ON COMMON NOTIONS OF PROBABILITY. 121 



necessary connection it is necessary that the two cir- 

 cumstances should always happen together, and that one 

 should never happen without the other. If it should 

 .only be observed that one is very frequently accompanied 

 by the other, we must then inquire into the probability 

 that either may happen without the other. If two 

 events are almost always happening, then it is evident 

 that very frequent coincidence is no evidence of connec- 

 tion., so long as exceptions tell us that there is no neces- 

 sary connection. And even if" we always observe A to 

 be immediately followed by B, it does not immediately 

 follow that they are necessarily connected. We must 

 remember that the phenomenon is this our perception 

 of A is immediately followed by our perception of B. 

 This may arise in different ways, as follows. 



1. A may make B necessarily follow it ; that is, the 

 common deduction from the phenomena may be true. 



2. Our perception of A may make B follow. This 

 is the case with regard to all effects produced upon our 

 own minds by A. 



3. A itself may make our perception of B follow. 

 The latter may be always happening, but it may require 

 the arrival of A to make us see it. 



4. Our perception of A may make our perception of 

 B follow ; that is, B may be always happening, 'but it 

 may need both the arrival of A and our knowledge of 

 that arrival to make us see B ; or the circumstances 

 which favour our perception of A may be the same, or 

 have necessary connection with, those which do the same 

 forB. 



5. It may be B which is the antecedent event ; but 

 our perception of A, the consequence of B^ may be ne- 

 cessary to our perception of B itself. 



We sometimes, for example, note what takes place 

 from the time A happens, and compare it with previous 

 events, merely because the arrival of A suggests the 

 comparison. In many instances we do this correctly, 

 and merely for convenience ; but whenever the events 



