ABSTRACT
The distinctive subject matter of logic, constituting, the core of the traditional Aristotelian logic, is what is called formal truth. The distinction between material and formal truth, like the related distinction between assumption and proof or between immediate and mediate truth, is not without its difficulties. The nature of the subject matter of logic may be better understood when it is seen to be identical with the subject matter of pure mathematics. This identity of logic and pure mathematics is the discovery of the nineteenth century, and was not possible until the discovery of non-Euclidean geometry and of multiple algebra revealed the true nature of pure mathematics. The employment of special symbols, instead of the more familiar symbols called words, is a practical convenience rather than a logical necessity. Deductive logic and pure mathematics generally deal with certain relations between propositions, and the knowledge of such relations is certainly one of the most potent instruments of scientific research.
