The following from Arnauld is pronounced by Jevons to be impracticable: " The sun is a thing insensible; The Persians worship the sun; .. The Persians worship a thing insensible. Here are five terms; yet the reasoning is obviously very good. The Canon of Replacement is directly applicable, the conclusion being obtained by replacing, in the minor premise, "the sun" by its undistributed genus, "a thing insensible," as declared in the major premise. But even under the common logical rules the resolution is very simple. From the major premise we may immediately infer, by complex conceptions, "They who worship the sun worship a thing insensible," and we then have a perfectly regular Barbara. The following would hardly puzzle a tyro: Whoever probes a wound is on the verge of crime; A wound is probed by the healer; .. The healer is on the verge of crime. For the passive minor, substitute the active form immediately inferred, "The healer probes a wound," and we have again Barbara. An example involving an immediate inference in opposition is as follows: That riches are often a bitter curse is true; And yet it is also true that most men desire riches; .. It is false to say that no men desire what is often a bitter curse. The syllogism which is slightly disguised in this is the following Darii: They who desire riches desire what is often a bitter curse; Most men desire riches; .. Most men desire what is often a bitter curse. This major premise is immediately inferred by complex conceptions; the conclusion, by opposition; for if E is false, then its contradictory, I, is true. Finally, we recall the example formerly cited (i, § 4) as directly solved by the Canon of Replacement. Aldrich (p. 99) pronounces it a false syllogism on the ground that it has five terms, and therefore must be invalid. He is wrong; the reasoning is evidently very good. The divine law commands us to honor kings; Louis XIV is a king; .. The divine law commands us to honor Louis XIV. Lessons in Logic, p. 158. It is sufficiently evident that the middle term here is "king." This, then, is the true subject of the major premise, which, being redressed in a form that may be accepted as equipollent, gives: All kings are of those whom the divine law commands us to honor; Louis XIV is a king; ..Louis XIV is one whom the divine law commands us to honor. The conclusion of this Barbara, again, is merely a similarly equipollent form for "The divine law commands us to honor Louis XIV." The following treatment will to some readers be more satisfactory: Louis XIV is a king; -by transference to the quantitative whole and inverting, we get : This king is Louis XIV (i. e., the one we are thinking of is Louis XIV). -by complex conceptions, we get: Whatever commands us to honor this king commands us to honor Louis XIV; But (Whatever commands us to honor all kings commands us to honor this king;) .. Whatever commands us to honor all kings commands us to honor Louis XIV. Now, The divine law commands us to honor all kings; .. The divine law commands us to honor Louis XIV. § 7. Logicians have distinguished, described, and named certain modes of arguing, some account of which may be fairly included under the present topic. The argumentum ad rem is the direct proof of the main point in question. The reductio ad absurdum indirectly proves an assertion by proving the absurdity of its contradictory. It is much used in geometry. It is sometimes called argumentum per impossibile. The refutation of an assertion may also be accomplished by an inverse treatment," by proving its contradictory true. In discussions we sometimes hear the remark, "Your argument proves too much." If an absurd consequence be shown, then either its reasoning is illogical or a premise is false. The argument from effects is very similar. In a question of mere expediency-as, for example, the passage of a law for the suppression of intemperance-we might argue from effects, and, showing that they are likely to be evil, and that they had actually resulted in evil in analogous or entirely similar cases, we might thus prove the inexpediency of such a measure. Questions of duty should always, if possible, be determined a priori, without regard to consequences; but in 10 Sce Part 3d, ii, § 8. some cases duty can be determined only by considering the consequences of the contemplated line of conduct. The argumentum ad populum is an appeal to such principles as arc cherished by the people. This indirectly supports the point, and is legitimate if the principles are sound. But when the appeal is to passion or prejudice, it is a sign that the speaker himself lacks confidence in his other arguments. The argumentum ad judicium is an appeal to the common judgments of mankind. We hear it often in conversation, in the phrases "Everybody says," "No one thinks," etc. The argument may possess great force. It is one of the strong supports of the Scottish doctrine of Natural Realism, hence called the philosophy of commonAristotle says, "What seems true to all, that we believe to be, and nothing is more worthy of credit." sense. The argumentum ad verecundiam is an appeal to authority, to some venerable institution, as an established religion, to antiquity, etc. E. g., with the scholastics it was a standing major premisc, "Stultum est dicere Aristotelem errare." The argumentum ad hominem is arguing on the ground of an opponent. It is also called argumentum ex concesso. As all disputation must proceed ex concessis, we may accept an opponent's principles on which to base a counter-argument, though, perhaps, we may believe his principles false, our argument being directed against him personally, ad hominem. Even if we believe his principles sound, they may not be such as we would use in arguing with another, or with mankind generally. The conclusion we establish is frequently not the absolute and general one in question, but one merely relative and particular. We may no more than convict our opponent of inconsistency, ignorance, bad faith, or illogical reasoning. We then can claim a victory, but not possession of the territory. Such a course is often necessary in order to silence those who will not yield to fair general argument, or to convince those whose weakness and prejudices will not allow them to assign it due weight. Our Lord often used this method against the Jews. See, for example, Matt. xxii, 41–45. The argumentum a fortiori has already been considered in iii, § 4. Its full form is: If A is greater than B, and B greater than C, still greater is A than C. This is essentially mathematical or quantitative. It may be described in general as the argument in, which, from an admitted and less probable proposition, one depending on it, and more probable, follows a fortiori. § 8. Praxis. State of each of the following examples whether it is a simple enthymeme, or an epichirema, or a sorites. Write out the syllogisms implied in full logical form. In case of an epichirema, distinguish the pro- and epi-syllogism. 1. Blessed are the merciful; for they shall obtain mercy. 2. Cunning cannot be a virtue; for no virtue degrades. 3. It is I; be not afraid. 4. Cogito, ergo sum.-See Hamilton's Metaphysics, p. 258. 5. Every man should be moderate; for excess will cause disease. 6. Kings, having no equals, have no friends. 7. Suppose ye that these Galileans were sinners above all the Galileans, because they suffered such things? I tell you nay. 8. Will, since it often combats desire, as also it often yields to it, is not desire. 9. The flesh of ruminants is good for food, and these animals, since they have horns and cloven hoofs, belong to that class. 10. Man, inasmuch as he is naturally selfish, and is, moreover, liable to desires and passions which have no limits or power of restraint in themselves, needs the restraints of law. 11. Occasional turbulence, being the less of two evils, is preferable to rigid despotism. 12. What if a rule never is, and a principle always is, a law admitting no exception? 13. A wise man is never surprised, because he is never disappointed; and this is because he forms no expectations that are not placed upon the most certain basis. 14. Suppose a man to say, "I dislike all foreigners;" find a premise which, with this saying, would authorize the further assertion, "No foreigner ought to be liked." 15. Whatever tends to withdraw the mind from pursuits of a low nature deserves to be promoted. This classical learning does, since it cultivates a taste for intellectual enjoyments. 16. The Scripture narratives are trustworthy, because the writers had the means of knowing the facts; also, they evidently were sincere and candid; and, besides, the narratives are consistent. 17. All true patriots are friends to religion, religion being the basis of national prosperity; but, since their lives are not in accordance with its precepts, it follows that some great statesmen are not friends to religion. 18. Lithium is an element; for it produces an alkali, therefore is a metal, and hence an element. 19. I will not do this act, because it is unjust; I know that it is unjust, because my conscience tells me so; and my conscience tells me so because the act is wrong. 20. When the observance of the first day of the week as a religious festival in commemoration of Christ's resurrection was introduced, it must have attracted much attention; for it was a striking innovation. In this case, since attention would naturally lead to inquiry respecting the truth of the resurrection, the story would surely have been exposed as an imposture had it been one. Put the following logical climax in the Goclenian form, and write the circular, linear, and graphic notation: 21. The prudent are temperate; The temperate are constant; The constant are unperturbed; The unperturbed are without sorrow; Those without sorrow are happy; .. The prudent are happy.-Seneca, Epist. 85. Put the following in its opposite form, and write the notations: 22. Nothing which is indissoluble is mortal; What has no composition of parts is indissoluble; A spirit has no composition of parts; A thinking substance is a spirit; .. The mind is not mortal.-Plato. State each of the following as a regular sorites in either form: 23. We must increase the income-tax; for war has become a necessity, and we cannot go to war without money, which can be raised only by taxation. But the only tax which the resources of the country can bear is the income-tax, since it will fall on the richer part of the population. 24. A demagogue must hold the people in contempt; for, being a favorite with them, he must know how to manage them; therefore he understands their weaknesses, and his contempt must follow. |