Logical Reasoning — Inductive
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Inductive reasoning moves from specific observations to a general principle. Unlike deductive reasoning, even good inductive arguments don’t guarantee their conclusions — they make them probable. The UI entrance test includes inductive reasoning questions that test your ability to identify patterns, make generalisations, and evaluate how strongly evidence supports a conclusion.
Types of Inductive Reasoning:
- Generalisation: Drawing a broad rule from specific examples. “All 10 observed cats have four legs → All cats have four legs.” Quality depends on sample size and representativeness.
- Analogy: Because two things share similarities in some respects, they likely share similarities in other respects. “Planet Earth has life. Mars is similar to Earth in having an atmosphere and moderate temperature. Therefore Mars might have life.” (Weak analogy — significant differences exist.)
- Causal reasoning: Establishing cause-and-effect relationships. Correlation does not imply causation.
- Statistical reasoning: Conclusions based on data patterns.
Key Principles:
- A generalisation from a small or unrepresentative sample is weak
- A strong analogy requires relevant similarities and no significant dissimilarities
- Counterexamples weaken inductive generalisations
⚡ Exam Tip: In the UI entrance test, “which conclusion is best supported” questions require you to assess how directly each answer choice is supported by the evidence. Eliminate answers that require additional assumptions, overgeneralise from limited data, or make unrelated claims.
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Generalisation and Sample Quality
A generalisation is only as strong as its evidence.
Strong generalisation: Large, representative sample. Example: Survey of 10,000 randomly selected students across Indonesia shows 73% prefer campus life. Conclusion: Approximately 73% of Indonesian university students prefer campus life. This is well-supported.
Weak generalisation: Small or biased sample. Example: 20 students in one class in Jakarta prefer online learning. Conclusion: Most Indonesian students prefer online learning. This is poorly supported — sample is small and not representative.
Evaluating Strength of Evidence
When asked which conclusion is best supported, evaluate each option:
- Does the evidence directly support this conclusion?
- Does the conclusion require additional unstated assumptions?
- Does the conclusion overgeneralise from the data?
- Are there plausible alternative explanations?
Example evidence: In a survey of 500 university graduates, 380 reported that their degree was “useful” or “very useful” for their career. Option A: “80% of all graduates find their degree useful.” — This overgeneralises slightly (500 out of total university graduates), but is reasonably supported. Option B: “Most university graduates find their degree useful.” — Well-supported, cautious. Option C: “All university graduates should study.” — Doesn’t follow (utility doesn’t determine necessity). Option D: “Every career requires a university degree.” — Clearly not supported.
Best answer: B or A depending on question framing.
Analogical Reasoning
An analogy claims: X and Y share properties a, b, c. X also has property d. Therefore Y probably has property d.
Example: “Birds and airplanes both fly through the air and have streamlined shapes. Birds need to eat to fuel their flight. Therefore airplanes probably need fuel to fly.” This is a strong analogy — the shared properties are directly relevant to the conclusion.
Weak analogy: “A university education resembles a prison because both involve restricted freedom, structured schedules, and mandatory attendance. Prisons have negative effects on mental health. Therefore university education probably has negative effects on mental health.” The similarities are superficial; the relevant causal factors differ.
Causal Reasoning
Correlation ≠ causation. Just because two things vary together doesn’t mean one causes the other.
Example: Ice cream sales and drowning deaths both increase in summer. Ice cream sales don’t cause drowning. Both are caused by a third factor: hot weather.
To establish causation, you need: temporal precedence (cause must come before effect), correlation, and elimination of alternative explanations.
Statistical Generalisation
When generalising from a sample to a population:
- Random sampling: each member has equal chance of selection — reduces bias
- Sample size: larger samples generally give more reliable estimates
- Margin of error: larger samples have smaller margins of error
- Confidence level: how sure we are that the result falls within the margin of error
Identifying Flaws in Arguments
Common flaws in inductive reasoning:
- Hasty generalisation: drawing broad conclusions from limited examples
- False cause: assuming one event caused another because they occurred together
- Weak analogy: comparing things that are not sufficiently similar
- Biased sample: sample not representative of the population
- Survivorship bias: focusing on things that passed a selection process while overlooking those that did not
Example flaw identification: “My grandmother smoked 30 cigarettes a day and lived to 95. Therefore smoking doesn’t cause cancer.” This is a hasty generalisation from n=1 and ignores the vast statistical evidence.
Problem-Solving Strategies:
- For “which conclusion is best supported” questions, check whether the evidence is sufficient to rule out alternatives
- In analogy questions, assess: how many relevant similarities? How significant are the dissimilarities?
- Always consider counterexamples — could a counterexample exist that the conclusion doesn’t account for?
- Watch for the difference between “most,” “some,” “all,” and “none”
Common Mistakes:
- Overgeneralising from personal experience or isolated examples
- Confusing correlation with causation
- Accepting an analogy as strong when only superficial similarities are cited
- Ignoring the base rate (prior probability) when evaluating statistical claims
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Probability in Inductive Reasoning
Inductive strength can be quantified using probability. A strong inductive argument makes its conclusion highly probable given the premises.
Bayesian reasoning: update the probability of a hypothesis based on new evidence. P(H|E) = P(E|H) × P(H) / P(E) where P(H) is prior probability, P(H|E) is posterior probability after evidence E.
Example: A test for a disease is 99% accurate (P(positive|disease) = 0.99, P(negative|no disease) = 0.99). The disease affects 1% of the population. If you test positive, what is the probability you have the disease? P(disease) = 0.01. P(positive|disease) = 0.99. P(positive|no disease) = 0.01 (false positive). P(positive) = P(positive|disease)P(disease) + P(positive|no disease)P(no disease) = 0.99×0.01 + 0.01×0.99 = 0.0099 + 0.0099 = 0.0198. P(disease|positive) = (0.99 × 0.01) / 0.0198 = 0.0099/0.0198 = 0.5 = 50%. Even with a positive test, there’s only a 50% chance of having the disease because the base rate is so low. This demonstrates why base rates matter in probabilistic reasoning.
Analogy in Legal and Scientific Reasoning
In law, analogical reasoning is used to apply precedents to new cases. The strength of the analogy depends on whether the relevant similarities outweigh the relevant differences. In science, analogical models are used to understand unfamiliar systems by comparing them to familiar ones. The strength depends on how well the mapped properties capture the essential features.
** Mill’s Methods for Causal Reasoning**
- Method of agreement: If multiple instances of an effect share only one common factor, that factor is the cause.
- Method of difference: If a case where the effect occurs differs from a case where it doesn’t only in one factor, that factor is the cause.
- Joint method: Combines agreement and difference.
- Method of concomitant variation: If one factor varies as another varies, there is a causal relationship.
- Method of residues: Subtract from an effect the part already known to be caused by known factors.
Hypothetico-Deductive Method
Scientific hypotheses are tested by deriving predictions and testing them empirically. A theory is supported if predictions are confirmed, and falsified if predictions are contradicted. No amount of confirming evidence definitively proves a theory — it only increases our confidence.
Scientific vs Legal Standards of Proof
Science: conclusions are provisional and subject to revision; requires reproducibility and falsifiability. Law (Indonesian and many civil law systems): proof “beyond reasonable doubt” or “preponderance of evidence” — different standards than science.
UI Entrance Exam Patterns
Inductive reasoning questions include:
- “Which conclusion is best supported by the passage?” — evaluate each option
- “Which answer most weakens/strengthens the argument?”
- Analogical reasoning: identify the analogy and evaluate its strength
- Statistical generalisation: assess sample size and representativeness
- Identifying logical flaws in arguments
- Causal reasoning: correlation vs causation questions
⚡ Exam Strategy: For “best supported” questions, the correct answer is often the most cautious one — the one that neither overgeneralises nor undergeneralises. Watch for answer choices that are factually accurate but answer a different question than what was asked.
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