146 THE PRINCIPLES OF SCIENCE. 



Induction of Simple Identities. 



Many of the most important laws of nature are ex- 

 pressible in the form of simple identities, and I can at once 

 adduce them as examples to illustrate what I have said 

 of the difficulty of the inverse process of induction. There 

 are many cases in which two phenomena are usually con- 

 joined. Thus all gravitating matter is exactly coincident 

 with all matter possessing inertia ; where one property 

 appears, the other likewise appears. All crystals of the 

 cubical system, are all the crystals which do not doubly 

 refract light. All exogenous plants are, with some ex- 

 ceptions, those which have two cotyledons or seed-leaves. 



A little reflection will show that there is no direct and 

 infallible process by which such complete coincidences m ;y 

 be discovered. Natural objects are aggregates of many 

 qualities, and any one of those qualities may prove to be 

 in close connection with some others. If each of a 

 numerous group of objects is endowed with a hundred 

 distinct physical or chemical qualities, there will be no 

 less than -^(100x99) or 4950 pairs of qualities, which 

 may be connected, and it will evidently be a matter of 

 great intricacy and labour to ascertain exactly which 

 qualities are connected by any simple law. 



One principal source of difficulty is that the finite powers 

 of the human mind are not sufficient to compare by a 

 single act any large group of objects with another large 

 group. We cannot hold in the conscious possession of the 

 mind at any one moment more than five or six different 

 ideas. Hence we must treat any more complex group by 

 successive acts of attention. The reader will perceive by 

 an almost individual act of comparison that the words 

 Roma and Mora contain the same letters. He may 

 perhaps see at a glance whether the same is true of 

 Causal and Casual, and of Logica and Caligo. To assure 



