Page:Mind (Old Series) Volume 9.djvu/239

THE PHILOSOPHY OF CHANCE. 227 different amounts of belief which we entertain upon different events, and which are recognised by various phrases in common use, have undoubtedly some meaning ; but the greater part of their meaning, and certainly their only justi- fication, are to be sought in the series of corresponding events to which they belong ; in regard to which it may be shown that far more events are capable of being referred to a series than might be supposed at first sight." In short, the author commands approbation as a judge, though as an advocate he may be needlessly polemical ; his conclusion seems correct, though his arguments prove too much. So far we have been concerned with the simplest type of probability ; the fact of a simple and perfect statistical uni- formity, such as occurs in games of chance, together with the partial belief accompanying that known fact. We have looked at the outside, and we have endeavoured to peer into the inside, of the simple unit-cell, by the multiplication of which the science of pure probabilities is built up. If this were a mathematical treatise, it would be proper in the next place to consider those compound structures, ascending through the first seven principles of Laplace. But the com- plexities thus presented would be of a merely mathematical character ; for, as Mr. Venn points out, inverse probability, qua inverse, does not differ essentially from the simple species ; a philosophical distinction arises, when the purity of the type above delineated becomes mixed with the imper- fections of real existence. Suppose, for instance, the regu- larity of our die has not been fully established by actual experience ; that we have only some reason to believe that it is not weighted, or only perhaps no reason to believe that it is weighted more upon one side than another. In con- templating this case let us endeavour to keep separate what may be called the outside view presented by the considera- tion of what Mr. Venn calls a ' series,' and the inside or sub- jective aspect of partial belief about the result of any par- ticular throw. The more objective view does not at first sight present any particular difficulty, any other difficulty than is pre- sented by ah 1 applications of mathematical conceptions to real existence. In such applications there is ever, as Mill has well pointed out, some admixture of assumption and hypothesis. Even geometrical axioms must be taken cniii grano. The fine remark of Burke, that the lines of morality are broad as well as long, is true also in some degree of physi- cal lines. Constants ascertained only to a certain number of decimal places are employed. Nay, we must sometimes be