"The fifth century saw the foundation of the Frank dominion in Gaul, and the first establishment of the German races in Britain. The former was effected in a single long reign, by the energy of one great ruling tribe, which had already modified its traditional usages, and now, by the adoption of the language and religion of the conquered, prepared the way for a permanent amalgamation with them." In the second of the above sentences a general proposition is assumed. Show in syllogistic form how the last proposition in the sentence depends upon it. "I do not mean to contend that active benevolence may not hinder a man's advancement in the world: for advancement greatly depends upon a reputation for excellence in some one thing of which the world perceives that it has present need: and an obvious attention to other things, though perhaps not incompatible with the excellence itself, may easily prevent a person from obtaining a reputation for it." Pick out the propositions here given as interdependent. Examine whether the principle alleged is sufficiently general to necessitate a conclusion. In what form would it be so? CHAPTER V. ENTHYMEMES. There is a certain variety in the use of the word Enthymeme among logicians. In the narrowest sense, it is a valid formal syllogism, with one premiss suppressed. In the widest sense it is simply an argument, valid or invalid, formal in expression or informal, with only one premiss put forward or hinted at, the other being held in the mind ([Greek: en thymo]). This last is the Aristotelian sense. It is only among formal logicians of the straitest sect that the narrowest sense prevails. Hamilton divides Enthymemes into three classes according as it is the Major Premiss, the Minor Premiss, or the Conclusion that is suppressed. Thus, a full syllogism being:-- All liars are cowards: Caius is a liar: [.'.] Caius is a coward:-- this may be enthymematically expressed in three ways. I. Enthymeme of the First Order (_Major understood_). Caius is a coward; for Caius is a liar. II. Enthymeme of the Second Order (_Minor understood_). Caius is a coward; for all liars are cowards. III. Enthymeme of the Third Order (_Conclusion understood_). All liars are cowards, and Caius is a liar. The Third Order is a contribution of Hamilton's own. It is superfluous, inasmuch as the conclusion is never suppressed except as a rhetorical figure of speech. Hamilton confines the word Enthymeme to valid arguments, in pursuance of his view that Pure Logic has no concern with invalid arguments.