Induction and Inductivism
Terms like ‘inductive logic’, or ‘inductive reasoning’, can however be used in a broad or a narrow sense.
In the broad sense, induction is inference from singular to general propositions. That is how Mill defines it: ‘Induction may be defined, the operation of discovering and proving general propositions’ (VII 284). (Note that he sees it here both as a logic of discovery and as a logic of proof.) There is no incompatibility between this definition and the thesis that all inference is from particulars to particulars, as Mill goes on to note. Any inference from particulars to particulars can be represented as involving an inductive step from particulars to generals. The point made by the thesis that inference is from particulars to particulars, on our interpretation of it, was that general propositions express habits of inference. Induction therefore becomes the operation by which we accumulate habits of inference, and inductive logic becomes the ‘theory of evidence’, of how to extract sound habits of inference from one’s data.