272 THE SCIENCE OP LOGIC 



any particular case we do not know what conditions are operative, we cannot 

 tell, on the one hand, what result will appear, nor, on the other, can we say 

 positively what conditions have produced a certain given event. In such cases 

 we are accustomed to speak of the occurrence as due to chance. But our whole 

 conception of the unity of nature forbids the idea that any element of reality 

 can be really casual. [The turning of any particular face, for example, is casual 

 relatively to the die itself, in the sense that the die itself contributes nothing to 

 wards this particular result ; and casual relatively to the whole concrete cast 

 of the die, in the sense that we do not know what combination of antecedents 

 brings about the result in the concrete case ; but not, of course, in the sense 

 that the result has no determining antecedents ; it must have them, by the prin 

 ciple of causality. Hence the author continues :] Every detail is, in the strictest 

 sense, necessary, and determined absolutely by conditions all is causal, nothing 

 casual [for casual here means, equivalently, causeless ]. Were our know 

 ledge complete, then, the idea of chance would disappear ; it is due solely to 

 the imperfection of that knowledge. This imperfection is, of course, greater 

 in some cases than in others ; it may affect the event as a whole, or it may 

 only affect some particular aspect of it. But, even with imperfect knowledge, 

 we are often called upon to come to a decision or to act. The question then 

 arises as to what we ought rationally to expect.&quot; 



265. CONDITIONS FOR THE MATHEMATICAL ESTIMATION 

 OF PROBABILITY. We have now seen that &quot;chance &quot; or &quot; coinci 

 dence &quot; connotes simply the possession of imperfect or incomplete 

 knowledge about the antecedents or causes of a phenomenon. 

 This is the first condition for the application of a calculus of 

 probability to the data of our experience : a knowledge sufficient 

 to assure us, for example, that a phenomenon must happen in 

 some one or other of a definite number of alternative ways, but 

 insufficient to assure us in which of these ways it will happen. 

 We know, for instance, that in any single throw of a die the 

 laws of gravity, inertia, motion, elasticity, action and reaction, the 

 antecedent position of the die and of the box, the intensity, direc 

 tion, and duration of each rattle, and innumerable other unknown 

 and inappreciable influences all conspire together for the pro 

 duction of the actual result of this particular throw. But we are 

 conscious, on the other hand, that the combination of factors de 

 termining this particular result, rather than any other, surpasses 

 our comprehension. x We know the general set of antecedents which 

 gives rise to some particular result out of a number of possible 

 alternative results. We recognize that while many of them are 



1 Cf. WBLTON, op. cit., p. 167 : &quot; For example, if a penny is tossed it will fall 

 with either head or tail uppermost. Now, which will be uppermost in any particular 

 throw will be exactly determined by such conditions as the position of the coin at 

 starting, how it is grasped in the fingers, the force and direction of the twist, etc. 

 But what special form these conditions will take we are totally ignorant. ...&quot; 



