INDUCTIVE ARGUMENTS

1
INDUCTIVE ARGUMENTS

• Chapter 10

2
Inductive Arguments

• Recall that inductive arguments are meant to show
  that, given the premises, the conclusion is
  probable.
• Remember also, that inductive arguments aim for
  strength, not validity. The latter implies that
  the truth of the premises guarantees the truth of
  the conclusion
• There are two primary types of inductive
  arguments
• Analogical Arguments
• Inductive Generalization

3
Analogical Arguments

• In analogical arguments, the arguer generally
  draws a conclusion about a single thing by
  comparing to another, similar thing.
• Example My friends 2006 Dodge Stratus
  overheats. Im considering buying one, but Im
  thinking that perhaps I shouldnt since it might
  also have an overheating problem.

4
Analogical Arguments - Vocabulary

• The items being compared are called the terms of
  analogy. (Ex. the two cars)
• The term of analogy about which we draw the
  conclusion is the target. (Ex. the car that the
  arguer considers purchasing)
• The property (or feature) in question is the
  property attributed to the target in the
  conclusion of the argument. (Ex. overheating)

5
Analogical Arguments Contd

• The general principle on which analogical
  arguments are based is
• The more similar the terms of the analogy, the
  higher the probability that the conclusion is
  true.
• So, in the previous example, the arguer could
  increase the strength of the argument, if the two
  Dodges were from the same factory, if they would
  both be driven by people with similar driving
  habits, etc

6
Inductive Generalizations

• Inductive Generalizations
• always have a class of things as a target
• argues from a sample of the targeted class to the
  targeted class as a whole
• Ex. All six peaches that I bought from my local
  grocer were mushy, so all the peaches in the
  grocers batch are probably mushy.

7
Inductive Generalizations- Vocabulary

• Note that in the previous example, the peaches
  that the arguer bought from the store constitute
  the sample.
• The peaches in the grocers batch constitute the
  targeted class.
• The property in question is mushiness.

8
Inductive Generalizations Contd

• The general principle for inductive
  generalizations is
• The more representative the sample of an
  inductive generalization is of the target, the
  stronger the argument.
• The sample is representative in so far as it is
  similar to the target class in all relevant
  respects.

9
Biased Samples

• In the previous example, if all of the arguers
  peaches were picked from the bottom of the fruit
  bin, then the purchased peaches would constitute
  a biased sample.
• A biased sample is significantly different from
  the target class in one or more relevant
  respects.
• Arguing from a biased sample weakens the
  argument.

10
Representative Samples

• In order to obtain representative samples, we
  should use randomly selected samples, of
  sufficient size.
• A random selection process gives every member of
  the target class an equal chance of becoming a
  member of the sample.
• For formal inductive arguments, a standard sample
  size between 1,000 and 1,500 is generally
  considered a reasonable sample size.

11
Inductive Generalizations contd

• A confidence level measures the arguments
  strength. A high confidence level indicates a
  highly probable conclusion.
• Our confidence increases
• as the size of the sample increases,
• as the error margin increases,
• An error margin is a range of percentage points
  within which a conclusion is claimed to fall.
  Wide error margins make for weaker arguments.
• Note With the same confidence level, a
  generalization from a larger sample will have a
  smaller or narrower error margin making the
  argument stronger.

12
Fallacious Inductive Reasoning

• Two examples of fallacious inductive reasoning
  are
• Hasty Generalization
• Generalizing from a sample that is too small.
• Ex. Both Harvard students Ive met have been very
  rich. Harvard must only take rich kids.
• Biased Generalizing
• Generalizing from a non-representative sample.
• Ex. I surveyed 2,000 students from New York
  Citys St. Thomas Catholic School. 95 said they
  never abused drugs. So we can safely conclude
  that New York doesnt really have a teenage drug
  abuse problem.

13
Class Exercises

• The last three cameras I bought from Roy were
  total junk. Its probably the case that all Roys
  cameras are junk.
• 1) Name the target class and the sample.
• 2) Name the property in question.
• 3) If all the cameras that the arguer purchased
  from Roy happened to be Sony brand, would that
  strengthen or weaken his argument?

14
Class Exercises Contd

• An organization randomly selected and polled
  3,000 Los Angeles residents on their abortion
  views, and from those results, the organization
  concluded that 75 of Californians 3 are
  pro-choice.
• 4) Is the sample size sufficient?
• 5) What is the margin of error?
• 6)What is the target class?
• 7) Whats wrong with the conclusion?

15
Review of Tuesdays Lesson

• Negation Claim Truth-Table
• P P
• T F
• F T

16
Review of Tuesdays Lesson contd

• Conjunction Truth-Table
• P Q PQ
• T T T
• T F F
• F T F
• F F F

17
Review of Tuesdays Lesson contd

• Disjunction Truth-Table
• P Q PvQ
• T T T
• T F T
• F T T
• F F F

18
Review of Tuesdays Lesson contd

• Conditional Truth-Table
• P Q P?Q
• T T T
• T F F
• F T T
• F F T

19
Review Contd

• Remember, to determine an arguments validity,
  construct a truth-table with the claim variables,
  the premises, and the conclusion. If you can find
  any row in which all the premises are true but
  the conclusion is false, then the argument is
  invalid!