Every syllogism has three and only three terms. These terms are major term, minor term and middle term. Each term occurs twice in the syllogism. In order to identify a term in a syllogism, we have to take in to account the conclusion of the given argument. Let us consider the following classical syllogistic argument.
All men are mortal.
Socrates is a man.
Therefore, Socrates is moral.
In the above argument,” Socrates is mortal” is the conclusion; “All men are mortal” and “Socrates is a man” are the premises. The subject term of the conclusion is called the minor term (symbolically called M). The predicate term of the conclusion is called the major Term (symbolically called P). The term which is common in both the premises but does not occur in the conclusion is called the middle term (symbolically called M).
In the above argument, “Socrates” stands for the minor term, “mortal” stands for the major term and “man” for the middle term. The middle term, which occurs in both the premises, acts like a bond or connection between the two premises. It is the common element in both the premises.
The major term and the minor term are called Extremes. The middle term is connected with both the extremes so that a conclusion can be drawn. The premise in which the minor term occurs is called the minor premise. The premise in which major term occurs is called the major premise. The conclusion is obtained by the joint assertion of both the major premise and the minor premise. In a syllogism generally the major premise is stated first, the minor premise second and the conclusion last. Let us take another example.
All ruminants are horned animals.
All cows are ruminants.
Therefore, all cows are horned animals.
Here ‘Cows’ stand for the minor term, ‘horned-animals’ for the major term and ‘ruminants’ for the middle term. If we symbolize them as per the symbols taken earlier, the above argument can be represented in the following manner.
All M is P.
All S is M.
Therefore, all S is P
This is the form of the argument. The from of the syllogism is the symbolic representation of the argument. The validity or invalidity of an argument depends exclusively on its form. It is independent of the subject matter or content of the argument. We may substitute any value for S, P and M in the form but the argument remains valid. Suppose we substitute “rabbit” in place of ‘S “having lungs” for ‘P’ and “mammals” for ‘M’, we may get a new argument after substitution in the following manner.
All mammals have lungs.
All rabbits are mammals.
Therefore, all rabbits have lungs.
This argument is also valid. So, we can conclude that a valid syllogism is a formally valid argument i.e. it is valid due to its form alone. Similarly, if a syllogism is invalid, its form is also invalid. The validity or invalidity of an argument is dependent on its form, not on the content of the syllogism.