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.”
(3) The middle term must be distributed at least once. The rule is usually given in this way, “The middle term must be distributed once at least, and must not be ambiguous.” In this treatment the last part of the rule has been omitted because it must be apparent to the student that a middle term used in two senses is virtually equivalent to two different terms; such an “ambiguous middle” would, in consequence, give a syllogism of four terms.
Rules 3 and 4 are of greater importance than the others because they are more frequently violated. If the middle term is not distributed at least once, the fallacy is referred to as “undistributed middle.” If the distributed major term of the conclusion is not distributed in the major premise, then the fallacy is called, “illicit process of the major term”; and finally, if the distributed minor term of the conclusion is not distributed in the minor premise the fallacy is denominated an “illicit process of the minor term.” These two illicit processes may be abbreviated to illicit major and illicit minor.
Recall that any term is distributed when it is referred to as a definite whole. Unless the whole of the middle term is considered it fails to become a common standardof comparison. This becomes clear when recourse is made to the circles.
Illustration.
Syllogism in which the middle term is not distributed: