426 THE SCIENCE OF LOGIC 



(4) Construct a syllogism in Ferison to prove that &quot; Some students are not 

 strong&quot;. (5) Prove by a syllogism in Camenes that &quot;No persecution is 

 justifiable &quot;. (6) Why can an O proposition not be a premiss in the first 

 figure, a major in the second, or a minor in the third ? (7) Why is one 

 special rule common to the first and second figure, and another common to 

 the first and third ? (8) Examine these assertions : (a) The conclusion of a 

 valid syllogism is simply convertible if in the premisses the extremes have the 

 same quantity ; (b] the extremes of a valid syllogism have the same quantity 

 in the premisses if the conclusion is simply convertible ? (9) &quot; No one will 

 hold that all virtuous men are happy, who remembers how many good men 

 have lost wealth and life for conscience sake.&quot; Express this reasoning in 

 Ferio, Festino, and Ferison. (10) Prove that every syllogism which dis 

 tributes the middle term twice has a strengthened premiss. 



CHAP. IV. What is direct reduction ? Is it the only test of the 

 validity of a syllogism outside the first figure ? What is its utility ? Ex 

 plain the significance of the consonants in the mnemonic lines. Give ex 

 amples. Define Indirect Proof. On what principles does it depend ? How 

 is the principle applied to prove the validity of syllogisms in figures other 

 than the first ? Apply it to Bocardo. Define Indirect Reduction. Is the 

 new syllogism employed in this process the only one involved in the original 

 syllogism ? If not, how do you know which of the possible ones to select ? 

 May all the moods of the other figures be reduced (i) directly, or (2) at least 

 by the aid of indirect reduction, to any mood of the first figure ? Reduce 

 Celarent to Ferio. Is the first figure the most perfect ? Is it the only 

 cogent figure ? What are its characteristics ? Why is the second called the 

 exclusive figure ? What are its characteristics ? State its axiom. Justify the 

 passage of thought in the second figure, and compare it with the first. What 

 arguments fall naturally into the third figure ? What are its characteristics ? 

 What is its axiom ? Why is it called the inductive figure ? Justify its 

 reasoning. Do any reasonings fall naturally into the fourth figure ? Does 

 it exhibit a distinctive type of inference ? Are the moods of the fourth figure 

 merely the moods of the first with converted conclusions ? Are they the same 

 as the indirect moods of the first ? Define an indirect mood of the first 

 figure. How many moods of the first figure yield both direct and indirect 

 conclusions ? How many direct only ? How many indirect only ? Does a 

 pair of premisses from which a proposition necessarily follows, always &quot;demon 

 strate,&quot; that proposition or prove it to be true? What is an antilogism? 



EXERCISES. (i) Can a purely formal proof be adduced for the state 

 ment that a true conclusion may validly follow from premisses that are 

 false? (2) Was Kant right in asserting about the other figures that &quot;the 

 very same conclusion would follow from the same middle term in the first 

 figure by pure and unmixed reasoning&quot;? (3) If the mnemonic of a valid 

 mood ends in &quot;j,&quot; construct the syllogism. (4) Given I as major premiss, 

 determine the syllogism by reference to the General Canons. (5) Why are 

 all moods with an O premiss excluded from the first and fourth figures, while 

 some such are admitted into the second and third ? (6) Prove that if a valid 

 syllogism contains an O premiss its middle term must occupy the same 

 position in both premisses. (7) State which of the following moods are 

 illegitimate or useless, naming the figures in which they are so : AAI, IEO, 



