Inductive Logic·Intermediate·5 lessons·62 practice activities·~280 min
Inductive Logic: Evidence, Generalization, and Causal Support
How to reason well under uncertainty
What you'll learn
By the end of this unit, you can…
- Assess inductive strength.
- Formalize generalization.
- Evaluate analogical argument.
- Critique causal claim.
Lessons
Lesson sequence
- 1Open →
What Makes an Inductive Argument Strong?
Introduces inductive strength, uncertainty, and defeasibility, and establishes the three-question routine students will use throughout the unit.
- 2Student Pro
Generalization and Sample Quality
Teaches students how to formalize sample-based arguments, evaluate sample quality, and recognize the common species of sampling failure.
- 3Student Pro
Analogical Reasoning
Teaches how to evaluate arguments from analogy by separating relevant similarities from superficial ones and identifying disanalogies that can block the inference.
- 4Student Pro
Causal Inference and Mill's Methods
Teaches the difference between correlation and causation, introduces Mill's methods for causal inference, and develops a rival-factor analysis routine students can apply to real causal claims.
- 5Student Pro
Capstone: Evaluating Inductive Arguments in the Wild
An integrative lesson that asks students to run the full inductive cycle on arguments drawn from research, journalism, and everyday claims: identify the inductive structure, assess sample quality and causal rivals, and calibrate the strength of the conclusion.
How to study
Three moves that work for this unit
Read the explanation
Each lesson opens with a guided walkthrough — read it before the activity.
Study the worked example
Look at why each step follows, not just what the answer is.
Practice with the target in mind
Know which rule applies and what would make the response weak before you start.
Reference materials
Optional context for the unit. Each lesson surfaces the concepts and rules it uses — these are here when you want the bigger picture.
Concept map (7 terms)
Inductive Strength
The degree to which premises make a conclusion probable or well-supported without guaranteeing it.
Defeasibility
The feature of an argument whose support can be weakened or defeated by new evidence.
Representativeness
The extent to which a sample reflects the broader population it is used to support claims about.
Sample Size
The number of observed cases in the evidence base from which a generalization is drawn.
Analogical Reasoning
An inference that supports a conclusion about one case because it is relevantly similar to another case.
Causal Inference
Reasoning that moves from evidence to a claim about what caused a given outcome.
Confounding Variable
A third factor that influences both the supposed cause and the supposed effect, producing a correlation that does not reflect direct causation.
Rules and standards (4)
- Sample Quality. A broader and more representative sample usually supports a stronger generalization, and projection should not exceed what the sample warrants. Common failures: The sample is too small for the claim's scope.; The sample is biased by self-selection or convenience sampling.; The target population is much broader than the evidence allows..
- Relevant Similarity. An analogical argument is stronger when the similarities cited are relevant to the conclusion and when important disanalogies are accounted for. Common failures: The similarities are superficial and not connected to the feature being projected.; Important differences between the source and target cases are ignored..
- Correlation Is Not Yet Causation. A causal conclusion requires more than noticing that two things occur together; rival explanations must be considered and ruled out. Common failures: A causal claim is drawn directly from a correlation.; Confounders, reverse causation, and coincidence are ignored.; A single case is treated as proof of a general causal pattern..
- Proportionate Conclusion. The language of the conclusion should match the strength of the support — probably, likely, some evidence for — rather than bare assertion. Common failures: Expressing defeasible conclusions with certainty language.; Making a universal claim on the basis of a limited sample..
Formalization patterns (3)
- Sample-to-Population Generalization. From natural_language_argument to structured_generalization — Identify the observed sample.; Identify the target population.; State the projected conclusion.; Evaluate sample size and representativeness.; State the conclusion with appropriate caution..
- Analogical Argument Schema. From pair_of_cases to structured_analogy — Identify the source case and its known features.; Identify the target case.; List the similarities claimed.; Ask whether those similarities are relevant to the projected feature.; List important differences that might block the projection.; State the conclusion proportionately..
- Causal Comparison Table. From causal_claim to rival_factor_analysis — State the observed correlation.; List the proposed cause.; List at least one rival factor or confounder.; Compare the evidence for each possibility.; State the conclusion proportionately..
Full mastery and assessment guidance
Mastery requirements
- Assess inductive strength. Percent Consistent · 80_percent_consistent
- Formalize generalization. Successful Attempts · 3_successful_attempts
- Evaluate analogical argument. Successful Analyses · 3_successful_analyses
- Critique causal claim. Successful Analyses · 4_successful_analyses
Assessment advice
- Is my conclusion proportionate to the evidence?
- Would new evidence be able to weaken this inference?
- Can I point to exactly what would count as a defeater?
- Using certainty language for a probabilistic claim.
- Confusing 'the premises don't guarantee the conclusion' with 'the argument is weak'.
- Who was actually observed?
- Who is the conclusion about?
- Is the sample good enough to support that leap?
- Assuming that any sample automatically represents the broader population.
- Treating a large but self-selected sample as equivalent to a random one.
- Are the similarities I cited relevant to the claim?
- What disanalogy could block this projection?
- Does my conclusion's specificity match the analogy's strength?
- Using analogies whose similarities are not relevant to the conclusion.
- Treating 'they're both X' as automatic support.
- What evidence actually supports the causal conclusion?
- What rival factors have not been ruled out?
- Is the conclusion a cause-claim, or just a strong correlation?
- Ignoring alternative causes or confounders.
- Assuming that any change after an intervention is caused by the intervention.
- Did I identify the inductive structure before evaluating?
- Did I name rival factors where the argument is causal?
- Letting the plausibility of the conclusion drive the evaluation of the evidence.
- Skipping rival-factor analysis on causal claims.
Historical context (3)
- Francis Bacon. In Novum Organum, argued that reliable knowledge of nature requires patient and systematic evidence collection rather than speculation from a few examples. Evidence-based reasoning, structured empirical support, and the ideal of a disciplined sample.
- David Hume. Raised the classical problem of induction: past regularities do not logically guarantee future ones, forcing us to treat induction as support rather than proof. The modern framing of inductive conclusions as defeasible rather than certain.
- John Stuart Mill. In A System of Logic, developed five methods (agreement, difference, joint, residues, concomitant variation) for isolating causes from mere correlations. Mill's methods survive in modern experimental design and statistical controls.