272 THE SCIENCE OF LOGIC 



we may doubt whether that is the meaning of the proposition. If it were, 

 the latter would probably be expressed, &quot;If a man plays recklessly he 

 always loses&quot;. If the original proposition be interpreted as A, how shall 

 we classify the form just stated ? 



137. EDUCTIONS FROM CONDITIONAL PROPOSITIONS. Tak 

 ing antecedent and consequent in the same way as we have taken 

 subject and predicate in the categorical, we can derive the same 

 eductions from a conditional as from the corresponding cate 

 gorical. 



Take the A proposition, If any S is M, that S is P. The 

 obverse will be got by changing the quality both of the proposi 

 tion itself and of its consequent. The form arrived at will be awk 

 ward : If any S is M, it does not happen that that S is not P &quot; ; 

 but the obverse is needed mainly for the contrapositive and the 

 inverse. In conversion, the original consequent will be the new 

 antecedent and the original antecedent will be the new conse 

 quent. 1 A converts to I. Hence the converse of the example 

 given above will be &quot; If an S is P, sometimes that S is M&quot;. 

 The contrapositive which is the most important eduction from 

 A will be &quot;If any S is not P, that S is not M&quot;. The inverse 

 will be &quot; If an S is not M, then sometimes it is not P &quot;. 



If the A proposition, &quot;If S is M it is P&quot; be interpreted 

 modally (to mean &quot; If S is M it must be P &quot;), its converse will be 

 &quot; If S is P it may be M&quot; ; its contrapositive &quot; // 5 is not P it 

 cannot be M &quot; ; its inverse &quot; If S is not M it need not be P &quot;. 



The conditional propositions, E, I, and O, yield inferences 

 analogous to the corresponding categoricals, just as in the case 

 of A. These inferences 2 illustrate the two rules commonly given 

 in scholastic text-books on logic : 



(1) Affirmata conditione affirmari potest conditionatum, sed 



non vice versa ; 



(2) Negato conditionato negari potest conditio, sed non vice 



versa. 



The student is recommended to take the following or some 

 other concrete examples, and to work out all the eductions from 

 each, firstly in the quantified, denotative, or assertoric form, and 

 secondly in the abstract, connotative, or modal form : 



1 The most important converse is the simple converse of E. &quot; If any S is M 

 that S is not P &quot; .- &quot; If any S is P that S is not M &quot;. 



a The validity of these inferences is influenced by the various suppositions 

 regarding existential import in precisely the same way as in the case of categoricals. 



