OPINION AND PROBABILITY 273 



an inseparable portion of the experience, or even exert a positive 

 causal influence on the general result the die itself and its natural 

 properties, for example, yet they contribute precisely in the same 

 way to every possible alternative result, and are therefore rightly 

 called &quot; indifferent &quot; causes of any one result in particular. We 

 know, too, that in each particular experience there are some ante 

 cedents whose combination determines this particular result rather 

 than any other. But we do not know what these are, or, at least, 

 how exactly they will combine. And it is our ignorance on this 

 point that allows and obliges us to estimate the &quot; chances &quot; or 

 &quot; probabilities &quot; which the indifferent antecedents have of being 

 united in a given case with a given concrete result out of many 

 possible alternative ones. In throwing dice, for example, we 

 know that the die itself so long as it is not &quot; loaded &quot; for the 

 purpose of giving it a &quot; natural inclination &quot; to fall on some 

 particular face is equally indifferent to each of the six faces. 

 Furthermore, we are unable either to control, or estimate, or re 

 duce to any law, the actual combination of the numerous influences 

 that determine a particular result forces which emanate with 

 varying intensity from the thrower at each successive throw, and 

 forces which, like gravity, operate independently of him. 1 



There is a second condition to which our data must conform, 

 before we can apply to them any definite rules for the estimation 

 of probability. The same general set of conditions and ante 

 cedents must be present and operative throughout the whole 

 region of time and space from which these data are drawn. An 



1 &quot; Take such a simple example as that of dropping a Stone to the ground. We 

 say, in accordance with the common expression of the causal relation, that if the 

 stone be dropped again just as it was before, it will fall on the same spot. True ; and 

 for most practical purposes the thing can be done readily enough ; but if perfect 

 quantitative accuracy were required we should soon find that we had undertaken a 

 troublesome task. The stone must be held in exactly the same position as before, 

 for the friction of the air influences its fall ; it must be dropped from exactly the same 

 height and over the same spot on the floor ; the atmospheric currents, nay the very 

 temperature of the air, must remain unchanged ; and so on indefinitely with further 

 demands, as quickly as those already formulated were assumed to be satisfied.&quot; 



&quot; If it be urged that all this is merely useless subtlety the retort is simple, and, I 

 think, conclusive, viz. that many millions of pounds have changed hands in accord 

 ance with these conditions of things. It is simply because we cannot do the same 

 thing over again, or calculate how far we shall fall short of doing so, even when our 

 instrument in hand is purposely made of as accurate a shape as possible, that the 

 roulette and the die can be employed for gambling purposes. So impossible is it 

 found to be to spin a top twice with the same velocity, or to discharge a cube twice 

 from the same position, that the fanatics of the gaming table never dream of pre 

 dicting results from this side, but put their trust in appeals to statistics and other 

 such considerations.&quot; VENN, Empirical Logic, pp. 65, 66 ; cf. ibid., pp. 100, 105. 

 VOL. II. 18 



