late 14c., "advancement toward the grace of God;" also (c. 1400) "formal installation of a clergyman," from Old French induction (14c.) or directly from Latin inductionem (nominative inductio) "a leading in, introduction," noun of action from past participle stem of inducere "to lead" (see induce).
As a term in logic (early 15c.) it is from Cicero's use of inductio to translate Greek epagoge "leading to" in Aristotle. Induction starts with known instances and arrives at generalizations; deduction starts from the general principle and arrives at some individual fact. As a term of science, c. 1800; military service sense is from 1934, American English.
