Quantitative Literacy

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Quantitative Literacy
Prologue
The ability to interpret and reason with
information that involves mathematical ideas or
numbers.
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Prologue
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Unit 1A

• Recognizing Fallacies

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ARGUMENT
An argument is a set of facts or assumptions,
called premises, that support a conclusion.
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Argument Examples

• In the below arguments, identify the premise(s)
  and conclusion.
• Everyone in San Francisco is a liberal.
• Michael Savage lives in San Francisco.
• Michael Savage is a liberal.
• All US Presidents have been men.
• JFK was a man.
• JFK was a US President.

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• People generally quarrel because they cannot
  argue.
• G.K. Chesterton (1874-1936)

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LOGIC
Logic is a branch of mathematics that studies the
methods and principles of reasoning.
Studying Logic enables one to learn how to create
valid arguments, reason clearly, and develop
excellent critical thinking skills. These skills
will allow you to interpret and analyze events in
every area of life.
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FALLACIES
Some arguments are invalid. There is an error in
reasoning. Such an argument is called a Fallacy.
A fallacy is a deceptive, misleading, or unsound
argumentan argument in which the conclusion is
not well supported by the premises.
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FALLACY STRUCTURES

• Appeal to Popularity
• False Cause
• Appeal to Ignorance
• Hasty Generalization
• Limited Choice

• Appeal to Emotion
• Personal Attack
• Circular Reasoning
• Diversion
• Straw Man

Remember, all fallacies contain faulty reasoning.
That is, the conclusion does not follow
logically from the premises.
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APPEAL TO POPULARITY
The fallacy of appeal to popularity (or appeal to
majority) uses the fact that large numbers of
people believe or act some way as evidence that
the belief is correct. Many people believe p
is true therefore p is true.
EXAMPLE Microsoft makes the best computer
operating system. After all, more people use
Windows than any other operating system.
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FALSE CAUSE
The fallacy of false cause uses the fact that one
event came before another as evidence that the
first event caused the second event. A came
before B therefore . . . A caused B.
EXAMPLE Timmy took some cold medication before
his math test. He made a 100 on the test. The
cold medication made Timmy ace his math test.
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APPEAL TO IGNORANCE
The fallacy of appeal to ignorance uses ignorance
(lack of knowledge) about the truth of a
proposition to conclude the opposite. There
is no proof that p is true therefore . . . p is
false.
EXAMPLE Scientist have not found any evidence
of Bigfoot. Therefore, anyone who claims to have
seen Bigfoot must be hallucinating.
An absence of evidence is not evidence of
absence.
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HASTY GENERALIZATION
The fallacy of hasty generalization draws a
conclusion from an inadequate number of cases or
cases that have not been sufficiently analyzed.
A and B are linked one or a few times
therefore . . . A causes B (or vice versa).
EXAMPLE Three cases of brain cancer have
occurred in people who use cell phones.
Therefore, cell phones must cause brain cancer.
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LIMITED CHOICE
The fallacy of limited choice artificially
precludes choices that ought to be considered.
p is false therefore . . . only q can be
true.
EXAMPLE You dont support the President, so
you are not a patriotic American. EXAMPLE
Have you stopped smoking? In court, this is
called Leading the Witness. EXAMPLE Youre
wrong, so I must be right.
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APPEAL TO EMOTION
The fallacy of appeal to emotion uses an
emotional reaction (instead of logic) as a tool
of persuasion. p is associated with an
emotional response therefore . . . p is true.
EXAMPLE In a commercial for Michelin tires, a
picture of a baby is shown with the words
because so much is riding on your
tires. EXAMPLE If my opponent is elected, your
tax burden will rise.
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PERSONAL ATTACK
The fallacy of personal attack (ad hominem) uses
a dislike of a person or group making an argument
to conclude the argument is not valid. I have
a problem with the person or group claiming p
therefore . . . p is not true.
EXAMPLE There is no way Senator Smiths bill
can help the cause of gun control because he is
one of the biggest recipients of campaign
contributions from the National Rifle Association.
The provisions of the Senators bill were not
challenged.
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CIRCULAR REASONING
The fallacy of circular reasoning just restates
the premise in different words. p is true p
is restated in different words.
EXAMPLE Schools must implement a zero tolerance
policy toward drug use, because any tolerance of
drugs is unacceptable.
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DIVERSION
The fallacy of diversion (or red herring) diverts
the attention from one issue, p, to another
(related) issue, q. p is related to q and I
have an argument concerning q therefore . . . p
is true.
EXAMPLE We should not drill for oil in the
Alaskan National Wildlife Refuge (ANWR), because
we have too many gas-guzzling automobiles as it
is.
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STRAW MAN
The fallacy of straw man makes an argument based
on a distortion of someones words or beliefs.
I have an argument concerning a distorted
version of p therefore . . . I hope you are
fooled into concluding that I have an argument
concerning the real version of p.
EXAMPLE The mayor of a large city has proposed
decriminalizing drug possession in order to
reduce overcrowding in jails. His challenger in
the upcoming election says, The mayor doesnt
think theres anything wrong with drug use, but I
do.