Page:Inaugural address delivered to the University of St. Andrews, Feb. 1st 1867.djvu/30

26 with scientific experiment at least does the useful service of inspiring a wholesome scepticism about the conclusions which the mere surface of experience suggests.

The study, on the one hand, of mathematics and its applications, on the other, of experimental science, prepares us for the principal business of the intellect, by the practice of it in the most characteristic cases, and by familiarity with the most perfect and successful models of it. But in great things as in small, examples and models are not sufficient: we want rules as well. Familiarity with the correct use of a language in conversation and writing does not make rules of grammar unnecessary; nor does the amplest knowledge of sciences of reasoning and experiment dispense with rules of logic. We may have heard correct reasonings and seen skilful experiments all our lives we shall not learn by mere imitation to do the like, unless we pay careful attention to how it is done. It is much easier in these abstract matters, than in purely mechanical ones, to mistake bad work for good. To mark out the difference between them is the province of logic. Logic lays down the general principles and laws of the search after truth; the conditions which, whether recognised or not, must actually have been observed if the mind has done its work rightly. Logic is the intellectual complement of mathematics and physics. Those sciences give the practice, of which Logic is the theory. It declares the principles, rules, and precepts, of which they exemplify the observance.

The science of Logic has two parts; ratiocinative and inductive logic. The one helps to keep us right in reasoning from premises, the other in concluding from observation. Ratiocinative logic is much older than inductive, because reasoning in the narrower sense of the word is an easier process than induction, and the science which works by mere reasoning, pure mathematics, had been carried to a considerable height while the sciences of observation were still in the purely empirical period. The principles of ratiocination, therefore, were the earliest understood and systematized; and the logic of ratiocination is even now suitable to an earlier stage in education than that of induction. The principles of induction cannot be properly understood without some previous study of the inductive sciences: but the logic of reasoning, which was already carried to a high degree of perfection by Aristotle, does not absolutely require even a knowledge of mathematics, but can be sufficiently exemplified and illustrated from the practice of daily life.

Of Logic I venture to say, even if limited to that of mere ratiocination, the theory of names, propositions, and the syllogism, that there is no part of intellectual education which is of greater value, or whose place can so ill be supplied by anything else. Its uses, it