My students know "deduction" and "induction" from school, though they often mix them up. I recently read that Charles Sanders Peirce added a third type of reasoning, abduction. Could someone explain all three clearly, with examples, and why Peirce thought abduction mattered for science?
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Deduction: if the premises are true, the conclusion must be (all metals conduct; copper is a metal; so copper conducts). Induction: generalising from observed cases (every copper sample we've tested conducts; so all copper conducts). Abduction, in Peirce's sense: inferring a hypothesis that would explain a surprising fact (the lights dimmed when the motor started; perhaps they share a circuit). Peirce thought abduction is the only kind of inference that introduces new ideas, which is why science needs it.