1. Read the model first
Each lesson opens with a guided explanation so the learner sees what the core move is before any saved response is required.
Inductive Logic
Inductive Logic: Evidence, Generalization, and Causal Support
How to reason well under uncertainty
Students learn how inductive reasoning differs from deductive reasoning, how to measure inductive strength, and how to assess generalizations, analogies, and causal claims responsibly. The unit builds from the idea of defeasible support through sampling, analogy, and Mill's methods for disentangling causation from correlation.
Study Flow
How to work through this unit without overwhelm
2. Study an example on purpose
The examples are there to show what strong reasoning looks like and where the structure becomes clearer than ordinary language.
3. Practice with a target in mind
Activities work best when the learner already knows what the answer needs to show, what rule applies, and what mistake would make the response weak.
Lesson Sequence
What you will work through
Lesson 1
What Makes an Inductive Argument Strong?
Introduces inductive strength, uncertainty, and defeasibility, and establishes the three-question routine students will use throughout the unit.
Start with a short reading sequence, study 2 worked examples, then use 15 practice activitys to test whether the distinction is actually clear.
Guided reading2 worked examples15 practice activitys
Lesson 2
Generalization and Sample Quality
Teaches students how to formalize sample-based arguments, evaluate sample quality, and recognize the common species of sampling failure.
Read for structure first, inspect how the example turns ordinary language into cleaner form, then complete 15 formalization exercises yourself.
Guided reading1 worked example15 practice activitystranslation support
Lesson 3
Analogical Reasoning
Teaches how to evaluate arguments from analogy by separating relevant similarities from superficial ones and identifying disanalogies that can block the inference.
Use the reading and examples to learn what the standards demand, then practice applying those standards explicitly in 15 activitys.
Guided reading1 worked example15 practice activitysstandards focus
Lesson 4
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.
Use the reading and examples to learn what the standards demand, then practice applying those standards explicitly in 15 activitys.
Guided reading2 worked examples15 practice activitysstandards focus
Lesson 5
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.
Each lesson now opens with guided reading, then moves through examples and 2 practice activitys so you are not dropped into the task cold.
Guided reading1 worked example2 practice activitys
Rules And Standards
What counts as good reasoning here
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
How arguments get translated into structure
Sample-to-Population Generalization
Input form
natural_language_argument
Output form
structured_generalization
Steps
- Identify the observed sample.
- Identify the target population.
- State the projected conclusion.
- Evaluate sample size and representativeness.
- State the conclusion with appropriate caution.
Common errors
- Projecting beyond the evidence.
- Ignoring sample bias.
- Using certainty language for a defeasible claim.
Analogical Argument Schema
Input form
pair_of_cases
Output form
structured_analogy
Steps
- 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.
Common errors
- Citing similarities that have nothing to do with the projected feature.
- Omitting disanalogies that matter.
Causal Comparison Table
Input form
causal_claim
Output form
rival_factor_analysis
Steps
- 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.
Common errors
- Ignoring rival factors.
- Treating one pattern as conclusive proof of causation.
Concept Map
Key ideas in the unit
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.
Assessment
How to judge your own work
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.
Mastery requirements
- Assess Inductive Strength
- Formalize Generalization
- Evaluate Analogical Argument
- Critique Causal Claim
History Links
How earlier logicians shaped modern tools
Francis Bacon
In Novum Organum, argued that reliable knowledge of nature requires patient and systematic evidence collection rather than speculation from a few examples.
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.
John Stuart Mill
In A System of Logic, developed five methods (agreement, difference, joint, residues, concomitant variation) for isolating causes from mere correlations.