CRW unit 5

Unit Five: Inductive Arguments

Overview of Inductive and Deductive Arguments

  • Inductive Reasoning:

    • Inductive reasoning allows for the conclusion to be false even if all premises are true.
    • Characterization: Inductive arguments are classified as either strong or weak based on how probable the conclusion is.
    • In contrast, deductive reasoning entails that if all premises are true, the conclusion cannot be false.

  • Deductive Reasoning:

    • The conclusion is necessary (valid) based on the premises.
    • Example of Deduction: "If A is true then B, C, and D are true"; therefore, "A is true, hence B, C, D must also be true".
    • Definition of Deductive Validity: The truth of the conclusion is implicit in the premises.
Key Differences
  • Deduction:
    • Validity relates to necessity.
    • Certainty is absolute; a conclusion follows necessarily from premises.
  • Induction:
    • Indicates a degree of probability.
    • Conclusion is supported but not guaranteed by premises (degrees of certainty).

Illustrative Examples of Inductive vs. Deductive Arguments

  • Example of Induction:

    • Observing that large craters exist (in the Gulf of Mexico) and positing a possibility that they led to the extinction of non-avian dinosaurs.
    • Disclaimers: Other events (like Deccan Traps) correlate with extinction, indicating that conclusions from induction are not absolute.

  • Incorrect Inductive Argument:

    • "All swans we have seen are white, therefore we know all swans are white."
    • Correct conclusion should be: "We expect that all swans are white."

Exclusion of Mathematical Induction

  • Clarification of Induction Types:
    • Mathematical Induction:
    • Is deductive reasoning used to prove properties of recursively defined sets.
    • Complete Induction:
    • Associated with deductive reasoning rather than the inductive reasoning described above.
  • Enumerative Induction:
    • Involves a finite number of cases, e.g., proof by exhaustion.

Distinguishing Strengths of Inductive Arguments

  • Strength vs. Weakness:
    • Inductive arguments classified as strong or weak, lacking a precise cut-off.
    • Strong Argument:
    • If premises true, conclusion likely true.
    • Example:
      • "John was found with a gun, running from the scene of a murder, witnesses heard gunshots, and ballistics match; thus John is likely the murderer."
    • Weak Argument:
    • Premises do not adequately support the conclusion.
    • Example:
      • "I saw your boyfriend talking to another girl; thus, he’s cheating."

Importance of Premise Truth about Argument Strength

  • Premises can be false, yet the argument can still be strong.
  • Inductive Reasoning in Practice:
    • Courts frequently apply inductive methods, offering premises as evidence rather than absolute conclusions.

Various Uses of Inductive Reasoning

  • Predicting the Future:

    • Based on past observations to make inferences about future events.
    • Example: Assuming waking up after sleeping based on experience.

  • Explaining Common Occurrences:

    • Inferences based on frequent observations to explain events.
    • Example: Assuming Bill is stuck in traffic when he’s late for an exam.

  • Generalizing from Cases:

    • Inductive reasoning allows general claims despite lack of universal observation.
    • Example: Drug studies projecting effects from a sample population.

Inductive Generalization Analysis

  • Careful consideration needed for bias and representativity in sampling.
  • Examples illustrating good vs. poor inductive arguments based on sample collectivity and relevance:
    • A poor argument would generalize from a non-representative group.
    • A strong argument requires ensuring representative samples from larger populations.

Inductive Argument Forms

  1. Statistical Syllogisms:
    • Moving from general statistics to specific instances, e.g., likelihood assessments.
    • Example: If 70% of politicians are corrupt, a specific politician is likely corrupt.
  2. Induction by Shared Properties:
    • Inferring properties based on shared characteristics among groups.
    • Example:
      • (P1) Patients with specific symptoms
      • (P2) Patient displays symptoms, leading to: (C) Probability of shared condition.
  3. Induction by Shared Relations:
    • Inferring links based on relation patterns.
    • Example: A friend's friends likely share connections, as inferred through mutual acquaintances.

Causality in Inductive Reasoning

  • Distinction between correlation and causation.
  • Emphasis on understanding the nature of causal relationships in science.
    • Example: Carbon dioxide emissions and implications for global warming.

Ockham's Razor Principle

  • Preference for simpler explanations over complex ones when analyzing evidence and claims.

Use of Analogies in Arguments

  • Structure of analogical reasoning:

    • A relates P, Q, R… and inferring properties Z based on similarities.

  • Importance of considering disanalogies that could weaken arguments.

  • Examples of successful and unsuccessful analogical arguments:

    • Valid: Ice skating vs. in-line skating balance requirements.
    • Invalid: Generalizing pollution properties from cars to Teslas.
Enhancing Strength of Analogical Arguments
  1. Increase number and closeness of analogies.
  2. Identify and reduce disanalogies.
  3. Use diverse examples from different cases.