(1) In determining their validity, arguments must be tested from the two viewpoints of form and matter.
(2) In testing categorical arguments it is quite necessary to be definite, to give reasons, and to give the author the benefit of the doubt.
With this in view the attending outline is suggestive:
1. Arrange logically and complete.
2. Determine the figure and mood.
3. Apply rules for negatives and particulars.
4. Indicate distribution.
5. Apply rules for distribution.
6. Name fallacies, if any, giving reasons.
The logical arrangement of syllogistic arguments is
1. Major premise.
2. Minor premise.
3. Conclusion.
Any proposition in a syllogism which answers the question “Why?” is a premise, whereas the conclusion follows “therefore”, or its equivalent either written or understood. If a conclusion is to be supplied, unite the two terms which are used but once in the premises, using the “minor premise term” as the subject. If a premise is to be supplied, unite the middle term with the “minor” to form the minor premise and with the “major” to form the major premise.
(3) Arguments which are regular, complete, and logically arranged, may be tested by symbolizing the mood and figure, underscoring the distributed terms, and then applying the general rules of the syllogism.
(4) Arguments with illogical premises may not be tested with impunity till the faulty premises are made logical. The exclusive, an illogical proposition introduced by only, alone, none but, and the like, may be made logical by interchanging subject and predicate and calling the proposition an A. The individual proposition is one with a singular subject. In testing, individual propositions are classed as universal. Propositions introduced by “all-not” are usually given the significance of “some-not”. These are called partitive propositions, which in the testing, should be denominated “O’s”.
Inverted propositions when subjected to the test for validity must be converted simply and then classified. (Usually as A’s.)
(5) In supplying propositions which are taken for granted, the aim should be to make the argument valid, provided this can be done without violating the rules of logic, English, and common sense.
Ability to substitute equivalent words, phrases, or clauses is demanded of the student of logic, inasmuch as such substitution is frequently needed in the testing of arguments.
Number and tense have little significance in dealing with arguments.
(6) The common mistakes of students made in testing arguments concern exclusive, partitive and inverted propositions, and an inability to recognize expressions equivalent in meaning.
(1) Name and explain the two standpoints from which all arguments must be viewed.
(2) Give an outline of procedure which may be serviceable in the testing of categorical arguments.
(3) Give illustrations showing that the logical order of categorical arguments is not the usual mode of procedure in common parlance.
(4) Offer suggestions which may aid in designating a premise; a conclusion.
(5) How would you proceed in forming any one of the three propositions of a syllogism when the other two are given?
(6) Designate the premises and the conclusion in the following, supplying any proposition which may be omitted, also arrange logically and test the validity.
(1) “The people of this country are suffering from an overdose of prosperity; consequently a period of hard times will be a valuable lesson.” (The conclusion should be recast so as to read, “A period of hard times will cure the people of this country.” The minor premise is, “Those who suffer from an overdose of prosperity may be cured by a period of hard times.”)
(2) “I am a teacher; you are not what I am; hence you are not a teacher.”
(3) “To kill a man is murder, therefore war is murder.”
(4) “You have not adopted the best policy since honesty has always been and will always be the best policy.”
(5) “Since the road is criminally mismanaged, why should not the authorities be indicted as criminals?”
(6) “Early to bed and early to rise makes a man healthy, wealthy and wise. I am none of these; hence my sleeping hours have been wrong.”
(7) Illustrate a weakened conclusion.
(8) Explain the exclusive proposition and indicate how the logician should treat it.
(9) Arrange logically and test the following:
(1) Only weak men become intemperate, and Edgar Allen Poe was surely intemperate.
(2) No admittance except on business; hence you cannot be admitted.
(3) Virtuous acts are praiseworthy, and indiscriminate giving is not a virtuous act.
(10) Explain why individual propositions are classed as universal.
(11) Write an argument whose major premise is a partitive proposition; arrange logically and test validity.
(12) Arrange and test this argument: “Blessed are the poor in spirit: for theirs is the kingdom of heaven.”
(13) Complete, arrange and test.
(1) “The object of war is to settle disputes; hence soldiers are the best peacemakers.”
(2) “The various species of brutes being created to prey upon one another proves that man is intended to prey upon them.”
(3) “The end of everything is its perfection; death being the end of life is its perfection.”
(4) “All the trees of the yard make a thick shade and this is one of them.”
(5) “Minds of moderate caliber ordinarily condemn everything which is beyond their range, and his is such a mind.”
(6) “The best of all medicines are fresh air and sleep, and you are sorely in need of both.”
(7) “Every hen comes from an egg; every egg comes from a hen; therefore every egg comes from an egg.”
(8) “He cannot have been there—otherwise I should have seen him.”
(14) “It is fair to give the author the benefit of the doubt when we set ourselves up as censors worthy of the name.” Explain this.
(15) Illustrate by citing arguments the need of detecting terms which are equivalents in signification.
(16) How does the logician look upon number and tense as treated in grammar?
(17) Illustrate and test an argument in which one of the premises is elliptical.
(18) Summarize the most common mistakes made by students in the testing of categorical arguments; illustrate these mistakes and then write in logical form.
(1) Give illustrations of arguments which are valid in form but invalid in meaning. Explain.
(2) May an argument be valid in meaning but invalid in form? Exemplify.
(3) Put a simple problem in arithmetic in syllogistic form and show that the minor premise naturally comes first.
(4) In the practice of law is there any custom analogous to giving the author the benefit of the doubt in logical argumentation?
(5) Test in detail the following arguments:
(1) “All wise presidents strive to give heed to the demands of the people, but this president has not done so.”
(2) “The existence of God is not universally believed, hence it cannot be true.”
(3) “The institution has prospered under the present régime therefore why change it?”
(4) “The man is guilty because seven out of the nine witnesses so testified.”
(5) “I know three men who cleared not less than ten thousand dollars in this business; and why cannot I do as much?”
(6) “Only members may vote and, since you are not a member, you will not be allowed to vote.” Change the exclusive in this argument in the two ways suggested in Chapter 8, page 126. Test the argument in both cases.
(7) Show by illustration that the quantity sign “all” when used with “not” may in some cases mean “no” and in others “some-not”.
(8) Make two selections from some poet of authority representing arguments with an inverted premise.
(9) Select from news papers three arguments which seem to illustrate the fallacy of four terms but which in reality do not. Explain.
(10) Wherein could the elliptical proposition lead to error?
(11) Put the following in syllogistic form and test:
(1) “That persons may reason without language is proven by the circumstances that infants reason and yet have no language.”
(2) “The scriptures cannot come from God because they contain some things which cannot be comprehended by man.”
(3) “When Columbus was sailing the ocean in search of a new world, he fell in with a flock of land birds and concluded that he could not be far from land.”
(4) “Bolingbroke in arguing against the truth of the Christian religion shows that the Christian religion has bred contentions.” “Burke answered him by showing that civil government had bred contentions.”