I SECT. 3.] Modes of establishing the Groups or Series. 77 



Let us take a very simple example, that of tossing up a 

 penny. Suppose that I am contemplating a succession of 

 two throws ; I can see that the only possible events are 1 

 HH., HT., TH., TT. So much is certain. We are more 

 over tolerably well convinced from experience that these 

 events occur, in the long run, about equally often. This is 

 of course admitted on all hands. But on the view commonly 

 maintained, it is contended that we might have known the 

 fact beforehand on grounds which are applicable to an indefi 

 nite number of other and more complex cases. The form in 

 which this view would generally be advanced is, that we are 

 enabled to state beforehand that the four throws above men 

 tioned are equally likely. If in return we ask what is meant 

 by the expression equally likely , it appears that there are 

 two and only two possible forms of reply. One of these seeks 

 the explanation in the state of mind of the observer, the 

 other seeks it in some characteristic of the things observed. 



(1) It might, for instance, be said on the one hand, that 

 what is meant is that the four events contemplated are 

 equally easy to imagine, or, more accurately, that our ex 

 pectation or belief in their occurrence is equal. We could 

 hardly be content with this reply, for the further enquiry 

 woulc- immediately be urged, On what ground is this to be 

 believed ? What are the chi acteristics of events of which 

 our expectation is equal ? If we consented to give an answer 

 to this further enquiry, we should be led to the second form 

 of reply, to be noticed directly; if we did not consent we 

 should, it seems, be admitting that Probability was only a 



1 For the use of those not ac- two successive throws of the penny 



quainted with the common notation give head ; HT that the first of 



employed in this subject, it may be them gives head, and the second 



remarked that HH is simply an tail ; and so on with the remaining 



abbreviated way of saying that the symbols. 



