LOGIC AS THE ESSENCE OF PHILOSOPHY S 5 



seems to be the case that we can sometimes know 

 molecular propositions, as in the above instance of the 

 umbrella, when we do not know whether the component 

 atomic propositions are true or false. The practical 

 utility of inference rests upon this fact. 



The next kind of propositions we have to consider are 

 general propositions, such as " all men are mortal," " all 

 equilateral triangles are equiangular." And with these 

 belong propositions in which the word " some " occurs, 

 such as " some men are philosophers " or " some philoso- 

 phers are not wise." These are the denials of general 

 propositions, namely (in the above instances), of " all men 

 are non-philosophers" and "all philosophers are wise." 

 We will call propositions containing the word " some ' 

 negative general propositions, and those containing the 

 word " all ' positive general propositions. These pro- 

 positions, it will be seen, begin to have the appearance 

 of the propositions in logical text-books. But their 

 peculiarity and complexity are not known to the text- 

 books, and the problems which they raise are only 

 discussed in the most superficial manner. 



When we were discussing atomic facts, we saw that we 

 should be able, theoretically, to infer all other truths by 

 logic if we knew all atomic facts and also knew that there 

 were no other atomic facts besides those we knew. The 

 knowledge that there are no other atomic facts is positive 

 general knowledge ; it is the knowledge that " all atomic 

 facts are known to me," or at least " all atomic facts are 

 in this collection " however the collection may be given. 

 It is easy to see that general propositions, such as "all 

 men are mortal," cannot be known by inference from 

 atomic facts alone. If we could know each individual 

 man, and know that he was mortal, that would not enable 

 us to know that all men are mortal, unless we knew that 



