Standard Form Categorical Syllogisms
A syllogism is composed of two statements, from which a third one, the conclusion, is inferred. Categorical syllogisms are syllogisms made up of three categorical propositions. They are a type of deductive argument, that is, the conclusion (provided the argument form is valid) follows with necessity from the premises. Here are two examples:
(1) All Greeks are mortal.
All Athenians are Greeks.
Therefore all Athenians are mortal.
(2) All mammals are animals.
All humans are mammals.
Therefore all humans are animals.
Such arguments were formulated by ancient Greek logicians and have been used by logicians ever since. Hence the trite examples. Both of these categorical syllogisms have the same form. Each one has two premises and a conclusion. The first premise in a standard form categorical proposition is the major premise; the second is the minor premise. The two premises share a common term, called the middle term. In the first example, the middle term is "Greeks"; in the second, "mammals". Since each one has the middle term in common, we cannot distinguish between the premises by means of the middle term. What indicates that the first premise is the major premise is the presence of the predicate term of the conclusion: "mortal" in the first example; "animals" in the second. Similarly, the minor premise contains the subject term of the conclusion--"Athenians" and "humans" respectively. The form of these two syllogisms--and of every other Figure 1 (figure will be explained below) standard form categorical syllogism--can be easily displayed:
Major Premise: Middle Term Predicate Term
Minor Premise: Subject Term Middle Term
Conclusion: Subject Term Predicate Term
Moreover, each of the three propositions in each example is an A proposition: All S are P. Thus we can display the form again, calling attention not only to the position of the terms, but also to the kind of propositions used:
Major Premise: All M are P.
Minor Premise: All S are M.
Conclusion: All S are P.
http://www.philosophy.uncc.edu/mleldrid/logic/