10 ESSAY ON PROBABILITIES. 



up all the vested interests at less than II. a piece,, I am 

 certain to gain ; if at more, I am certain to lose. 1 /. 

 a piece is what I ought to give for each, if I buy all : 

 it is the universal practice to consider that II. a piece is 

 still the value, if I buy a part. To say this is in fact 

 to say that the force of the impression called certainty 

 should, in this case, be considered as made up of 26 

 equal parts, each of which is to be considered as the 

 representative of the impression of probability which a 

 right-minded man would derive from the possession of 

 one ticket. 



On this I have to remark, 1. That so soon as any 

 notion receives the exactness of mathematical language, 

 though it be thereby not altered, objections are taken to 

 it. The reason is, that we frequently not only use ex- 

 pressions which can be rendered quite exact, but also 

 fairly act upon them as if they were exact, but not be- 

 cause we consider them exact. Why does the lottery 

 ticket of the preceding instance bear the character of 

 being exactly worth 11. ? Not as any consequence of 

 the accuracy of the preceding process, supposing it ac- 

 curate, but because we do not know why we should 

 exceed rather than fall short of it. It appears to me 

 that many of our conclusions are derived from this 

 principle, which is called in mathematics the want of 

 sufficient reason. A ball is equally struck in two dif- 

 ferent directions, the table being uniform throughout. 

 In what direction will it move ? In the direction which 

 is exactly between those of the blows. Why ? No posi- 

 tive reason is assignable (experiment being excluded) ; 

 but from the complete similarity of all circumstances on 

 one side and the other of the bisecting direction, it is 

 impossible to frame an argument for the ball going more 

 towards the direction of one blow, which cannot imme- 

 diately be made equally forcible in favour of the other. 

 The conclusion remains, then, balanced between an in- 

 finity of possible arguments, of which we can only see 

 that each has its counterpoise. Now whether we adopt 

 the above conclusion as to probability for its exactness 



