Immediate Inference

in traditional logic, an inference from one premise or, in Aristotelian logic, a conclusion drawn from axioms or a premise “to which no other is prior.” The theory of immediate inference in any of the above senses did not fall directly within the scope of syllogistics, but it was believed that the theory must in some sense be prior to syllogistics. Moreover, it was in precisely this area that traditional logic proved to be “insufficiently formal”: the rules of immediate inference often were justified by reference to (intuitive) “self-evidence,” and concepts such as the “latent meaning of a proposition” played a significant role in the “theory of immediate inference.”

From the standpoint of contemporary formal (mathematical) logic, the number of premises of an inference cannot be a significant characteristic of the inference, inasmuch as any (finite) number of premises can always be replaced by one formula—their conjunction. An inference whose premises and conclusion are connected by a single application of some rule of inference, that is, by a relation of “immediate deducibility,” is sometimes called an immediate inference in contemporary logic. But even this concept cannot be considered essential for logic, inasmuch as the length of an inference (even with fixed premises and a fixed conclusion) is not an “invariant” of the inference: it depends on the method used to define the given logical calculus, although even this method of definition would not affect the deductive strength of the calculus.