12 THE PRINCIPLES OF SCIENCE. [CHAP. 



Experience gives us the materials of knowledge : induction 

 digests those materials, and yields us general knowledge. 

 When we possess such, knowledge, in the form of 

 general propositions and natural laws, we can usefully 

 apply the reverse process of deduction to ascertain the 

 exact information required at any moment. In its ultimate 

 foundation, then, all knowledge is inductive in the sense 

 that it is derived by a certain inductive reasoning from 

 the facts of experience. 



It is nevertheless true, and this is a point to which 

 insufficient attention has been paid, that all reasoning 

 is founded on the principles of deduction. I call ^ in 

 question the existence of any method of reasoning which 

 can be carried on without a knowledge of deductive pro- 

 cesses. I shall endeavour to show that induction is really 

 the inverse process of deduction. There is no mode of 

 ascertaining the laws which are obeyed in certain pheno- 

 mena, unless we have the power of determining what 

 results would follow from a given law. Just as the 

 process of division necessitates a prior knowledge of multi- 

 plication, or the integral calculus rests upon the obser- 

 vation and remembrance of the results of the differential 

 calculus, so induction requires a prior knowledge of 

 deduction. An inverse process is the undoing of the 

 direct process. A person who enters a maze must either 

 trust to chance to lead him out again, or he must carefully 

 notice the road by which he entered. The facts furnished 

 to us by experience are a maze of particular results ; we 

 might by chance observe in them the fulfilment of a law, 

 but this is scarcely possible, unless we thoroughly learn 

 the effects which would attach to any particular law. 



Accordingly, the importance of deductive reasoning is 

 doubly supreme. Even when we gain the results of in- 

 duction they would be of no use unless we could deduc- 

 tively apply them. But before we can gain them at all 

 we must understand deduction, since it is the inversion of 

 deduction which constitutes induction. Our first task in 

 this work, then, must be to trace out fully the nature of 

 identity in all its forms of occurrence. Having given any 

 series of propositions we must be prepared to develop 

 deductively the whole meaning embodied in them, and 

 the whole of the consequences which flow from them. 



