There is? if I am not mistaken, a certain confusion in the [Pg 152] minds of some authors as to the relation, between propositions, in virtue of which an inference is valid. In order that it may be valid to infer from , it is only necessary that should be true and that the proposition "not- or " should be true. Whenever this is the case, it is clear that must be true. But inference will only in fact take place when the proposition "not- or " is known otherwise than through knowledge of not- or knowledge of . Whenever is false, "not- or " is true, but is useless for inference, which requires that should be true. Whenever is already known to be true, "not- or " is of course also known to be true, but is again useless for inference, since is already known, and therefore does not need to be inferred. In fact, inference only arises when "not- or " can be known without our knowing already which of the two alternatives it is that makes the disjunction true. Now, the circumstances under which this occurs are those in which certain relations of form exist between and . For example, we know that if implies the negation of , then implies the negation of . Between " implies not-" and " implies not-" there is a formal relation which enables us to know that the first implies the second, without having first to know that the first is false or to know that the second is true. It is under such circumstances that the relation of implication is practically useful for drawing inferences.