The logic of John Venn (1834–1923), sketched briefly in the Princeton Review (1880) and more fully elaborated in his Symbolic Logic (London, 1881), shows a greater understanding of George Boole's intentions and a better acquaintance with the historical background than had yet been displayed by anyone else. Though he did not suppose the new methods to have any great practical advantage over the old, he saw no reason, either, to suspect them of being anything more than a generalization of traditional practices, couched, for convenience, in a mathematical form. He therefore resisted the Jevonian simplifications and was at pains to bring out the logical significance of such operations as subtraction and division, though the latter is admitted to merit inclusion more on grounds of consistency than for any use made of it in the reasoning of everyday life.

Venn's own account of the matter proceeds from what he calls the "compartmental...