The value of the theory consists in correcting and guiding our belief, and rendering our states of mind and consequent actions harmonious with our knowledge of exterior conditions. [110] *Formal Logic*, p. 172. This objection has been clearly perceived by some of those who still used quantity of belief as a definition of probability. Thus De Morgan adds--“Belief is but another name for imperfect knowledge.” Donkin has well said that the quantity of belief is “always relative to a particular state of knowledge or ignorance; but it must be observed that it is absolute in the sense of not being relative to any individual mind; since, the same information being presupposed, all minds *ought* to distribute their belief in the same way.”[111] Boole seemed to entertain a like view, when he described the theory as engaged with “the equal distribution of ignorance;”[112] but we may just as well say that it is engaged with the equal distribution of knowledge. [111] *Philosophical Magazine*, 4th Series, vol. i. p. 355. [112] *Transactions of the Royal Society of Edinburgh*, vol. xxi. part 4. I prefer to dispense altogether with this obscure word belief, and to say that the theory of probability deals with *quantity of knowledge*, an expression of which a precise explanation and measure can presently be given. An event is only probable when our knowledge of it is diluted with ignorance, and exact calculation is needed to discriminate how much we do and do not know. The theory has been described by some writers as professing *to evolve knowledge out of ignorance*; but as Donkin admirably remarked, it is really “a method of avoiding the erection of belief upon ignorance.” It defines rational expectation by measuring the comparative amounts of knowledge and ignorance, and teaches us to regulate our actions with regard to future events in a way which will, in the long run, lead to the least disappointment. It is, as Laplace happily said, *good sense reduced to calculation*. This theory appears to me the noblest creation of intellect, and it passes my conception how two such men as Auguste Comte and J. S. Mill could be found depreciating it and vainly questioning its validity. To eulogise the theory ought to be as needless as to eulogise reason itself. *Fundamental Principles of the Theory.*