228 THE PRINCIPLES OF SCIENCE. 



eulogise the theory is as needless as to eulogise reason 

 itself. 



Fundamental Principles of the TJieory. 



The calculation of probabilities is really founded, as 

 I conceive, upon the principle of reasoning set forth in 

 preceding chapters. We must treat equals equally, and 

 what we know of one case may be affirmed of every 

 other case resembling it in the necessary circumstances. 

 The theory consists in putting similar cases upon a par, 

 and distributing equally among them whatever know- 

 ledge we may possess. Throw a penny into the air, and 

 consider what we know with regard to its mode of falling. 

 We know that it will certainly fall upon a flat side, so 

 that either the head or tail will be uppermost, but as 

 to whether it will be head or tail, our knowledge is 

 equally divided. Whatever we know concerning head, 

 we know as much concerning tail, so that we have no 

 reason for expecting one more than the other. The least 

 predominance of belief to either side would be irrational, 

 as it would consist in treating unequally things of which 

 our knowledge is equal. 



The theory does not in the least require, as some 

 writers have erroneously supposed, that we should first 

 ascertain by experiment the equal facility of the events 

 we are considering. So far as we can examine and 

 measure the causes in operation, events are removed 

 out of the sphere of probability. The theory comes into 

 play where ignorance begins, and the knowledge we 

 possess requires to be distributed over many cases. 

 Nor does ' the theory show that the coin will fall as 

 often on one side as the other. It is almost impossible 

 that this should happen, because some inequality in the 

 form of the coin, or some uniform manner in throwing 

 it up, is almost sure to occasion a slight preponderance 



