Section 1.2
Evidence and Inference
Proving Your Point
3/15/2016
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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.
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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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