(major) (middle) | | (2) No shell fish are vertebrates, (minor) (middle) | | All trout are vertebrates, (minor) (major) | | ∴ No trout are shell fish. The necessity of having but _three_ different terms in any syllogism may be understood by supposing that there are four different terms; then it would follow that there could be _no standard_ or common link. In the axiom, “Things equal to the same thing are equal to each other,” the _same thing_ is the common standard or link. Two things which equal two different things are not equal to each other. The impossibility of reasoning from four terms may be shown by circles. All men are mortal. All trees grow. Illustration: FIG. 8. These circles show that no connection can be established between either group. Using four terms in any syllogism is known as the _fallacy of four terms_. (2) _A syllogism must have three and only three propositions._ The proposition containing the major term is called the _major premise_, while the one containing the minor term is called the _minor premise_. In a strictly logical syllogism the major premise is written first, the minor premise second and the conclusion third. In common parlance, however, the minor premise or even the conclusion may appear first. The conclusion of a syllogism is always preceded by _therefore_, or its equivalent, which may be written or understood. The premises always answer the question, Why is the conclusion true? The premises are often preceded by such words as _for_ and _because_. The attending irregular syllogisms are arranged logically and the premises and conclusions indicated: (1a) _Illogical._ “You must take an examination because all who enter the school are examined and you, as I understand it, are planning to enter.” (2a) “Some of these books are not well bound, for they are going to pieces as no well bound book would do.” (1b) _Logical._ All who enter this school are examined, Major premise. You are planning to enter this school, Minor premise. You must be examined. Conclusion. (2b) No well bound book goes to pieces, Major premise. Some of these books are going to pieces, Minor premise. Some of these books are not well bound. Conclusion. The fact that all syllogisms must have three and only three premises follows from rule “1.” One premise must compare the middle term with the “major”; another premise must compare the middle term with the “minor”; while the conclusion links together the “major” and the “minor.”