Note 507 — Chapter V

“Boole,” says Jevons, “first put forth the problem of Logical Science in its complete generality:—Given certain logical premisses or conditions, to determine the description of any class of objects under those conditions. Such was the general problem of which the ancient logic had solved but a few isolated cases—the nineteen moods of the syllogism, the sorites, the dilemma, the disjunctive syllogism, and a few other forms. Boole shewed incontestably that it was possible, by the aid of a system of mathematical signs, to deduce the conclusions of all these ancient modes of reasoning, and an indefinite number of other conclusions. Any conclusion, in short, that it was possible to deduce from any set of premisses or conditions, however numerous and complicated, could be calculated by his method” (Philosophical Transactions, 1870). Compare also Principles of Science, 6, § 5.