In-depth Notes on Inductive Reasoning and Argument Types

Types of Argument

  • Induction

    • Aims to provide probable support for its conclusion.
    • Could be assessed as strong, weak, or somewhere in between.

  • Deduction

    • Seeks to offer logically conclusive support for its conclusion.
    • Conclusions must either necessarily follow from or not follow from the premises.

Deductive vs Inductive Arguments

  • Deductive Argument:

    • Provides logically conclusive support for its conclusion.

  • Inductive Argument:

    • Provides probable support for its conclusion.
    • The strength can vary (strong/weak), meaning the conclusion could be more likely to be true than not.
    • Forms the basis of much reasoning in Logic, Math, and Computer Science, delivering knowledge of empirical world workings in science and daily life.

Inductive Reasoning Examples

  • Statements provide examples of inductive reasoning:
    • "I don't have allergy to peanuts."
    • "Canadian Geese are mean!"
    • "Elephants can't jump."
    • "The sun will rise tomorrow!"
    • Extends beyond existing evidence.

Understanding Inductive Arguments

  • Strong Argument:

    • If all premises are true, conclusion is likely true but not guaranteed.
    • Example:
    • “My dad had a severe car accident; he died the next day. Most probably he died because of the accident.”
    • “I saw a black cat, and my dad died the next day. Most probably he died because of the black cat.”

  • Weak Argument:

    • Premises do not support conclusion strongly.
    • Example:
    • “Nearly 85% of Canadians live in cities. You’re a Canadian; therefore, you most probably live in a city.”
    • This might be true statistically but not guaranteed for an individual instance.

Evaluating Arguments

  • Argument evaluation involves determining logical strength:
    • Humans existed long after dinosaurs, concluding that human fossils should be found with dinosaur fossils is flawed.
    • Evidence suggests that human fossils and dinosaur fossils should not co-exist given timeline.

What Constitutes a Cogent Argument?

  • Cogent Argument:
    • A strong argument whose premises are true.
    • Absoluteness of premises leads to a logically coherent conclusion.

Forms of Inductive Reasoning

  • Various forms of inductive reasoning include:
    • Enumerative Induction
    • Statistical Syllogism
    • Analogical Induction
    • Causal Arguments
    • Inference to the Best Explanation

Enumerative Induction Explained

  • Conclusion drawn from several observed instances.

  • Moving from specifics to general conclusions about a group.

  • Formula:

    • From observed instances, if X% of observed members of group A have property P, conclude that X% of all members of group A probably have property P.

Sample Size Considerations

  • Larger sample sizes generally yield more reliable reflections of target group properties.

  • Hasty Generalization:

    • A conclusion drawn from too small a sample size, e.g., concluding all Americans are rude from experiencing a few.

  • Representativeness:

    • A sample must reflect the target group's relevant characteristics to draw valid conclusions.

Common Sampling Errors

  • Biased Sample:
    • Selection bias leads to sample misrepresentation.
    • A good sample should reflect populations across several aspects like ethnicity, political affiliation, etc.

Effective Opinion Polls

  • Characteristics of a good opinion poll:
    • Must use a strong, representative, and large enough sample.
    • Accurate premises lead to valid conclusions.

How Surveys Can Go South

  • Questionnaires can skew results through biased or poorly framed questions.
  • Small sample sizes, non-representative samples, and interviewer effects contribute to inaccuracies.

Examples of Survey Flaws

  • Bad Polling Methods:
    • Poorly designed questions influence misleading outcomes.
  • Example Cases of Polling Errors:
    • A survey selects patrons from an art exhibit may not accurately reflect general Canadian opinions about arts funding; this flawed selection can indicate a bias.