ENTHYMEME , in formal logic, the technical name of a syllogistic argument which is incompletely stated. Any one of the premises may be omitted, but in general it is that one which is most obvious or most naturally present to the mind. In point of fact the full formal statement of a syllogism is rare, especially in rhetorical language, when the deliberate omission of one of the premises has a dramatic effect. Thus the suppression of the conclusion may have the effect of emphasizing the idea which necessarily follows from the premises. Far commoner is the omission of one of the premises which is either too clear to need statement or of a character which makes its omission desirable. A famous instance quoted in the Port Royal Logic, pt. iii. ch. xiv., is Medea's remark to Jason in Ovid's Medea, "Servare potui, perdere an possim rogas?" where the major premise "Qui servare, perdere possunt" is understood. This use of the word enthymeme differs from Aristotle's original application of it to a syllogism based on probabilities or signs , i.e. on propositions which are generally valid or on particular facts which may be held to justify a general principle or another particular fact (Anal. prior. β xxvii. 70 a 10).
See beside text-books on logic, Sir W. Hamilton's Discussions (1547); Mansel's ed. of Aldrich, Appendix F; H.W.B. Joseph, Introd. to Logic, chap. xvi.
Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)