Logical Thinking

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Logical Thinking

• EH 1301
• Spring 2005

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INDUCTIVE REASONING

• Drawing a GENERAL conclusion from incomplete
  evidence.
• Polar bear
• All we have seen are white
• We have not seen EVERY one
• Basket of apples
• First six are sweet
• Assume that the rest are the same

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INDUCTIVE REASONING

• For a claim to be credible, its sample must be
• 1) KNOWN
• 2) SUFFICIENT
• 3) REPRESENTATIVE

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INDUCTIVE REASONING

• IS THE SAMPLE KNOWN?
• Secret is preferred by 7 out of 10 women.
• Seven out of 10 husbands cheat on their wives.
• Procter Gamble is involved in Satan worship.
• Easy to dismiss such claims because there is no
  real evidence to support them.

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INDUCTIVE REASONING

• IS THE SAMPLE KNOWN?
• Beings from outer space built Stonehenge.
• President Warren Harding was murdered by his
  wife.
• Bigfoot is alive and well in
• Exposé writers like to make extravagant claims
  and then point to conclusive evidence which
  happens to be unavailable.

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INDUCTIVE REASONING

• IS THE SAMPLE SUFFICIENT?
• Most labor leaders are crooks. Look at Tony
  Boyle, Frank Brewster, Jimmy Hoffa, and Roy
  Williams.
• Running is dangerous. You saw what happened to
  Jim Fixx.
• Dont talk to me about Puerto Ricans. I lived
  next to a Puerto Rican family for two years.
• The indicated samples (FOUR labor leaders, ONE
  runner, and ONE family) are inadequate evidence
  to base a broad conclusion.

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INDUCTIVE REASONING

• IS THE SAMPLE REPRESENTATIVE?
• Sample must be typical of the whole class of
  things being studied.
• Cannot gauge attitude of a towns support of a
  proposed liquor tax by polling only those at the
  local baror those at the local fundamentalist
  church.

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INDUCTIVE REASONING

• IS THE SAMPLE REPRESENTATIVE?
• The following conclusion sounds persuasive on
  first hearing
• Women are better drivers than men they have
  fewer accidents.

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INDUCTIVE REASONING

• IS THE SAMPLE REPRESENTATIVE?
• Sample is large enough, but not broad enough to
  be meaningful.
• The conclusion (Women are better drivers than
  men.) concerns ALL DRIVERS
• Sample group includes ONLY DRIVERS WHO HAVE HAD
  ACCIDENTS

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INDUCTIVE REASONING

• IS THE SAMPLE REPRESENTATIVE?
• The sample must include all four groups involved
• 1) men
• 2) women
• 3) drivers who had accidents
• 4) drivers who had no accidents
• Broad sample shows there are fewer women in auto
  accidents because there are fewer women drivers.

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INDUCTIVE REASONING

• IS THE SAMPLE REPRESENTATIVE?
• Any poll with a selective sample (where some
  individuals choose to respond to it and others do
  not) is unrepresentative.

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DEDUCTIVE REASONING

• Opposite of induction.
• Start with a general truth and makes a specific
  application.
• Syllogism an argument which takes two existing
  truths and puts them together to create a new
  truth.

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DEDUCTIVE REASONING

• Syllogism
• MAJOR PREMISE (existing truth)
• MINOR PREMISE (existing truth)
• CONCLUSION (new truth)

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DEDUCTIVE REASONING

• Syllogism
• MAJOR PREMISE All men are mortal.
• MINOR PREMISE Socrates is a man.
• CONCLUSION Socrates is mortal.

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DEDUCTIVE REASONING

• MAJOR PREMISE
• Every band member performed in the Rose Bowl
  Parade.
• MINOR PREMISE
• Jean is a member of the band.
• CONCLUSION
• Therefore, Jean performed in the Rose Bowl Parade.

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DEDUCTIVE REASONING

• MAJOR PREMISE
• All soldiers must complete basic training.
• MINOR PREMISE
• Joe is a soldier.
• CONCLUSION
• Therefore, Joe must have completed basic
  training.

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DEDUCTIVE REASONING

• Enthymeme
• A syllogism with an unstated premise or an
  unstated conclusion
• Are frequently found in arguments and can be very
  effective in writing
• Should be examined carefully since the omitted
  statement may be inaccurate.

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DEDUCTIVE REASONING

• Enthymeme
• You havent registered, so you cant vote.
• IMPLICIT MAJOR PREMISE
• Anyone who does not register cannot vote.

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DEDUCTIVE REASONING

• Enthymeme
• Anyone can make a mistake. After all, Roger is
  only human.
• IMPLICIT CONCLUSION
• Roger has made a mistake.

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DEDUCTIVE REASONING

• Inaccurate Enthymeme
• Samuel is from Louisiana, so he must like Cajun
  food.
• Unacceptable premise
• there is no reason to assume that everyone from a
  particular region shares the same taste in food
  (even if it happens to be a local specialty.)

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DEDUCTIVE REASONING

• Reliable syllogism fulfills three conditions
• 1) Premises must be true
• 2) Terms must be unambiguous
• 3) Syllogistic form must be valid

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DEDUCTIVE REASONING

• ARE THE PREMISES TRUE?
• MAJOR PREMISE All redheads are brilliant.
• MINOR PREMISE Jane is a redhead.
• CONCLUSION Therefore, Jane is brilliant.
• Major premise is not true/unproven.

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DEDUCTIVE REASONING

• COMMON ARGUMENT FOR LOWERING THE DRINKING AGE
• MAJOR PREMISE Anyone old enough to fight in a
  war is old enough to drink.
• MINOR PREMISE Eighteen-year-olds are old enough
  to fight.
• CONCLUSION They should be old enough to drink.

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DEDUCTIVE REASONING

• IS THE LANGUAGE UNAMBIGUOUS?
• Definitions are important
• What does the word mean as it is being used?
• Terms used must be clear and consistent.
• Definitions cannot change within the syllogism.

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DEDUCTIVE REASONING

• Advertising can mislead the public
• See
• Apollo 13
• the
• ACADEMY- AWARD WINNER

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DEDUCTIVE REASONING

• MISLEADING ARGUMENT
• MAJOR PREMISE The Academy Award-winning movie
  is worth seeing.
• MINOR PREMISE Apollo 13 is an Academy
  Award-winning movie.
• CONCLUSION Apollo 13 is worth seeing.
• Ambiguity in the term Academy Award-winning

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DEDUCTIVE REASONING

• IS THE SYLLOGISM VALID?
• Reliable syllogism must have valid form.
• VALID FORM General subject or condition of major
  premise must appear in the minor premise as well.

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DEDUCTIVE REASONING

• IS THE SYLLOGISM VALID?
• MAJOR PREMISE All murderers have ears.
• MINOR PREMISE All Methodists have ears.
• CONCLUSION All murderers are Methodists.
• The argument is false because the term
  murderers does not recur in the minor
  premise.The major premise about all murderers
  can only lead to a conclusion about murderers.

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DEDUCTIVE REASONING

• IS THE SYLLOGISM VALID?
• MAJOR PREMISE The father of Miss Smiths baby
  has blood type O.
• MINOR PREMISE Billy Garrison has blood type O.
• CONCLUSION Therefore

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DEDUCTIVE REASONING

• COMBINING SYLLOGISMS TO CREATE DEDUCTIVE
  ARGUMENT
• MAJOR PREMISE When a man becomes emotionally
  disturbed, there is a recognizable change in his
  voice patterns.
• MINOR PREMISE When a man tells a lie, he
  becomes emotionally disturbed.
• CONCLUSION When a man tells a lie, there is a
  recognizable change in his voice patterns.

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DEDUCTIVE REASONING

• COMBINING SYLLOGISMS TO CREATE DEDUCTIVE
  ARGUMENT
• MAJOR PREMISE When a man tells a lie, there is
  a recognizable change in his voice patterns.
• MINOR PREMISE Senator Ted Kennedy is a man.
• CONCLUSION When Senator Ted Kennedy tells a lie,
  there is a recognizable change in his voice
  patterns.

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DEDUCTIVE REASONING

• COMBINING SYLLOGISMS TO CREATE DEDUCTIVE
  ARGUMENT
• MAJOR PREMISE When Senator Ted Kennedy tells a
  lie, there is a recognizable change in his voice
  patterns.
• MINOR PREMISE There was a recognizable change
  in the Senators voice patterns during his
  interview on the Today show.
• CONCLUSION Senator Kennedy lied during his
  interview on the Today show.

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DEDUCTIVE REASONING

• COMBINING SYLLOGISMS TO CREATE DEDUCTIVE
  ARGUMENT
• This kind of reasoning produced the National
  Enquirer headline Senator Kennedy Lied about
  Rape Case
• Notice that all three syllogisms have doubtful
  premises, and the last has an invalid form.