, The algebra of symbolic logic, as developed by LEIBNIz, BOOLE, C. S. PEIRCE, E. SCHR6DER, and others, t is described by WHITEHEAD as "the only known member of the non-numerical genus of universal algebra." t This algebra, although originally studied merely as a means of handling certaini problems in the logic of classes and the logic of propositions, has recently assumed some importance as an independent calculus; it may therefore be not without interest to consider it from a purely mathematical or abstract point of view, and to show how the whole algebra, in its abstract form, may be developed from a selected set of fundamental propositions, or postulates, which shall be independent of each other, and from which all the other propositions of the algebra can be deduced by purely formal processes. In other words, we are to consider the construction of a purely deductive theory, withouit regard to its possible applications.