226 F. Y. EDGEWOETH: fragment of the Calculus of Hedonics ; an ill-defined tract of speculation irregularly grouped about a central spot, the theory of exchange, which is distinguished from the general phenomena of human life by the same attribute as the statistically measured belief, namely a certain quasi-mathe- matical precision. (5) Whereas, it is said, full belief about an event is either verified or disproved by the event, fractional belief can only be justified or disproved by a series of events. There is a sort of Greek subtlety about this airopia, by which I must confess myself baffled. I may observe, perhaps, that in cases of very high probability the correctness of the fraction may very nearly be disproved by even a single event ; that in order to verify the fraction there is perhaps required, not a whole series, but only as many terms as there are units in the denomination of the fraction. If the fraction is two- thirds, and if out of three trials the event occurs twice, may we say that the fraction is, not indeed proved, but in some sense verified ? (6) It is finally objected that the phenomenon of a fraction being assigned to belief may be accounted for otherwise than on the supposition that the quantity of belief is measurable. The fraction is the measure of the quantity of advantage which Laplace calls esptfrance. Thus if p be the fraction which expresses the probability of an event, each occur- rence of which brings me 1, and N the (large) number of trials to be made, then pN is the value of my expecta- tion. There is no doubt a large portion of truth in this explanation. Still it may be observed that, upon theories which are current that belief is of the nature of volition and that all volition is determined by the prospect of pleasure, the explanation propounded does not so much destroy as fulfil the theory that the fraction in question is the measure of quantity of belief. If belief cannot be identified with volition, then indeed those who dissent from Mr. Venn will have to postulate a sort of pre-established harmony between the distinct processes of volition and intellect. Yet this postulate cannot be regarded as very extravagant,, considering the admitted interdependence of the different departments of mind, which, as Aristotle says of his evepyeia and r)86vrj, " seem to be joined together and not to admit of separation." To resolve such distinctions exceeds the range of the present observer's metaphysical microscope. I seem to see that gradations of belief are more capable of precision than some of Mr. Venn's arguments admit. Yet I cannot refuse assent to his summing up. " The
