Questions: Inductive Justification and Generalization

Question 1

Why is it circular to defend induction by saying 'induction has worked reliably in the past, so it will continue to work in the future'?

• A. It is not circular — past reliability is strong empirical evidence for future reliability
• B. The defense itself uses an inductive inference (from past success to future reliability), which is exactly what was in question
• C. The argument confuses inductive reasoning with probabilistic reasoning
• D. Past success is logically irrelevant to the reliability of inference methods

Answer: (B)

Hume's circularity point is precise: defending induction by appealing to its past success is itself an inductive argument — it moves from observed cases (induction worked) to a general claim (induction works). You cannot use induction to justify induction without presupposing what you set out to establish. This is not a defect of one bad argument; it afflicts every attempt to give induction an inductive justification.

Question 2

A researcher observes 500 patients at a single urban hospital, all of whom respond well to a new drug, and concludes it is effective for all patients. Compared to a trial of 200 patients drawn from diverse demographics across multiple sites, the researcher's argument is weaker primarily because:

• A. 500 patients is too small a sample to support any generalization
• B. Hospital observations cannot be used in inductive arguments
• C. The single-site, homogeneous sample is less representative, so the evidence provides weaker support for the universal conclusion
• D. The conclusion should say 'most patients' rather than 'all patients,' making the argument invalid

Answer: (C)

Inductive strength depends on sample size, representativeness, and the diversity of conditions observed. A single urban hospital may systematically differ from other populations in demographics, comorbidities, diet, and access to care. The 200-patient diverse trial provides stronger inductive support because its sample is more representative of the population the conclusion is about — even though it is smaller. Option D raises a valid point about specificity, but the primary weakness here is representativeness.

Question 3

An inductively strong argument can have true premises and a false conclusion.

• T. True
• F. False

Answer: True

This is the fundamental asymmetry between deduction and induction. Inductive strength means the premises make the conclusion probably true — not that they guarantee it. A strong inductive argument can fail: all 1,000 observed ravens were black, yet there might still be a white raven. This revisability in light of new evidence is not a defect but the defining character of empirical reasoning. A deductively valid argument, by contrast, cannot have true premises and a false conclusion.

Question 4

Hume's problem of induction shows that inductive reasoning is irrational and should be abandoned in favor of deductive inference.

• T. True
• F. False

Answer: False

Hume showed that induction cannot be non-circularly justified — not that it is irrational. The major responses (Strawson's analytic reply, Reichenbach's pragmatic vindication, Quine's naturalism) each explain why continued use of induction is reasonable without claiming Hume's challenge was solved. No serious epistemologist proposes replacing empirical science with pure deduction. The point is to understand induction's epistemic status accurately, not to abandon the most successful method for extending knowledge.

Question 5

What makes an inductive generalization stronger, and why does the absence of a non-circular justification for induction not undermine the practical distinction between strong and weak inductive arguments?

Model answer: An inductive generalization is stronger when the sample is larger, more representative, drawn across diverse conditions, and when the conclusion is appropriately modest. The circularity problem operates at the meta-level — it concerns why induction as a method is rational in general — and does not dissolve object-level differences between better and worse samples. A diverse trial of 1,000 patients provides more inductive support than 10 patients from one location regardless of whether induction itself has a non-circular foundation.

The circularity problem and the evaluation of argument strength are independent concerns. One can acknowledge Hume's challenge while still recognizing that a representative sample supports a conclusion better than an unrepresentative one. The practical skills of assessing sample quality, identifying bias, and calibrating conclusion strength remain valid and important even without a foundational resolution to the problem of induction.