Inductive Reasoning and Scientific Method
Induction versus deduction
Inductive arguments make the conclusion probable, not certain; they are assessed as strong or weak, cogent or uncogent, never valid or invalid. Types include generalization (sample to population), analogy, causal inference and statistical inference. The inductive leap goes beyond the premises, which makes induction ampliative but risky.
Mill’s methods
- Agreement: find the one common circumstance in cases where the effect occurs.
- Difference: compare a case where the effect occurs with one where it does not.
- Joint method of agreement and difference combines the two.
- Residues: subtract effects already explained; the remainder is due to the remaining antecedent.
- Concomitant variation: the effect varies as the supposed cause varies.
Scientific method
Observation → hypothesis → deduction of test implications → experiment/verification → acceptance, revision or rejection. A good hypothesis is testable, falsifiable, simple and fruitful. Popper stresses falsification: confirmation is provisional, but one contrary instance can refute a hypothesis.
Worked example
Five people fall ill after a dinner; the only food all five ate was the paneer. By the method of agreement, the paneer is the probable cause. To strengthen the claim, use the method of difference: a sixth person who ate everything except the paneer did not fall ill.
Traps that cost marks
Never call an inductive argument “valid”; do not claim one confirming case proves a hypothesis; do not confuse agreement (common factor present) with difference (factor absent).