Inference

Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.

Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing." P. R. Halmos reviewing the book summarised the central thesis of the book thus: ". . . a good guess is as important as a good proof."