224 EXAMPLE OF ANALYSIS. [CHAP. XIV. 



4. It would thus be easy, even from the limited system of 

 premises before us, to deduce a great variety of additional infe- 

 rences, involving, in the conditions which are given, any pro- 

 posed combinations of the elementary propositions. If the con- 

 dition is one which is inconsistent with the premises, the fact 

 will be indicated by the form of the solution. The value which 

 the method will assign to the combination of symbols expressive 

 of the proposed condition will be 0. If, on the other hand, the 

 fulfilment of the condition in question imposes no restriction upon 

 the propositions among which relation is sought, so that every 

 combination of those propositions is equally possible, the fact 

 will also be indicated by the form of the solution. Examples 

 of each of these cases are subjoined. 



If in the ordinary way we seek the consequences which would 

 flow from the condition that matter is a necessary being , and at 

 the same time that motion exists, as aifecting the Propositions, 

 The world is merely material, and without a presiding intelligence, 

 and, Gravitation is necessarily present, we shall obtain the equa- 

 tion 



xw = 0, 



which indicates that the condition proposed is inconsistent with 

 the premises, and therefore cannot be fulfilled. 



If we seek the consequences which would flow from the con- 

 dition that Matter is not a necessary being, and at the same time 

 that Motion does exist, with reference to the same elements as 

 above, viz., the absence of a presiding intelligence, and the neces- 

 sity of gravitation, we obtain the following result, 



which might literally be interpreted as follows : 



If matter is not a necessary being, and motion exists, then 

 either the world is merely material and without a presiding intel- 

 ligence, and gravitation is necessary, or one of these two results fol- 

 lows without the other, or they both fail of being true. Wherefore 

 of the four possible combinations, of which some one is true of 

 necessity, and of which of necessity one only can be true, it is 



