ambiguity (3)

• Slippery Slope—an argument that moves through a continuum of cases, from a premise involving a certain expression that appears determinately true, to a conclusion that seems the unavoidable result of sound reasoning. Yet it’s not sound, since it fails to notice that small differences in a series of cases can add up to a big difference between the initial case and that described in the argument’s conclusion.

• Example:– The adoption of a single payer health plan will lead

inevitably to the adoption of all sorts of other socialist measures.

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Fallacies of ambiguity (4)

• Composition—rests on the mistake of thinking that since each of the parts of some whole, or each of the members of some class or group, has a certain property, therefore the whole, class, or group itself also has that same property.

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Fallacies of ambiguity (4)

• Composition— the informal fallacy committed in arguing that because the parts of some complex whole, or the members of a class, have a certain attribute, it follows that the whole or class itself has that attribute. An attribute of the parts must be an attribute of the whole.

• Each player of the Chicago Cubs is an excellent player; therefore, the Chicago Cubs is an excellent team.

• Each part of a computer consumes very little energy A computer consumes very little energy.

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Fallacies of ambiguity (5)

• Division— the informal fallacy committed in arguing that because some complex whole or class has a certain attribute, it follows that each part of that whole or each member of that class has that attribute.

• Division—rests on the mistake of thinking that, because the whole has a certain property, therefore each of the parts or members that make it up has that same property.

• Example: The US Congress represents every state in the Union Each member of the US Congress represents every state in the Union.

• All the rooms in a large hotel must be large?