MODES OF TRANSFORMING PROPOSITIONS. 339 



When the facts from which we draw our inferences are 

 new ones, as in the case of new observations, and of new 

 results obtained by means of experiments, then the infer- 

 ences we draw from them also contain new knowledge. 

 Even when known scientific facts are treated in a 

 similar manner, we are sometimes led to new and unex- 

 pected conclusions. In other cases, where the existing 

 facts are not in themselves sufficient, we are often led by 

 a similar process to form new hypotheses, and thus to sus- 

 pect the existence of new truths, which have to be proved 

 by additional experiments or observations. 



When we transform a proposition into new ones, as in 

 the instances given, we must: 1st, preserve its quality of 

 affirmative or negative ; and, 2nd, not distribute (or take 

 universally) a term in the converted proposition, unless it 

 was distributed in the original. For instance, we may 

 convert a universal affirmative proposition (see p. 88) 

 such as, ' all gases are ponderable substances,' into c some 

 ponderable substances are gases,' but not into 'all ponder- 

 able substances are gases,' because the original proposition 

 did not say anything about ' all ponderable substances,' 

 and we should therefore break the second rule. We may 

 also transform a particular affirmative proposition, such as 

 6 some gases are transparent substances' into 'some trans- 

 parent substances are gases,' because both the terms in the 

 original and in the converted propositions were undistri- 

 buted. Or we may convert a universal negative one, such 

 as fc no metals are salts,' into ' no salts are metals,' because 

 both the terms in both the propositions were distributed. 

 We may also transform a universal affirmative proposition, 

 such as, ' all metals are conductors of heat,' into ' all non- 

 conductors of heat are not metals,' because ' conductors of 

 heat ' include all the metals, and therefore any non-conduc- 

 tors must be not metals. We may further change a uni- 



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