ABSTRACT
It has been customary, in treatises on logic, to confound the two kinds of implication, and often to be really considering the formal kind where the material kind only was apparently involved. For example, when it is said that “Socrates is a man, therefore Socrates is a mortal”, Socrates is felt as a variable: he is a type of humanity, and one feels that any other man would have done as well. If, instead of therefore, which implies the truth of hypothesis and consequent, we put “Socrates is a man implies Socrates is a mortal”, it appears at once that we may substitute not only another man, but any other entity whatever, in the place of Socrates. Thus although what is explicitly stated, in such a case, is a material implication, what is meant is a formal implication; and some effort is needed to confine our imagination to material implication.
