SYLLOGISM, in logic, denotes a mediate argument, that is an argument in which an inference is drawn about the relation between two terms from two premises which state the relation of each of the two terms to the same third term. For instance, "The morning star is Venus ; the evening star is Venus ; therefore the evening star is the morning star" (or vice versa). It is usual to say that syllogism is not only mediate but also deductive reasoning, that is to say that it requires the application of a general premiss to relevant cases. For example, "All planets move in elliptical orbits; Venus is a planet ; therefore Venus moves in an elliptical orbit." This argument is mediate, like the previous example ; but it is also deductive (or involves the application of a general premiss, or a premiss concerning a whole class of objects) whereas the previous example was not deductive. Now, it is true that syllogisms are mostly deductive as well as mediate, but there is no sufficient reason for restricting the term to deductive cases only. Moreover, just as an argument may be mediate without
being also deductive, so an inference may be deductive without being mediate. For instance, "All watches have a hair-spring; therefore my watch has one." It is also customary to restrict the term syllogism to arguments the propositions of which involve only relations of substance and attribute, as in the above examples. But for this also there is no good reason. The arguments (I) "x=y; y=z; therefore x=z," and (2) "M is north of P; S is west of M; therefore S is north-west of P," are also syllogisms. For, after all, "syllogism" means "thinking together" or, as one might say, "putting two and two together." It is true, however, that syllogisms involving other relationships than those of identity or of substance and attribute require special care, much more than the others. See LOGIC.