But if any one is so incautious as to commit this mistake, the very earliest lesson in the logic of inference, the Conversion of propositions, will correct it. The first of the two forms in which I have stated the axiom, is in some degree open to Mr. Bain’s criticism: when B is said to co-exist with A (it must be by a lapsus calami that Mr. Bain uses the word coincide), it is possible, in the absence of warning, to suppose the meaning to be that the two things are only found together. But this misinterpretation is excluded by the other, or practical, form of the maxim; Nota notœ est nota rei ipsius. No one would be in any danger of inferring that because a is a mark of b, b can never exist without a; that because being in a confirmed consumption is a mark of being about to die, no one dies who is not in a consumption; that because being coal is a mark of having come out of the earth, nothing can come out of the earth except coal. Ordinary knowledge of English seems a sufficient protection against these mistakes, since in speaking of a mark of any thing we are never understood as implying reciprocity. A more fundamental objection is stated by Mr. Bain in a subsequent passage (p. 158). “The axiom does not accommodate itself to the type of Deductive Reasoning as contrasted with Induction—the application of a general principle to a special case.

Any thing that fails to make prominent this circumstance is not adapted as a foundation for the syllogism.” But though it may be proper to limit the term Deduction to the application of a general principle to a special case, it has never been held that Ratiocination or Syllogism is subject to the same limitation; and the adoption of it would exclude a great amount of valid and conclusive syllogistic reasoning. Moreover, if the dictum de omni makes prominent the fact of the application of a general principle to a particular case, the axiom I propose makes prominent the condition which alone makes that application a real inference. I conclude, therefore, that both forms have their value, and their place in Logic. The dictum de omni should be retained as the fundamental axiom of the logic of mere consistency, often called Formal Logic; nor have I ever quarreled with the use of it in that character, nor proposed to banish it from treatises on Formal Logic. But the other is the proper axiom for the logic of the pursuit of truth by way of Deduction; and the recognition of it can alone show how it is possible that deductive reasoning can be a road to truth.