The name "induction," derived from the Latin translation of Aristotle's epagoge, will be used here to cover all cases of nondemonstrative argument, in which the truth of the premises, while not entailing the truth of the conclusion, purports to be a good reason for belief in it. Such arguments may also be called "ampliative," as C. S. Peirce called them, because the conclusion may presuppose the existence of individuals whose existence is not presupposed by the premises.

Thus, the conclusion "All A are B" of an induction by simple enumeration may apply to A's not already mentioned in the finite number of premises having the form "A_i is B." Similarly, in eduction (or arguments from particulars to particulars) the conclusion "Any A is B" is intended to apply to any A not yet observed as being a B.

It would be convenient to have some such...