fact makes them both the possessors of striking conferentia which might easily obscure the differentia that hold them apart as distinct kinds. 1. Write out the sixty-four permutations alphabetically. 2. Write out the sixteen permutations of propositions in the premises. 3. Reject all the permutations in the premises that are invalid, citing the rule governing each rejection. 4. Cite the rules in each instance by which we are limited to the conclusions which follow from the valid premises. 5. Refer to the table on p. 95 showing distribution of terms, use + or over the term to indicate its character in regard to distribution, and cite the proper rule of the syllogism (1 or 2, IV), in order to explain whether each instance of rejection of a mood from a figure is a case of undistributed middle, illicit minor, or illicit major. 6. Make a false syllogism in illustration of each of the moods rejected from the several figures. 7. Make a syllogism in illustration of each of the strong moods valid in the several figures. 8. Prepare to prove the special canon of the fourth figure. 9. Reduce all the valid syllogisms in the second, third and fourth figures, that were made in answer to Exercise 7, to the first figure, showing clearly all transformations and transpositions. 10. Make an A O O (2d figure) and an O A O (3d figure) and prove indirectly. 11. Make examples of the syllogisms in weak moods and reduce to the first figure, getting a universal conclusion when possible. 12. Make a syllogism in E I O, any figure, and exhibit the conversions necessary to accommodate it to each of the other figures. 13. Prove some one mood (in addition to A O O and O A O) from each figure by indirect proof. 14. Make a syllogism in A II, first figure, and accommodate it to the third (A I I) and fourth (I A I) figures. 15. Make a syllogism in E A E, first figure, and accommodate it to the second and fourth figures, naming the mood obtained and showing all steps. CHAPTER XII.-HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS AND THE DILEMMA 74. CONDITIONAL SYLLOGISMS.-Up to this point only categorical propositions have been regarded as going to form the syllogism. It has already been explained' that judging may be conditional and give rise to the conditional form of proposition. This proposition may enter into the composition of the syllogism. The conditional judgment may be either hypothetical or disjunctive. The hypothetical judgment states a supposition, and is usually introduced by the words if, in case, provided that, etc. The disjunctive judgment states alternatives, and is most commonly expressed by the disjunctive words either or. 75. HYPOTHETICAL FORM OF CONDITIONAL SYLLOGISM. In a conditional proposition of the hypothetical form the clause introduced by if or its synonyms is called the antecedent, while the clause stating the result on the condition instanced is known as the consequent. In the syllogism the conditional proposition occurs only as major premise. The minor premise is categorical. It either affirms the antecedent or denies the consequent. In the former case it leads to an affirmative conclusion, which asserts the consequent to be true; in the latter case, to a negative conclusion, which denies the truth 1 See p. 71 f. of the antecedent. The one is called a constructive hypothetical syllogism, and the argument expressed by such a syllogism is said to be of the modus ponens, or mood which posits or affirms; the other is called a destructive hypothetical syllogism, and the argument expressed is spoken of as modus tollens, or mood that removes the consequent. EXAMPLES: CONSTRUCTIVE HYPOTHETICAL SYLLOGISM (Modus ponens) If these creatures have six legs, they are insects; Therefore they are insects. DESTRUCTIVE HYPOTHETICAL SYLLOGISM (Modus tollens) If these creatures have six legs, they are insects; Therefore they have not six legs. 76. REDUCTION OF THE HYPOTHETICAL TO THE CATEGORICAL SYLLOGISM.-An examination of the hypothetical proposition shows that the same meaning can usually be expressed in a categorical form. For example, the proposition, If these creatures have six legs, they are insects, is equivalent in logical value to the A proposition, Six-legged creatures are insects. Using this as a major premise, we have as a substitute for the constructive syllogism: Six-legged creatures are insects; And for the destructive syllogism the substitute: Six-legged creatures are insects; These are not insects; Therefore these are not six-legged. The first is in this new form A A A (1st fig.), and the second A E E (2d fig.). Oftentimes the change from a hypothetical to a categorical form demands a somewhat awkward use of language. Thus in the sentence, If Plato is right, communism is the best form of society, adaptation to the categorical form compels us to use some such awkward expression as this, The case of Plato's being right is the case of communism's being the proper form of society. But in all instances some mode of expression can be invented to put the thought in categorical form. 77. FALLACIES OF THE HYPOTHETICAL SYLLOGISM. A moment's examination of the hypothetical proposition, with a view to a clear determination of its meaning, will show us the fallacies that are liable to arise when it is used in the syllogism, and will also give us the rule governing its proper use. In the sentence, If a man is born in France, he is a European, the condition named, birth on French soil, is not the only condition of his being a European. One could also say with equal truth, If a man is born in England, if a man is born in Germany, etc., he is a European. In other words, while all cases of birth in France are cases of being Europeans, the converse is not true. This amounts to saying that the antecedent, if a man is born in France, is distributed, while the consequent, he is a European, is undistributed, as appears at once when we state the meaning in simple categorical form (A), All Frenchmen are Europeans. Suppose, now, that with the above stated hypothetical proposition as a major premise we should take as minor premise the proposition, But this man was not born in France, and reason to the conclusion, Therefore he is not a European, it is evident that we should be guilty of a fallacy that is readily seen to be illicit major when the syllogism is stated in categorical form, as follows: + All instances of birth in France are instances of Europeans; Therefore this is not an instance of a European; + + (Therefore this man is not a European). This is the mood A E E and the first figure, whereas we know that this mood in the first figure gives illicit major. On the other hand, suppose that with the same major premise we use the minor premise, But this man is a European, and reason to the conclusion, Therefore he was born in France, we should have what the categorical form of syllogism shows to be undistributed middle, as the following reconstruction in categorical form shows: All instances of birth in France are instances of Europeans; + (All Frenchmen are Europeans) + This man is an instance of a European; + (This man is a European) + Therefore this man is an instance of birth in France; + (Therefore this man is a Frenchman). |