Evaluating Inductive Arguments and Probabilistic and Statistical Fallacies

Inductive Arguments and Statistical Generalizations

  • Inductive arguments have conclusions that follow with high probability, but not certainty.

  • They are "defeasible," meaning additional premises can weaken them.

  • Statistical generalizations are based on empirical observations:

    • Universal generalizations apply to 100% of a class.

    • Partial generalizations apply to a percentage of a class.

  • Deductive arguments use universal generalizations; inductive arguments use partial generalizations.

  • Evaluating statistical generalizations involves assessing the truth of premises.

  • Conditions for a good statistical generalization:

    • Adequate sample size

    • Non-biased sample

  • A sample is a portion of a population. A population is the totality of members of some specified set of objects or events

  • A representative sample mirrors the population's characteristics.

Hasty Generalization

  • Hasty generalization is an informal fallacy that infers a statistical generalization from too few instances.

Sampling Bias

  • Sampling bias occurs when a sample is not representative of the population.

  • Bias can arise from:

    • How the sample is collected.

    • The questions asked.

Random Sampling

  • Random sampling aims to avoid bias by giving everyone in the population an equal chance of being selected.

  • Techniques must adapt to changing social and technological landscapes.

Inference to the Best Explanation

  • Inference to the best explanation is an inductive argument that concludes a hypothesis is true because it best explains observed facts.

  • Form:

    1. Observed facts

    2. Hypothesis explaining the facts

    3. Comparison of competing explanations

    4. Conclusion that the hypothesis is true

Explanatory Virtues

  • Criteria for a good explanation:

    1. Explanatoriness: Explains all observed facts.

    2. Depth: Doesn't raise more questions than it answers.

    3. Power: Applies to similar contexts.

    4. Falsifiability: Can be proven incorrect.

    5. Modesty: Claims no more than necessary.

    6. Simplicity: Posits fewer entities or processes (Ockham’s razor).

    7. Conservativeness: Conflicts with fewer well-established beliefs.

Analogical Arguments

  • Arguments from analogy infer that if things x and y share similar properties, and y has characteristic A, then x probably has characteristic A.

  • Key conditions for strong arguments from analogy:

    1. Relevant similarities between compared things.

    2. Absence of relevant disanalogies.

Causal Reasoning

  • Causal reasoning identifies causes that produce specific effects.