3. For instance, Sir J. F. Stephen explains it by drawing a distinction between chances and probabilities, which he says that Butler has confused together; "the objection that very ordinary proof will overcome a presumption of millions to one is based upon a confusion between probabilities and chances. The probability of an event is its capability of being proved. Its chance is the numerical proportion between the number of possible cases--supposed to be equally favourable--favourable to its occurrence; and the number of possible cases unfavourable to its occurrence" (_General view of the Criminal Law of England_, p. 255). Donkin, again (_Phil. Magazine_, June, 1851), employs the terms improbability and incredibility to mark the same distinction. 4. In the extreme case of the witness himself merely guessing, or being as untrustworthy as if he merely guessed, the two stories will of course stand on precisely the same footing. This case will be noticed again in Chapter XVII. It may be remarked that there are several subtleties here which cannot be adequately noticed without some previous investigation into the question of the credibility of witnesses. 5. According to Dante, something resembling this prevailed amongst the occupants of the _Inferno_. The cardinals and others whom he there meets are able to _give_ information about many events which were yet to happen upon earth, but they had to _ask_ it for many events which actually had happened. CHAPTER XIII. _ON THE CONCEPTION AND TREATMENT OF MODALITY._ 1. The reader who knows anything of the scholastic Logic will have perceived before now that we have been touching in a variety of places upon that most thorny and repulsive of districts in the logical territory;--modality. It will be advisable, however, to put together, somewhat more definitely, what has to be said upon the subject. I propose, therefore, to devote this chapter to a brief account of the principal varieties of treatment which the modals have received at the hands of professed logicians. It must be remarked at the outset that the sense in which modality and modal propositions have been at various times understood, is by no means fixed and invariably the same. This diversity of view has arisen partly from corresponding differences in the view taken of the province and nature of logic, and partly from differences in the philosophical and scientific opinions entertained as to the constitution and order of nature. In later times, moreover, another very powerful agent in bringing about a change in the treatment of the subject must be recognized in the gradual and steady growth of the theory of Probability, as worked out by the mathematicians from their own point of view.