In 1835 Whewell published a pamphlet on mathematics in liberal education—one of the fruits of his philosophical studies. In it he maintains that mathematics is superior to formal logic as an educational discipline, and he discusses faults in teaching by which its benefits are diminished. In reply to the pamphlet an article appeared in the Edinburgh Review, written by Sir William Hamilton, professor of logic and mathematics at Edinburgh, which became notorious as a wild and indiscriminate attack on mathematical work by a person only slightly acquainted with it. In the succeeding number Whewell asks for the titles of some treatises on practical logic and philosophy which the reviewer would recommend for their educational efficiency as rivals to the well-known mathematical treatises. In this tilt between the expounder of the renovated Baconian logic and an official representative of the old scholastic logic, the modern champion came off victorious.
In 1837 Whewell finished the first part of his History of the Inductive Sciences. In this book he notes the epochs when the great steps were made in the principal sciences, the preludes and the sequels of these epochs, and the way in which each step was essential to the next. He attempts to show that in all great inductive steps the type of the process has been the same. The prominent facts of each science are well selected and the whole is written with a vigor of language and a facility of illustration rare in the treatment of scientific subjects. This book was, however, introductory to his Philosophy of the Inductive Sciences which appeared three years later; its preparation had indeed gone along with that of the History. In this work Whewell explained the process of induction, the elements of which it consists, what conditions it requires, and what facilities it calls into play. He maintains that, in order to arrive at knowledge or science, we must have besides impressions of sense, certain mental bonds of connection, ideal relations, or ideas. Thus space is the ideal relation on which the science of geometry depends; time, cause, likeness, substance, life, are ideal relations on which other sciences depend. Whewell's philosophy was, in fact, a blending of Kant and Bacon.
