A New Law of Thought and Its Logical Bearings

Two of the three fundamental Laws of Thought, which are traditionally regarded as the cardinal principles of Formal Logic, are concerned with the relation of propositions to each other. According to the Law of Contradiction, two propositions of the form "A is B" and "A is not B" cannot both be true. According to the Law of Excluded Middle, they cannot both be false. Now it is clear that if there is another principle which expresses the fundamental condition of the possibility of any proposition taken by itself, without reference to others, this also must be regarded as a fundamental Law of Thought, and as being logically prior to the Laws of Contradiction and Excluded Middle.

It is the aim of this brief essay to show that there is such a Law, and to exhibit in detail its vital importance in the treatment of the whole range of topics with which Formal Logic deals. This Law of "Significant Assertion" is formulated as follows:- "Every Subject of Predication is an identity (of denotation) in diversity (of intension)".