It is generally supposed that Boole adopted the second view, and treated logic as an application of algebra, a special case of analytical reasoning which admits only two quantities, unity and zero. It is not easy to ascertain clearly which of these views really was accepted by Boole. In his interesting biographical sketch of Boole,[88] the Rev. R. Harley protests against the statement that Boole’s logical calculus imported the conditions of number and quantity into logic. He says: “Logic is never identified or confounded with mathematics; the two systems of thought are kept perfectly distinct, each being subject to its own laws and conditions. The symbols are the same for both systems, but they have not the same interpretation.” The Rev. J. Venn, again, in his review of Boole’s logical system,[89] holds that Boole’s processes are at bottom logical, not mathematical, though stated in a highly generalized form and with a mathematical dress. But it is quite likely that readers of Boole should be misled. Not only have his logical works an entirely mathematical appearance, but I find on p. 12 of his *Laws of Thought* the following unequivocal statement: “That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.” A few lines below he adds, “It is not of the essence of mathematics to be conversant with the ideas of number and quantity.” [88] *British Quarterly Review*, No. lxxxvii, July 1866. [89] *Mind*, October 1876, vol. i. p. 484. The solution of the difficulty is that Boole used the term mathematics in a wider sense than that usually attributed to it. He probably adopted the third view, so that his mathematical *Laws of Thought* are the common basis both of logic and of quantitative mathematics. But I do not care to pursue the subject because I think that, in either case Boole was wrong. In my opinion logic is the superior science, the general basis of mathematics as well as of all other sciences. Number is but logical discrimination, and algebra a highly developed logic. Thus it is easy to understand the deep analogy which Boole pointed out between the forms of algebraic and logical deduction. Logic resembles algebra as the mould resembles that which is cast in it. Boole mistook the cast for the mould. Considering that logic imposes its own laws upon every branch of mathematical science, it is no wonder that we constantly meet with the traces of logical laws in mathematical processes. *The Nature of Number.*