Section 1.2Evidence and Inference

Proving Your Point

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Logic vs. Psychology

• Logic attempts to determine how people should reason if they want to avoid error and falsehood.

• Psychology attempts to determine how people do reason.

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Arguments

• Argument—a group of statements that attempt to establish a claim.

• Conclusion—the claim that an argument is trying to establish.

• Premise—a reason for accepting the conclusion of an argument.

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Conclusion Indicators

“thus,” “therefore,” “hence,” “so,” “then,” “consequently,” “shows that,” “means that,” “implies that,” “it follows that,” etc.

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Premise Indicators

“because,” “since,” “for,” “if,” “as,” “follows from,” “given that,” “provided that,” “assuming that,” etc.

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Deductive vs. Inductive Arguments

• In a valid deductive argument, the truth of the premises guarantees the truth of the conclusion; if the premises are true, the conclusion has to be true.

• In a strong inductive argument, the truth of the premises only makes the conclusion probable; if the premises are true, the conclusion may still be false.

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Deductive Arguments

• A deductive argument is valid when the conclusion logically follows from the premises; that is, when it’s impossible for the premises to be true and the conclusion false.

• A deductive argument is sound when it’s valid and all of the premises are true.

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Affirming the Antecedent

• (1) If p, then q. (2) p. (3) Therefore q.• (1) If the soul is immortal, then thinking

doesn’t depend on brain activity.(2) The soul is immortal.(3) Therefore, thinking doesn’t depend on brain activity.

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Denying the Consequent

• (1) If p, then q. (2) Not q. (3) Therefore, not p.

• (1) If the soul is immortal, then thinking doesn’t depend on brain activity.(2) Thinking does depend on brain activity.(3) Therefore, the soul is not immortal.

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Hypothetical Syllogism

• (1) If p, then q. (2) If q, then r. (3) Therefore, if p, then r.

• (1) If the Fed raises interest rates, it will be more difficult to borrow money.(2) If it’s more difficult to borrow money, home sales will fall.(3) Therefore, if the FED raises interest rates, home sales will fall.

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Disjunctive Syllogism

• (1) Either p or q. (2) Not p. (3) Therefore q.• (1) Either Sally walked or she rode the bus.

(2) She didn’t walk.(3) Therefore, she rode the bus.

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Affirming the Consequent (Invalid)

• (1) If p, then q. (2) q. (3) Therefore, p.• (1) If Chicago is the capital of Illinois, then

Chicago is in Illinois.(2) Chicago is in Illinois.(3) Therefore, Chicago is the capital of Illinois.

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Denying the Antecedent (Invalid)

• (1) If p, then q. (2) Not p. (3) Therefore, not q.• (1) If Joe is a bachelor, then Joe is a male.

(2) Joe is not a bachelor.(3) Therefore, Joe is not a male.

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Affirming a Disjunct (Invalid)

• (1) Either p or q. (2) p. (3) Therefore, not q.• (1) Either the car battery is dead or the car is

out of gas. (2) The car battery is dead. (3) Therefore, the car is not out of gas.

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Inductive Arguments

• A strong inductive argument is one that would establish its conclusion with a high degree of probability if its premises were true.

• A cogent inductive argument is a strong one which contains only true premises.

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Enumerative Induction

• (1) X per cent of the observed members of A are B. (2) Therefore, X percent of the entire group of A are B.

• (1) 54 per cent of the students in this college are female.(2) Therefore, probably, 54 per cent of all college students are female.

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Analogical Induction

• (1) Object A has properties F, G, H, etc. as well as the property Z. (2) Object B has properties F, G, H, etc. (3) Therefore, object B probably has property Z.

• (1) The Earth has air, water, and life.(2) Mars has air and water.(3) Therefore, Mars probably has life.

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Hypothetical Induction(Inference to the Best Explanation)

• (1) Phenomena p. (2) If hypothesis H were true, it would provide the best explanation of p. (3) Therefore, it’s probable that H is true.

• (1) My car won’t start.(2) The best explanation of that fact is that the battery is dead.(3) Therefore, it’s probable that the battery is dead.

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Criteria of adequacy used to decide between competing hypotheses:

• Consistency—internal and external.• Simplicity—number of assumptions made

by a hypothesis.• Scope—the amount of diverse phenomena

explained by a hypothesis.• Conservatism—fit with confirmed

hypotheses.• Fruitfulness—successful novel predictions

or problems solved.19

Fallacious Arguments

Fallacious arguments fail to provide good reasons for accepting a claim because either:

• The premises are dubious or• They do not support the conclusion.

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An argument is fallacious if it contains:

• Unacceptable premises (premises as dubious as they claim they’re trying to support)

• Irrelevant premises (premises that have no bearing on the truth of the conclusion) or

• Insufficient premises (premises that do not establish the conclusion beyond a reasonable doubt).

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Informal Fallacies

• Unacceptable Premises: Begging the Question, False Dilemma

• Irrelevant Premises: Equivocation, Composition, Division, Appeal to the Person, Genetic Fallacy, Appeal to Unqualified Authority, Appeal to the Masses, Appeal to Tradition, Appeal to Ignorance, Appeal to Fear

• Insufficient Premises: Hasty Generalization, Faulty Analogy, False Cause

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Begging the Question

• An argument begs the question – or argues in a circle – when its conclusion is used as one of its premises.

• Example: “Jane has telepathy,” says Susan. “How do you know?” asks Jill. “Because she can read my mind,” replies Susan.

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False Dilemma

• An argument proposes a false dilemma when it presumes that only two alternatives exist when in actuality there are more than two.

• Example: “Either science can explain how she was cured or it was a miracle. Science can’t explain how she was cured. So it must be a miracle.”

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Equivocation

• Equivocation occurs when a word is used in two different senses in an argument.

• Example: “(i) Only man is rational. (ii) No woman is a man. (iii) Therefore no woman is rational.”

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Composition

• An argument may claim that what is true of the parts is also true of the whole; this is the fallacy of composition.

• Example: “Subatomic particles are lifeless. Therefore anything made out of them is lifeless.”

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Division

• The fallacy of division is the converse of the fallacy of composition. It occurs when one assumes that what is true of a whole is also true of its parts.

• Example: “We are alive and we are made out of subatomic particles. So they must be alive too.”

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Appeal to the Person

• When someone tries to rebut an argument by criticizing or denigrating its presenter rather than by dealing with the issues it raises, that person is guilty of the fallacy of appeal to the person. This fallacy is referred to as “ad hominem,” or “to the man.”

• Example: “You can’t believe Dr. Jones’s claim that there is no evidence for life after death. After all, he’s an atheist.”

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Genetic Fallacy

• To argue that a claim is true or false on the basis of its origin is to commit the genetic fallacy.

• Example: Jones’s idea is the result of a mystical experience, so it must be false (or true).” Or: “Jane got that message from a Ouiji board, so it must be false (or true).”

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Appeal to Unqualified Authority

• An appeal to authority is perfectly valid provided that the person cited really is an expert in the field in question. If not, it is fallacious.

• Example: Psychiatry must be bogus because Tom Cruise says it is.

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Appeal to the Masses

• A remarkably common but fallacious form of reasoning is, “It must be true (or good) because everybody believes it (or does it).”

• Example: Said in 1800: “Slavery must be a good thing because every culture has had slaves.”

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Appeal to Tradition

• We appeal to tradition when we argue that something must be true (or good) because it is part of an established tradition.

• Example: “Women should work at home because that’s what they’ve always done.”

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Appeal to Ignorance

• The appeal to ignorance comes in two varieties: using an opponent’s inability to disprove a conclusion as proof of the conclusion’s correctness, and using an opponent’s inability to prove a conclusion as proof of its incorrectness.

• Example: “Bigfoot must exist because no one has been able to prove that he doesn’t.”

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Appeal to Fear

• To use the threat of harm to advance one’s position is to commit the fallacy of the appeal to fear.

• Example: “If you do not convict this criminal, one of you may be her next victim.”

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Hasty Generalization

• You are guilty of hasty generalization or jumping to conclusions when you draw a general conclusion about all things of a certain type on the basis of evidence concerning only a few things of that type.

• Example: “I know one of those psychics. They’re all a bunch of phonies.”

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Faulty Analogy• An argument from analogy claims that things that

resemble one another in certain respects resemble one another in further respects. The success of such arguments depends on the nature and extent of the similarities between the two objects.

• Example: “Astronauts wear helmets and fly in spaceships. The figure in this Mayan carving seems to be wearing a helmet and flying in a spaceship. Therefore it is a carving of an ancient astronaut.”

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False Cause

• The fallacy of false cause consists of supposing that two events are causally connected when they are not. Latin scholars dubbed this the fallacy of post hoc, ergo propter hoc, which means “After this, therefore because of this.”

• Example: “My cold got better after I wore this crystal around my neck. So it must have cured it.”

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