CONTRADICTORY AND EQUIVALENT PROPOSITIONS. 89 



Of two sub-contrary ones, both may be true, and one 

 only can be false. 



Equivalent propositions are those which contain the 

 same kind and amount of meaning ; thus ' All metals are 

 some heat-conductors ' is equivalent to ' Some heat-con- 

 ductors are all metals.' There is no method or rule by 

 means of which the exact equivalents of propositions can 

 in all cases be definitely ascertained, partly because of 

 want of precision in the meaning of terms ; and it is 

 sometimes difficult to tell what is included in a given 

 term or idea, and therefore also what is included or not in 

 a proposition containing it ; for instance, does the idea of 

 6 all metals' include that of a mixture of metals ? 



The degree of equivalency (and, conversely, that of in- 

 consistency) of propositions is an important point to be 

 considered when we have to draw inferences from them ; 

 and as affirmative truths are usually of more value than 

 negative ones, so a knowledge of the degree of equivalency 

 or agreement of propositions is more important usually than 

 that of their degree of inconsistency. Propositions may be 

 classed as a quantitative series in accordance with these 

 degrees, from those which are entirely consistent to those 

 which are wholly inconsistent, somewhat as follows : 



1. Equivalent, or those which entirely agree. 



2. Inferrible agree in part only. 



3. Consistent have no relation. 



4. Contrary disagree in part only. 



5. Contradictory entirely disagree. 



Logic of quality only deals either with all or none ; 

 but as an idea or thing may agree or disagree with 

 another idea or thing in every intermediate degree, the 

 quantification of ideas and propositions is a very important 

 matter. In the proposition 4 Metals are heat- conductors ' 



^lTY) 



.aK /J 



