Critical Thinking


1
Critical Thinking

• Chapter 9
• Induction

2
Argument from Analogy

• Is a kind of inductive argument that concludes
  that something is true of one item because its
  similarity to something else or another item.
• Was discussed briefly in Chapter 1
• Example Jax and Brandon both love action Movies.
  Jax likes the new James Bond movie so we can
  conclude that Brandon probably would like the
  movie as well.

3
Principles used in evaluating Arguments from
analogy

• Relevance of similarities
• Number of similarities
• Nature and Degree of Disanalogy
• Number of primary analogues
• Diversity among primary analogues
• Specificity of the conclusion

4
Probability

• Probability is a topic that is central to the
  question of induction but like causality it has
  different meanings.
• Three distinct theories of probability
• 1) Classical Theory
• 2) Relative Frequency Theory
• 3) Subjectivist Theory

5
Probability

• Classical Theory Determines better odds for a
  games.
• Relative Frequency Theory Depends on actual
  observations of the frequency with which certain
  events happen.
• Subjectivist Theory interprets the meaning of
  probability in terms of the beliefs of individual
  people.

6
Probability Calculus

• Probability Calculus A set of rules for
  computing the probability of compound events from
  the probabilities of simple events.
• 6 Rules Restricted Conjunction General
  Conjunction Restricted Disjunction General
  Disjunction Negation and Bayes.

7
Six Rules of Probability Calculus

• Restricted Conjunction Rule is used to compute
  the probability of two events occurring together
  when the events are independent of each other.

• General Conjunction Rule is used to compare the
  probability of two events occurring together
  whether or not the events are independent.

8
Six Rules of Probability Calculus

• Restricted Disjunction Rule is used to compute
  the probability of either of two events occurring
  when the events are mutually exclusive that is
  when they cannot both occur.

• General Disjunction Rule is used to compare the
  probability of either of the two events whether
  or not they are mutually exclusive.

9
Six Rules of Probability Calculus

• Negation Rule is useful for computing the
  probability of an event when the probability of
  the event not happening is either known or easily
  computed.

• Bayess Theorem is a useful rule for evaluating
  the conditional probability of two or more
  mutually exclusive and jointly exhaustive events.

10
Statistical Reasoning

• Samples that are not representative are said to
  be biased.
• A sample is random if and only if every number of
  the population has an equal chance of being
  selected.
• The sampling error is the difference between the
  relative frequency with which some
  characteristics occurs in the population.

11
Average

• Average has three different terms mean median
  and mode.
• Mean value of a set of data is arithmetical
  average. It is computed by dividing the sum of
  the individual values by the number of data in
  the set.
• Median a set of data is the middle point when
  the data are arranged in ascending order.
• Mode is the value that occurs with the greatest
  frequency.

12
Dispersion

• Dispersion is an indicator of how spread out
  the data are in regard to numerical value.
• Three important measures of dispersion are range
  variance and standard deviation.

13
Dispersion

• Range the difference between the largest and
  the smallest values.
• Standard Deviation a measure of how far the
  data may vary or deviate from the mean value
• Variance - a measure of how far the data may vary
  or deviate from the mean value