QUESTIONS AND EXERCISES 421 



how the connotative interpretation gives what is most fundamental in predica 

 tion. Discuss Mill s advocacy of this reading, especially in regard to con 

 tingent propositions. Can the comprehensive interpretation be applied to 

 synthetic judgments ? Compare the class-inclusion view with the predicative 

 view. Is any one of these views correct, to the exclusion of all the others? 

 Is the predicate always, or ever, quantified in thought ? What are Euler s 

 circles ? Explain the formation of Hamilton s eightfold scheme. Is Hamil 

 ton s postulate admissible ? Does it justify his interpretation of the judgment ? 

 Can we have intelligible predication about indefinite classes ? Can this sort 

 of predication be expressed in prepositional forms that are interpreted as 

 relating definite classes to each other ? Show that if the Hamiltonian forms 

 deal with definite classes the scheme is both defective and redundant. Show 

 that if &quot;some &quot; means &quot;some only,&quot; A is equivalent to 77, Y to O, and &&amp;gt; to U, 

 thus yielding a fivefold scheme. Show that I is ambiguous in this view. 

 What is &quot; Integration &quot; ? Why cannot &quot; some,&quot; interpreted as &quot; some only,&quot; 

 yield a scheme of simple, irreducible propositions ? Interpreting &quot; some &quot; in 

 the traditional, indefinite sense, draw the five combinations of Euler s circles : 

 represent them by the numerals i, 2, 3, 4, 5 : set down the symbols for the 

 eight Hamiltonian propositions in a vertical column : and place after each the 

 numeral or numerals which indicate the diagrams compatible with it. Give 

 examples of the U proposition, with their equivalents in the predicative scheme ; 

 also of the Y proposition ; also of the r; proposition. Examine the o&amp;gt; proposi 

 tion. What is a logical equation ? Are our ordinary judgments equations ? 

 Are Hamilton s forms equational ? Suggest an equational method of express 

 ing the four predicative forms. 



CHAP. V. Define logical opposition of propositions. Are all &quot; op- 

 posites &quot; incompatible? Explain the &quot;square of opposition&quot;. State and 

 prove the laws of subalternation. Define contradictory opposition. State 

 and prove its laws. Why is contradiction the most perfect sort of logical 

 opposition ? What are its characteristics ? Has every proposition a con 

 tradictory ? Has any proposition more than one contradictory ? Why is 

 there no mean between two contradictories? Define contrary opposition. 

 State and prove its laws. Compare it with contradictory opposition. There 

 are two ways of disproving a universal : which is the easier and safer ? 

 Have all propositions contraries ? What is material opposition ? Define 

 subcontrary opposition. State and prove its laws. Apply the doctrine of 

 opposition to singulars ; to modals. Summarize the inferences by opposition. 



CHAP. VI. Define immediate inference, eduction. Show how, from 

 the form S-P t seven other forms are derivable. Name the four processes of 

 eduction. Which are fundamental ? Define accurately each process. 

 State the rule for obversion. Connect it with the laws of thought. Does it 

 deserve to be called an inference ? Give some synonyms for obversion. Is 

 &quot; material &quot; obversion an inference ? Distinguish the geometrical from the 

 logical converse. State the rules of conversion. Apply and prove them. 

 Distinguish simple conversion from conversion per accidens. Does A ever 

 admit of simple conversion ? Prove that E and I convert simply. Why 

 has O no converse ? Show that conversion involves real progress of thought. 

 Is the validity of logical conversion self-evident ? Distinguish the partial 

 from the full contrapositive. State the rule for contraposition. Why has I 



