V. _That the Middle Term must be distributed; (that is, taken universally) in at least one premise._ This "because, otherwise, the Major Term may be compared with one part of the Middle Term, and the Minor Term with another part of the latter; and there will be actually no common Middle Term, and consequently no common ground for an inference." The violation of this rule causes what is commonly known as "The Undistributed Middle," a celebrated Fallacy condemned by the logicians. In the Syllogism mentioned as an example in this chapter, the proposition "_Man_ is mortal," really means "_All_ men," that is, Man in his universal sense. Literally the proposition is "All men are mortal," from which it is seen that Socrates being "_a_ man" (or _some_ of _all_ men) must partake of the quality of the universal Man. If the Syllogism, instead, read: "_Some_ men are mortal," it would not follow that Socrates _must_ be mortal--he might or might not be so. Another form of this fallacy is shown in the statement that (1) White is a color; (2) Black is a color; hence (3) Black must be White. The two premises _really_ mean "White is _some_ color; Black is _some_ color;" and not that either is "_all_ colors." Another example is: "Men are bipeds; birds are bipeds; hence, men are birds." In this example "bipeds" is not distributed as "_all_ bipeds" but is simply not-distributed as "_some_ bipeds." These syllogisms, therefore, not being according to rule, must fail. They are not true syllogisms, and constitute fallacies. To be "_distributed_," the Middle Term must be the Subject of a Universal Proposition, or the Predicate of a Negative Proposition; to be "_undistributed_" it must be the Subject of a Particular Proposition, or the Predicate of an Affirmative Proposition. (See chapter on Propositions.) VI. _That an extreme, if undistributed in a Premise, may not be distributed in the Conclusion._ This because it would be illogical and unreasonable to assert more in the conclusion than we find in the premises. It would be most illogical to argue that: (1) "All horses are animals; (2) no man is a horse; therefore (3) no man is an animal." The conclusion would be invalid, because the term _animal_ is distributed in the conclusion, (being the predicate of a negative proposition) while it is not distributed in the premise (being the predicate of an affirmative proposition). As we have said before, any Syllogism which violates any of the above six syllogisms is invalid and a fallacy. There are two additional rules which may be called derivative. Any syllogism which violates either of these two derivative rules, also violates one or more of the first six rules as given above in detail. The _Two Derivative Rules of the Syllogism_ are as follows: VII. _That one Premise at least must be Universal._ This because "from two particular premises no conclusion can be drawn."