To assign the antecedent probability of any proposition, may be a matter of difficulty or impossibility, and one with which logic and the theory of probability have little concern. From the general body of science in our possession, we must in each case make the best judgment we can. But in the absence of all knowledge the probability should be considered = 1/2, for if we make it less than this we incline to believe it false rather than true. Thus, before we possessed any means of estimating the magnitudes of the fixed stars, the statement that Sirius was greater than the sun had a probability of exactly 1/2; it was as likely that it would be greater as that it would be smaller; and so of any other star. This was the assumption which Michell made in his admirable speculations.[119] It might seem, indeed, that as every proposition expresses an agreement, and the agreements or resemblances between phenomena are infinitely fewer than the differences (p. 44), every proposition should in the absence of other information be infinitely improbable. But in our logical system every term may be indifferently positive or negative, so that we express under the same form as many differences as agreements. It is impossible therefore that we should have any reason to disbelieve rather than to believe a statement about things of which we know nothing. We can hardly indeed invent a proposition concerning the truth of which we are absolutely ignorant, except when we are entirely ignorant of the terms used. If I ask the reader to assign the odds that a “Platythliptic Coefficient is positive” he will hardly see his way to doing so, unless he regard them as even. [119] *Philosophical Transactions* (1767). Abridg. vol. xii. p. 435. The assumption that complete doubt is properly expressed by 1/2 has been called in question by Bishop Terrot,[120] who proposes instead the indefinite symbol 0/0; and he considers that “the *à priori* probability derived from absolute ignorance has no effect upon the force of a subsequently admitted probability.” But if we grant that the probability may have any value between 0 and 1, and that every separate value is equally likely, then *n* and 1 - *n* are equally likely, and the average is always 1/2. Or we may take *p* . *dp* to express the probability that our estimate concerning any proposition should lie between *p* and *p* + *dp*. The complete probability of the proposition is then the integral taken between the limits 1 and 0, or again 1/2. [120] *Transactions of the Edinburgh Philosophical Society*, vol. xxi. p. 375. *Difficulties of the Theory.*