422 THE SCIENCE OF LOGIC 



no contrapositive ? How is the reciprocal of S a P, -viz. P a S, established in 

 inductive inquiries? State the rules for inversion. Why have particulars 

 no inverses ? On what assumptions, as to the existence of the classes S, /*, 

 5, and /*, in the sphere of reference of the proposition, are those various in 

 ferences valid ? What is inference by added determinants ? Is it formal or 

 material? Give some valid, and some invalid, examples. Define inference 

 by complex conception, and immediate inference by converse relation. 

 Derive all the immediate inferences you can, both by way of opposition and 

 by way of eduction, from the following propositions : (i) All logicians are 

 wise ; (2) Discretion is the better part of valour ; (3) Any fool can ask the 

 question ; (4) Not every wise man can answer the question ; (5) No boy was 

 ever an old man ; (6) Few men live a century ; (7) All solids contain carbon ; 

 (8) Not to all men is it given to be philosophers ; (9) The soul does not think 

 always; (10) All trees are not pines; (n) Not all whom we admire deserve 

 our admiration 5(12) All cannot receive this saying ; (13) Two straight lines 

 cannot enclose a space ; (14) Many rules of grammar overload the memory ; 

 (15) Nemo mortalium omnibus horis sapit. 



CHAP. VII. In what sense does every judgment imply the existence oi 

 its &quot;subject&quot;? Is this reference to an &quot;objective sphere&quot; implied in the 

 intelligible use of every term ? Does the use of a term in a proposition not 

 only imply the existence of some sphere of denotation, but also the actual 

 existence of the object denoted, in that sphere? Is this a question for logic 

 to deal with, and why? What assumptions as to existence justify the tradi 

 tional doctrine on Opposition and Eduction? How is the &quot;universe of 

 discourse,&quot; to which a judgment refers, to be determined ? Does logic decide 

 the nature of these spheres of reference, or of &quot;existence &quot; in these spheres? 

 State the question of existential import. Does it admit of alternative answers ? 

 What considerations should guide us in the choice of an interpretation ? 

 Discuss fully the influence of four distinct suppositions : (a) on Opposition; 

 (b) on Eduction. What does ordinary usage tell us about the existential 

 import (a] of universals ; (b) of particulars ? Give some reasons for adopt 

 ing the view that particulars imply, and universals do not imply, the ex 

 istence of their subjects. Do modal propositions usually imply the existence 

 of their subjects ? Can we infer the assertoric from the modal, or vice versa ? 

 Discuss the relation between the proposition All S is P and All not-S is P. 

 Can you derive a valid inverse from the proposition, All human actions are 

 foreseen by the Deity? On the assumption made in 129, examine the 

 validity of the following inferences: (a) All S is P and Some R is not 5, 

 therefore Some not-S is not P ; (b) All S is P and Some R is not /*, there 

 fore Some not-S is not P. 



CHAP. VIII. What are the two parts of an &quot;//&quot; proposition called ? 

 What is the function of such propositions ? On what does their truth or 

 falsity depend? Show how every &quot;If&quot; judgment rests on an underlying 

 categorical affirmation or denial. Distinguish two classes of &quot;//&quot; judg 

 ments, giving the main characteristics, with examples, of each class. Is the 

 difference between them fundamental ? Can all &quot;//&quot;&quot; judgments be reduced 

 to the form, &quot; If S is M it is P &quot; ? How does this form show the relation of 

 the &quot;If&quot; judgment to the categorical judgment? Can the proposition &quot; //&quot; 

 this S is M it is P &quot; be expressed categorically ? Whether does &quot;//&quot; ex- 



