352 PERSONAL PREPARATION FOR RESEARCH. 



affirmative. Thus c all metals are heat-conductors ' dis- 

 proves ' no metals are heat-conductors,' and ' some metals 

 are not heat-conductors,' but proves 'some metals are 

 heat-conductors.' Similarly a universal negative disproves 

 both a universal affirmative and a particular one, but 

 proves a particular negative ; thus ' no metals are salts ' 

 disproves ' all metals are salts,' and 6 some metals are salts,' 

 but proves ' some metals are not salts.' Also a particular 

 negative disproves a universal affirmative ; thus ' some 

 metals are ductile ' disproves ' no metals are ductile ' ; and 

 6 some metals are not ductile ' disproves ' all metals are 

 ductile.' A particular affirmative leaves doubtful a uni- 

 versal affirmative and a particular negative ; thus { some 

 elementary bodies are metals ' renders uncertain ' all ele- 

 mentary bodies are metals,' and ' some elementary bodies are 

 not metals.' And similarly, a particular negative makes 

 doubtful a universal negative and a particular affirmative ; 

 thus, ' some elementary bodies are not metals,' leaves un- 

 certain ' all elementary bodies are not metals,' and ' some 

 elementary bodies are metals.' A universal affirmative is 

 best disproved by a particular negative, and a universal 

 negative by a particular affirmative, and vice versa ; and 

 anyone who asserts a universal proposition must either 

 explain or disprove any exception brought against it. A 

 particular affirmative does not disprove a particular nega- 

 tive, nor vice versa ; for instance, c some metals are ductile ' 

 does not disprove ' some metals are not ductile,' nor the 

 reverse. 



We may prove a truth either by proving its equal, 

 disproving its contradictory or negative, or by proving 

 that of all possible alternatives it cannot be anything else ; 

 or instead of simply proving its equal, we may prove it to 

 be identical with, or equivalent to, or included in something 

 known to be true, or we may combine these several 



