QUESTIONS AND EXERCISES 425 



tributed middle in the latter, and vice versa. Show how the violation of the 

 rule (5) forbidding two negative premisses involves the violation of the rule (3) 

 forbidding undistributed middle. Show that the rule against two negatives 

 (5) involves the rule that a negative premiss necessitates a negative conclusion 

 (6, a}. To how many may the six or eight general rules be reduced ? Ex 

 plain the statement that &quot;undistributed middle involves indirectly illicit 

 process &quot;. State the rules as given in scholastic treatises on logic, and com 

 pare with the more modern statements of these rules. 



EXERCISES. ( i) Prove that if the middle term be distributed twice in 

 the premisses of a syllogism, the conclusion must be particular. (2) If the 

 major term is distributed in its premiss and undistributed in the conclusion, 

 determine the syllogism. (3) Prove that if three prop9sitions involving three 

 terms (each of which occurs in two of the propositions) are together incom 

 patible, then (a) each term is distributed at least once, and (b] one and only 

 one of the propositions is negative ; show that these rules are equivalent to 

 the rules of the syllogism. (4) Given the premisses of a valid syllogism, 

 examine (a) in what cases it is possible, and (&} in what cases impossible, to 

 determine which is the major and which the minor term. (5) (a) Given that 

 the major premiss is O, determine the syllogism ; () given that the minor 

 premiss is O, determine the syllogism. (6) How many distributed terms 

 may there be in the premisses, more than in the conclusion, of a valid 

 syllogism ? (7) If the minor premiss of a valid syllogism is negative, can 

 you determine the position of the terms in the major premiss ? 



CHAP. III. Define Figure and Mood. Can you distinguish between 

 the y?r.y/ and the fourth figure unless you know which premiss is major and 

 which minor? Show how many possible moods of syllogism there are. 

 How can you determine the valid moods? How many of the sixty-four 

 forms do the general rules and corollaries eliminate as invalid ? State and 

 prove the special rules of each figure. Name the moods which the special 

 rules leave intact in each of the four figures. Why does the special rule of 

 quality precede the special rule of quantity ? Why are the rules of the fourth 

 figure hypothetical ? How many valid moods are there in each figure ? How 

 many valid moods altogether? How many of these are &quot;named&quot; or 

 &quot;original &quot; ? What is a Subaltern Mood? How many of these are there ? 

 Why are there none in the third figure ? Repeat the mnemonic lines for the 

 named &quot; moods. What is a Strengthened Mood of syllogism ? How many 

 of these are there among the twenty-four ? Among the nineteen &quot; named &quot; 

 moods ? Are all the &quot; subaltern &quot; moods &quot; strengthened &quot; moods ? What is 

 a &quot; fundamental &quot; mood ? What are the fundamental moods corresponding 

 to each of the named strengthened moods? Determine directly, by the 

 general rules of syllogism, the number of moods in which A, E, I, and O 

 may be proved, respectively. Why can A be proved only in the first figure ? 

 Why can A or I not be proved in the second ? Why can A or E not be 

 proved in the third ? What influence have the various suppositions regard 

 ing existential import, on the validity of the syllogism ? 



EXERCISES. (i) Why do the premisses E /yield a conclusion in every 

 figure, and the premisses / E in no figure ? (2) Besides E /, does any other 

 combination yield a conclusion in all the figures ? (3) Construct a syllogism 

 in Cesare, of which the conclusion will be &quot; No birds are quadrupeds &quot;. 



