Formal Fallacies

Question 1

FORMAL

FALLACY

Answer 1

1. a fallacious argument that is not formally valid
2. a non-validating form of argument

LF.FF

Question 2

PROPOSITIONAL

FALLACY

Answer 2

a fallacious argument from the perspective of the logical relations that hold between propositions taken as a whole and those compound propositions which are constructed from simpler ones with truth-functional connectives such that the argument has true premises and a false conclusion

LF.FF.PF

Question 3

AFFIRMING

THE

CONSEQUENT

Answer 3

FORM:

if p, then q.
q.
therefore, p.

EXAMPLE:

if it’s raining, then the streets are wet.
the streets are wet.
therefore, it’s raining.

SIBLING FALLACY:

denying the antecedent

LF.FF.PF.AC

Question 4

CONDITIONAL

PROPOSITION

Answer 4

a proposition which asserts a condition for the truth of another proposition, as with the “if…then…” form

EXAMPLE: if it rains, then the street will be wet

Question 5

CONSEQUENT

OF A

CONDITIONAL

PROPOSITION

Answer 5

the consequent of a conditional proposition is the part that usually follows “then”

EXAMPLE: if it rains, then the street will be wet

CONSEQUENT: the street will be wet

Question 6

ANTECEDENT

OF A

CONDITIONAL

PROPOSITION

Answer 6

the antecedent of a conditional proposition is the part that usually follows “if”

EXAMPLE: if it rains, then the street will be wet

ANTECEDENT: it rains

Question 7

DENYING

THE

ANTECEDENT

Answer 7

FORM:

if p, then q.
not-p.
therefore, not-q.

EXAMPLE:

if you behead the king, then he will die.
you won’t behead the king.
therefore, the king won’t die.

SIBLING FALLACY:

affirming the consquent

LF.FF.PF.DA

Question 8

AFFIRMING

A

DISJUNCT

Answer 8

FORM:

p or q.^{[p or q.]}
p.^[q.]
therefore, not-q.^{[therefore, not-p.]}

EXAMPLE:

either it’s raining or the sun is shining.
it’s raining.
therefore, the sun is not shining.

LF.FF.PF.AD

Question 9

COMMUTATION

OF

CONDITIONALS

Answer 9

FORM:

if p, then q.
therefore, if q, then p.

EXAMPLE:

if it’s raining, then the streets are wet.
therefore, if the streets are wet, then it’s raining.

LF.FF.PF.CC

Question 10

DENYING

A

CONJUNCT

Answer 10

FORM:

not both p and q.^{[not both p and q.]}
not-p.^[not-q.]
Therefore, q.^{[therefore, p.]}

EXAMPLE:

it isn’t both sunny and overcast.
it isn’t sunny.
therefore, it’s overcast.

LF.FF.PF.DC

Question 11

“EITHER…OR…”

AS

INCLUSIVE

Answer 11

1. the logically weaker sense in which at least one disjunct is true and both may be true
2. also known as “alternation”

Question 12

“EITHER…OR…”

AS

EXCLUSIVE

Answer 12

1. the logically stronger sense in which exactly one disjunct is true and both cannot be true
2. also known as “disjunction”

Question 13

IMPROPER

TRANSPOSITION

Answer 13

FORM:

If p, then q.^{[If not-p, then not-q.]}
Therefore, if not-p, then not-q.^{[therefore, if p, then q.]}

EXAMPLE:

if we guillotine the king, then he will die.
therefore, if we don’t guillotine the king, then he won’t die.

LF.FF.PF.IT

Question 14

MASKED MAN

FALLACY

Answer 14

FORM:

a = b.
Ca (where C is an intensional context).
therefore, Cb.

…………………….

Ca (where C is an intensional context).
not-Cb.
therefore, it is not the case that a = b.

EXAMPLE:

the masked man is Mr. Hyde.
the witness believes that the masked man committed the crime.
therefore, the witness believes that Mr. Hyde committed the crime.

LF.FF.MMF

Question 15

PROBABILISTIC

FALLACY

Answer 15

a probabilistic argument is one which concludes that something has some probability based upon information about probabilities given in its premisses. such an argument is invalid when the inference from the premisses to the conclusion violates the laws of probability. probabilistic fallacies are formal ones because they involve reasoning which violates the formal rules of probability theory. thus, understanding probabilistic fallacies requires a knowledge of probability theory.

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Question 16

BASE RATE

FALLACY

Answer 16

when judging the probability of an event―for instance, diagnosing a patient’s disease―there are two types of information that may be available:

1. generic information about the frequency of events of that type. In the case of diagnosing a disease, this would be information about the prevalence of the disease.
2. specific information about the case in question. In the case of diagnosis, this would be information about the patient revealed by an examination or tests.

when contrasted with information of type 2, type 1 information is called “base rate” information. for example, if a doctor is considering whether a patient has a certain rare disease, the rarity of the disease is its base rate. in other words, the base rate is the frequency of a generic type of event, leaving aside any information about the specific case at hand.

people who have only generic information tend to use it to judge probabilities, which is the rational thing to do since that’s all that they have to go on. in contrast, when people have both types of information, they tend to make judgments of probability based entirely upon specific information, leaving out the base rate. This is the base rate fallacy.

LF.FF.PF.BRF

Question 17

CONJUNCTION

FALLACY

Answer 17

the probability of a conjunction is never greater than the probability of its conjuncts. in other words, the probability of two things being true can never be greater than the probability of one of them being true, since in order for both to be true, each must be true. however, when people are asked to compare the probabilities of a conjunction and one of its conjuncts, they sometimes judge that the conjunction is more likely than one of its conjuncts. this seems to happen when the conjunction suggests a scenario that is more easily imagined than the conjunct alone.

EXAMPLE:

Q. which of the following events is most likely to occur within the next year:

1. the united states will withdraw all troops from Iraq.
2. the united states will withdraw all troops from Iraq and bomb Iranian nuclear facilities.

A. 1 is more probable than 2.

• no matter how unlikely it is that all American troops will be withdrawn from Iraq within a year, it is less likely that this will happen and that the U.S. will bomb Iranian nuclear facilities.

LF.FF.PF.CF

Question 18

GAMBLER’S
FALLACY

Answer 18

the gambler’s fallacy is based on a failure to understand statistical independence, that is, two events are statistically independent when the occurrence of one has no statistical effect upon the occurrence of the other.

EXAMPLE:

a fair gambling device has produced a “run” ― that is, a series of similar results, such as a series of heads produced by flipping a coin. therefore, on the next trial of the device, it is less likely than chance to continue the run — believing that this is actually the case is the gambler’s fallacy.

SIBLING FALLACY:

hot hand fallacy

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Question 19

HOT HAND

FALLACY

Answer 19

the hot hand fallacy is based on a failure to understand statistical independence, that is, two events are statistically independent when the occurrence of one has no statistical effect upon the occurrence of the other.

EXAMPLE:

a gambler has had a streak of good luck. therefore, the gambler is “hot” and the good luck will continue at a probability greater than chance. ^{[or vice versa]}

hence, just as roulette wheels and dice do not have memories, so too are a gambler’s odds of winning a current bet not affected by whether the gambler has won or lost previous ones.

SIBLING FALLACY:

gambler’s fallacy

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Question 20

TRUTH-FUNCTIONAL

CONNECTIVES

Answer 20

1. disjunction — or
2. negation — not
3. conditional — only if
4. biconditional — if and only if

Question 21

MULTIPLE COMPARISONS

FALLACY

Answer 21

in a statistical study that compares groups of things, the kind of reasoning used to draw conclusions from such studies is called “inductive.” in inductive reasoning, there is always some chance that the conclusion will be false even if the evidence is true. in other words, the connection between the premisses and conclusion is never 100%―that’s only for deductive reasoning. so, the question arises: what level of probability ― called a “confidence level” ― is one willing to accept in one’s reasoning? in scientific contexts, the confidence level is usually set at 95%; thus, when a result occurs with a probability less than or equal to 5%, it is said to be “statistically significant” at the 95% confidence level. when the confidence level is set at 95%, there is a probability of one in twenty ― that is, 5% ― that a misleading result will occur simply by chance. this has an important consequence that, when overlooked, leads to the multiple comparisons fallacy.

EXAMPLE:

a shooter first draws a bullseye on a barn and then, randomly shoots twenty times at the barn. having made one bullseye, the shooter then proceeds to conceal the nineteen misses and claims to be a sharpshooter.

LF.FF.PF.MCF

Question 22

SYLLOGISTIC

FALLACY