ABSTRACT
The principle is employed whenever a proposition is said to be proved; for what happens is, in all such cases, that the proposition is shown to be implied by some true proposition. Another form in which the principle is constantly employed is the substitution of a constant, satisfying the hypothesis, in the consequent of a formal implication. A formal implication is one which holds of every term, and therefore every cannot be explained by means of formal implication. Some logical notions will be elicited which, though they seem quite fundamental to logic, are not commonly discussed in works on the subject; and thus problems no longer clothed in mathematical symbolism will be presented for the consideration of philosophical logicians. The verb, which is the distinguishing mark of propositions, remains with the assertion; but the assertion itself, being robbed of its subject, is neither true nor false.
