Deduction, according to Peirce, proceeds from rule/guess (e.g., “All the beans from this bag are white”) to case (“These beans are from this bag”) to result/observation (“These beans are white”), whereas induction proceeds rather more tediously — from case to result to rule. I say “tediously” because a guess based upon both case and result/observation is a safe, habitual guess; detectives, who form hypotheses and then test them against the case (evidence), are more romantic figures. ...Though Doyle’s stories do a terrific job explaining how deduction ought to work, Holmes’ skill at solving crimes is due, they claim, to a brilliant abductive ability — i.e., the ability to proceed, swiftly and with unerring accuracy, from rule/guess to result/observation to case....
Like the deductive reasoner, the abductive reasoner begins with a rule/guess: e.g., “All the beans from this bag are white.” By comparing a result/observation (“These beans are white”) against the rule, though, the abductive reasoner doesn’t seek to test the validity of her hypothesis, but instead to detect any deviations from it. Which shouldn’t exist!In summary:
- Deductive reasoning: Rule/Guess --> Case/Evidence --> Result/Observation
- Inductive reasoning: Result/Observation --> Case/Evidence --> Rule/Guess
- "Abductive" reasoning: Rule/Guess --> Result/Observation // Case/Evidence