(71) The troops took one hour in passing the saluting point. (72) Nemo mortalium omnibus horis sapit. (73) Fugaces labuntur anni. (74) Αὐτὸς εγὼ εἰμί. (75) Communia sunt amicorum inter se omnia. (76) Dictum sapienti sat est. (77) The Romans conquered the Carthaginians. (78) The fear of the Lord, that is wisdom. (79) To live in hearts we leave below is not to die. (80) "Tis only noble to be good. (81) Dum spiro spero. 2. In looking over the following list of propositions distinguish between those which have a distributive and those which have a collective subject. (1) All the asteroids have been discovered during the present century. (2) All Albinos are pink-eyed people. (3) The facts of aboriginal life seem to indicate that dress is developed out of decorations. (4) Non omnes omnia decent. (5) Dirt and overcrowding are among the principal causes of disease. (6) Omnes apostoli sunt duodecim. (7) Many artisans are unemployed. (8) The side and diagonal of a square are incommensurable. (9) Omnis homo est animal. (10) Nihil est ab omni parte beatum. 3. Ascertain exactly how many distinct assertions are made in each of these sentences, and assign the logical characters of the propositions. (1) 'Tis not my profit that doth lead mine honour: mine honour, it. (2) True, 'tis a pity; pity 'tis, 'tis true. (3) Hearts, tongues, figures, scribes, bards, poets, cannot think, speak, cast, write, sing, number, ho! his love to Antony. (4) A horse, a horse! my kingdom for a horse. (5) Istuc est sapere, non quod ante pedes modo est videre: sed etiam illa, quae futura sunt, prospicere. (6) Virtue consists neither in excess nor defect of action, but in a certain mean degree. (7) The glories of our blood and state are shadows, not substantial things. (8) 'To gild refined gold, to paint the lily, To throw a perfume on the violet, To smooth the ice, or add another hue To seek the beauteous eye of heaven to garnish Is wasteful and ridiculous excess.' (9) All places that the eye of heaven visits, Are to a wise man ports and happy havens. (10) The age of chivalry is gone, and the glory of Europe extinguished for ever. (11) Poeta nascitur, non fit. (12) Not all speech is enunciative, but only that in which there is truth or falsehood. (13) Devouring Famine, Plague, and War, Each able to undo Mankind, Death's servile emissaries are. (14) Many are perfect in men's humours, that are not greatly capable of the real part of business, which is the constitution of one that hath studied men more than books. (15) Vivre, ce n'est pas respirer, c'est agir. (16) Justice is expediency, but it is expediency speaking by general maxims, into which reason has concen trated the experience of mankind. (17) Men, wives, and children, stare, cry out, and run as it were doomsday. 4. Distinguish so far as you can between the propositions in the following list which are to you explicative and ampliative. (See Elementary Lessons, pp. 68-69. Thomson's Outline of the Necessary Laws of Thought, § 81.) (1) Homer wrote the Iliad and Odyssey. (2) A parallelopiped is a solid figure having six faces, of which every opposite two are parallel. (3) The square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the sides containing the right angle. (4) The swallow is a migratory bird. (5) Axioms are self-evident truths. 5. Classify the following signs of logical quantity according as they are generally used to indicate universality, affirmative or negative, or particularity, affirmative or negative Several, none, certain, few, ullus, nullus, nonnullus, not a few, many, the whole, almost all, not all. CHAPTER V CONVERSION OF PROPOSITIONS, AND IMMEDIATE INFERENCE I. THE student is referred to the Elementary Lessons in Logic, or to other elementary text-books, for the common. rules of conversation and immediate inference, but, for the sake of easy reference, the ancient square of opposition is given below. All the relations of propositions and the methods of inference applying to a single proposition will be found fully exemplified and described in the following questions and answers. 2. It appears to be indispensable, however, to endeavour to introduce some fixed nomenclature for the relations of propositions involving two terms. Professor Alexander Bain has already made an innovation by using the name obverse, and Professor Hirst, Professor Henrici and other reformers of the teaching of geometry have begun to use the terms converse and obverse in meanings inconsistent with those attached to them in logical science (Mind, 1876, p. 147). It seems needful, therefore, to state in the most explicit way the nomenclature here proposed to be adopted with the concurrence of Professor Robertson. Taking as the original proposition 'all A are B,' the following are what we may call the related propositions It must be observed that the converse, obverse, and contrapositive are all true if the original proposition is true. The same is not necessarily the case with the inverse and reciprocal. These latter two names are adopted from the excellent work of Delboeuf, Prolegomènes Philosophiques de la Géométrie, pp. 88-91, at the suggestion of Professor Croom Robertson. (Mind, 1876, p. 425.) |