QUESTIONS AND EXERCISES 427 



IAI, EAO, AEO. (8) Determine by the General Canons of Syllogism the 

 valid moods (a) in which the major premiss is I ; (b] in which the minor 

 premiss is O ; (c} in which the mnemonic ends in &quot; s &quot;. (9) Can it be shown 

 that the reasoning in Bocardo is founded on the Dictum de omni et nullo ? 

 (10) Why are D and C excluded from the mnemonics of the second and 

 third figures respectively? 



CHAP. V. Define the pure hypothetical syllogism. On what axioms is 

 it based ? On what does the quantity of each antecedent and of each con 

 sequent depend? Do the rules of the categorical syllogism apply here? 

 Construct a pure hypothetical syllogism in Dimaris, and reduce it to the first 

 figure. Define the mixed hypothetical syllogism. What is the basis of the 

 reasoning here ? What are the valid &quot; moods &quot; and their respective forms ? 

 Why is there no valid ground for inference in sublating the antecedent, or in 

 positing the consequent, of the major premiss ? Can the mixed hypothetical 

 syllogism be reduced to the categorical? Is the reasoning mediate or 

 immediate? What is a pure disjunctive syllogism? Is the conclusion 

 merely the sum of the premisses ? Examine the syllogism : 5 is either P or 

 Q; either P or Q is R; therefore S is R. Define the mixed disjunctive 

 syllogism. Is it &quot;a syllogism one of whose premisses is a disjunctive propos 

 ition &quot; ? What is the basis of the reasoning here ? What is the name of 

 the valid mood ? What are its forms ? Are they reducible to mixed hypo 

 thetical syllogisms ? Is the Modus Ponendo Tollens always invalid ? Why ? 

 When the major premiss is disjunctive in the strict sense, as distinct from 

 alternative, which mood is valid ? Define the Dilemma. Explain its struc 

 ture and its relation to the mixed hypothetical syllogism. How do you 

 arrive at its valid forms ? Name, explain, and illustrate these latter. How 

 may the forms be reduced to one another? Is there any formal fallacy in 

 the dilemma besides positing consequents or sublating antecedents ? What 

 conditions must the premisses fulfil in order that the dilemma be conclusive ? 

 In what ways may an inconclusive dilemma be met? What do you under 

 stand by &quot;rebutting &quot; a dilemma? May a perfectly valid dilemma be &quot;re 

 butted &quot; ? Why can simple dilemmas and destructive dilemmas not be 

 &quot; rebutted &quot; ? State and criticize some alternative views of the dilemma. 

 Give some examples of defective dilemmas. May the simple destructive 

 form be rejected consistently with retaining the simple constructive form ? 



EXERCISES. (i) Classify the following argument: &quot; If he managed to 

 escape he must have been either very clever or very rich ; but he was both 

 stupid and poor ; so he cannot have escaped &quot;. (2) &quot; If X is true, then either 

 Y or Z is true : but Y is not true &quot;. What conclusion can be drawn ? 



CHAP. VI. What is an enthymeme? Explain and exemplify the three 

 orders of enthymeme. Can you determine the order, the figure, and the 

 mood, to which a given enthymeme belongs ? Supply the missing premiss in 

 the enthymeme &quot;C is D because A is B &quot;. What is a polysyllogism ? a 

 prosyllogism ? an episyllogism ? a progressive, and a regressive, polysyllogism ? 

 Define the sorites. How many forms are there ? Why are they so called ? 

 What are the essential points of difference between the two forms ? What 

 orders of enthymeme are involved in each ? Are pure or mixed hypothetical 

 sorites possible ? Illustrate. Determine and prove the special rules for the 

 Aristotelean and the Goclenian forms respectively. Exemplify the sorites in 



