Charles Sanders Peirce - Philosophy: Logic, or Semiotic - Modes of Inference

Modes of Inference

Main article: Inquiry

Borrowing a brace of concepts from Aristotle, Peirce examined three basic modes of inference — abduction, deduction, and induction — in his "critique of arguments" or "logic proper". Peirce also called abduction "retroduction", "presumption", and, earliest of all, "hypothesis". He characterized it as guessing and as inference to an explanatory hypothesis. He sometimes expounded the modes of inference by transformations of the categorical syllogism Barbara (AAA), for example in "Deduction, Induction, and Hypothesis" (1878). He does this by rearranging the rule (Barbara's major premiss), the case (Barbara's minor premiss), and the result (Barbara's conclusion):

Deduction. Rule: All the beans from this bag are white. Case: These beans are from this bag. Result: These beans are white.

Induction. Case: These beans are from this bag. Result: These beans are white. Rule: All the beans from this bag are white.

Hypothesis (Abduction). Rule: All the beans from this bag are white. Result: These beans are white. Case: These beans are from this bag.

Peirce 1883 in "A Theory of Probable Inference" (Studies in Logic) equated hypothetical inference with the induction of characters of objects (as he had done in effect before). Eventually dissatisfied, by 1900 he distinguished them once and for all and also wrote that he now took the syllogistic forms and the doctrine of logical extension and comprehension as being less basic than he had thought. In 1903 he presented the following logical form for abductive inference:

The surprising fact, C, is observed;

But if A were true, C would be a matter of course,

Hence, there is reason to suspect that A is true.

The logical form does not also cover induction, since induction neither depends on surprise nor proposes a new idea for its conclusion. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. "Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be." Peirce did not remain quite convinced that one logical form covers all abduction. In his methodeutic or theory of inquiry (see below), he portrayed abduction as an economic initiative to further inference and study, and portrayed all three modes as clarified by their coordination in essential roles in inquiry: hypothetical explanation, deductive prediction, inductive testing.