The above criticisms of Hamilton's system are primarily due to Augustus De Morgan (1806–1871), whom Hamilton, in 1846, had misguidedly accused of plagiarizing his quantification. In the famous and protracted controversy that ensued, De Morgan was led into a thorough dissection of the whole system, and subsequent critics, from Mill, Peirce, and Venn onward, have taken most of their ammunition from him.

Though greatly superior as to insight and technical ability, the logic of De Morgan has affinities with that of his rival in that it, too, lays stress on the autonomy of logic and on the extensional point of view. It equally shares Hamilton's interest in reforming and enlarging the traditional syllogistic, an enterprise now outdated, which has caused it to fall into unmerited neglect. Apart from his early Formal Logic (London, 1847; 2nd ed., Chicago, 1926), the bulk of De Morgan's logical writings are to be found in...