Symbolic or Formal Logic—I shall use these terms as
synonyms—is the study of the various general types of deduction. The word
*symbolic* designates the subject by an accidental characteristic, for
the employment of mathematical symbols, here as elsewhere, is merely a
theoretically irrelevant convenience. The syllogism inall its figures belongs to
Symbolic Logic, and would be the whole subject if all deduction were
syllogistic, as the scholastic tradition supposed. It is from the recognition of
asyllogistic inferences that modern Symbolic Logic, from Leibniz onward, has
derived the motive to progress. Since the publication of Boole’s Laws of Thought (1854), the subject has been pursued with
a certain vigour, and has attained to a very considerable technical development^{[4]}. Nevertheless, the subject achieved almost nothing
of utility either to philosophy or to other branches of mathematics, until it
was transformed by the new
methods of Professor Peano^{[5]}.
Symbolic Logic has now become not only absolutely essential to every
philosophical logician, but also necessary for the comprehension of mathematics
generally, and even for the successful practice of certain branches of
mathematics. How useful it is in practice can only be judged by those who have
experienced the increase of power derived from acquiring it; its theoretical
functions must be briefly set forth in the present chapter^{[6]}.(§ 11 ¶ 1)

§ 11 n. 1. By far the most complete account of the non-Peanesque methods will be found in the three volumes of Schröder, Vorlesungen über die Algebra der Logik, Leipzig, 1890, 1891, 1895. ↩

§ 11 n. 2. See Formulaire de Mathématique, Turin, 1895, with subsequent editions in later years; also Revue de Mathématiques, Vol. VII, No. 1 (1900). The editions of the Formulaire will be quoted as F. 1895 and so on. The Revue de Mathématiques, which was originally the Revisti di Matematica, will be referred to as R. d. M.. ↩

§ 11 n. 3. In what follows the main outlines are due to Professor Peano, except as regards relations; even in those cases where I depart from his views, the problems considered have been suggested to me by his works. ↩

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.