Inductive Reasoning and Its Various Forms

Inductive Reasoning

  • Inductive reasoning is a type of logical reasoning that involves drawing general conclusions from specific observations.
  • Types of Inductive Reasoning:
    • Enumerative Induction: Relying on specific instances to draw general conclusions.
    • Statistical Syllogism: Applying a statistical generalization to a specific case.
    • Analogical Induction: Drawing conclusions based on similarities between instances.
    • Causal Arguments: Making claims about cause and effect relationships.
    • Inference to the Best Explanation: Choosing the most plausible explanation among various hypotheses.

Statistical Syllogism

  • Definition: A statistical syllogism applies a statistical generalization to a particular member of a group.
  • Concept of Statistical Generalization:
    • A claim about the attributes of most members of a group or category.
    • It is often the conclusion drawn from enumerative induction.

Example of Statistical Syllogism

  • Premise 1: Nearly 85% of Canadians live in cities.
  • Premise 2: You’re a Canadian.
  • Conclusion: Therefore, you live in a city.
    • Another Example: Most professional basketball players are over 6 feet tall, and since Paul plays for the Raptors, we conclude he is likely over 6 feet tall.

Evaluating Statistical Syllogism

  • When evaluating a statistical syllogism, consider:
    1. Acceptability of Premises: Are the premises generally accepted truths? Where is the statistical generalization sourced from?
    2. Statistical Strength: Assess the strength of the generalization (e.g., 60% vs. 90%).
    3. Typical or Randomly Selected: Does the individual being discussed represent a typical member of the group?

Example of Application

  • If 85% of Canadians don’t know CPR, consider whether it is reasonable to assume your neighbor doesn’t know CPR, especially if she is a doctor.

Argument by Analogy (Analogical Induction)

  • Definition: An argument that draws a conclusion based on similarities between two or more things.
  • Structure of an Analogical Argument:
    • Instance A: has properties P1, P2, P3 and P4.
    • Instance B: has properties P1, P2, and P3.
    • Conclusion: Therefore, Instance B likely has property P4.
  • Uses of Analogical Arguments:
    • Common in law, science, ethics, and more.

Example of Analogical Induction

  • Case in Law:
    • A police search of a homeless man’s shelter without a warrant is compared to a previous court ruling involving the RCMP.
    • Ruling: Both searches violate citizens’ rights under section 8 of the Canadian Charter.

Evaluating an Analogical Argument

  • Consider the following:
    1. Relevant Similarities: More similarities increase the probability of the conclusion.
    2. Relevant Dissimilarities: They weaken the argument.
    3. Number of Instances Compared: More examples of relevant similarities lead to stronger arguments.
    4. Diversity Among Cases: Diverse examples strengthen an argument.

Example Analysis of Arguments by Analogy

  • Argument: "I studied poorly and performed badly on exams; thus, my philosophy exam will also suffer."

    • Instances: Studying methods across different subjects.
    • Similarities: Study habits leading to poor performance.
    • Conclusion: Likely strong due to repetition of failure, but may be weakened by unique circumstances in each subject.

  • Argument Discussing Suicide:

    • Explores parallels between self-defense and terminal illness impacting moral justification for suicide.
    • Analysis Would Include:
    • Examining relevant moral principles at play.
    • Evaluating similarities and differences with traditional views on self-defense.