While Mr Mill was amending the Syllogistic theory so as to ensure for Formal Logic its legitimate place among the essentials of scientific procedure, Sir W. Hamilton was at the same time enlarging it on its technical side, in two modes which are highly esteemed both by himself and by others: 1. The recognition of two kinds of Syllogisms; one in Extension, the other in Comprehension: 2. The doctrine of the Quantification of the Predicate.--Both these novelties are here criticised by Mr Mill in chapter xxii., which we recommend the reader to peruse conjointly with Lectures 15 and 16 of Sir W. Hamilton on Logic. Now whereas the main objection, by which the study of the syllogistic logic has been weighed down and discredited in modern times, is this, that it encumbers the memory with formal distinctions, having no useful application to the real process and purposes of reasoning--the procedure of Sir W. Hamilton might almost lead us to imagine that he himself was trying to aggravate that objection to the uttermost. He introduces a variety of new canons (classifying Syllogisms as Extensive and Intensive, by a distinction founded on the double quantity of notions, in Extension and in Comprehension) which he intimates that all former logicians have neglected--while it plainly appears, even on his own showing, that the difference between syllogisms, in respect to these two sorts of quantity, is of no practical value; and that 'we can always change a categorical syllogism of the one quantity into a categorical syllogism of the other, by reversing the order of the two premises, and by reversing the meaning of the copula' (Lect. xvi. p. 296); nay, that every syllogism is already a syllogism in both quantities (Mill, p. 431). Against these useless ceremonial reforms of Sir W. Hamilton, we may set the truly philosophical explanation here given by Mr Mill of the meaning of propositions.