200 THE PRINCIPLES OF SCIENCE. [CHAP. 



of belief upon ignorance." It defines rational expectation 

 by measuring the comparative amounts of knowledge and 

 ignorance, and teaches us to regulate our actions with 

 regard to future events in a way which will, in the long 

 run, lead to the least disappointment. It is, as Laplace 

 happily said, good sense reduced to calculation. This theory 

 appears to me the noblest creation of intellect, and it 

 passes my conception how two such men as Auguste Comte 

 and J. S. Mill could be found depreciating it and vainly 

 questioning its validity. To eulogise the theory ought to 

 be as needless as to eulogise reason itself. 



Fundamental Principles of the Theory. 



The calculation of probabilities is really founded, as I 

 conceive, upon the principle of reasoning set forth in pre- 

 ceding chapters. We must treat equals equally, and what 

 we know of one case may be affirmed of every case 

 resembling it in the necessary circumstances. The theory 

 consists in putting similar cases on a par, and distributing 

 equally among them whatever knowledge we possess. 

 Throw a penny into the air, and consider what we know 

 with regard to its way of falling. We know that it will 

 certainly fall upon a side, so that either 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 also 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; it would consist in treating unequally things 

 of which our knowledge is equal. 



The theory does not require, as some writers have 

 erroneously supposed, that we should first ascertain by 

 experiment the equal facility of the events we are con- 

 sidering. 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 ignor- 

 ance 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 the 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 



