A man in good health would doubtless like to know whether he will be alive this time next year. The fact will be settled one way or the other in due time, if he can afford to wait, but if he wants a present decision, Statistics and the Theory of Probability can alone give him any information. He learns that the odds are, say five to one that he will survive, and this is an answer to his question as far as any answer can be given. Statisticians are gradually accumulating a vast mass of data of this general character. What they may be said to aim at is to place us in the position of being able to say, in any given time or place, what are the odds for or against any at present indeterminable fact which belongs to a class admitting of statistical treatment. Again, outside the regions of statistics proper--which deal, broadly speaking, with events which can be numbered or measured, and which occur with some frequency--there is still a large field as to which some better approach to a reasoned intensity of belief can be acquired. What will be the issue of a coming war? Which party will win in the next election? Will a patient in the crisis of a given disease recover or not? That statistics are lying here in the background, and are thus indirectly efficient in producing and graduating our belief, I fully hold; but there is such a large intermediate process of estimating, and such scope for the exercise of a practised judgment, that no direct appeal to statistics in the common sense can directly help us. In sketching out therefore the claims of an Ideal condition of knowledge, we ought clearly to include a due apportionment of belief to every event of such a class as this. It is an obvious defect that one man should regard as almost certain what another man regards as almost impossible. Short, therefore, of certain prevision of the future, we want complete agreement as to the degree of probability of every future event: and for that matter of every past event as well. Technically speaking, if we extend the name Modality (see p. 78) to any qualification of the certainty of a statement of belief, what Dr. Venn here desiderates, as he has himself suggested, is a more exact measurement of the Modality of propositions. We speak of things as being certain, possible, impossible, probable, extremely probable, faintly probable, and so forth: taking certainty as the highest degree of probability[2] shading gradually down to the zero of the impossible, can we obtain an exact numerical measure for the gradations of assurance?