Rev José Mario O Mandía
A syllogism is an argumentation in which, from two propositions (the premises or antecedent) which have a term common to both of them (called the “middle term”) a third proposition (the conclusion), distinct from the two previous ones, follows necessarily. The middle term must be universal in at least one of the two premises. It is often written in the following way:
S is M. (minor premise)
M is P. (major premise)
Therefore, S is P. (conclusion)
Remember what we said last time about “connecting the dots”? Here we make the connection between S and P through M.
The subject (S) and the predicate (P) of the conclusion are called the extremes. The subject (S) is called the “minor extreme” or “minor term,” or simply “minor.” The predicate (P) is called the “major extreme,” “major term,” or simply “major.” The premise which contains the minor term is called the “minor premise” and the premise which contains the major term is called the “major premise.” Quite straightforward, isn’t it?
Why is the predicate called the major? Because it represents a class or set which is bigger than the class represented by the minor. The minor is only one member of the class or set of the predicate. Technically, we say that the extension of the major term is greater than that of the minor term. For example:
All mammals are animals.
All dogs are mammals.
Therefore, all dogs are animals.
The major term is “animals” and the minor is “dogs”. The set of “animals” is bigger than the set of “dogs.”
Last time we saw that true premises lead to true conclusions except when there is faulty reasoning (expressed in language as “argumentation” or “discourse”). In reasoning, we need to take two aspects into account: the content or the matter (are the premises true?) and the way or form of reasoning (is the reasoning correct?).
For the argument to be correct, the matter has to be true and the form has to be correct. This means that when we analyze syllogisms, we should remember these two things: the truth of the premises (the matter) and correctness in reasoning (the form). Many philosophers are extremely logical in their arguments, but they start from false premises. On the other hand, there are people who start from true premises, but do not know how to organize the syllogism properly.
The most important work in syllogism lies in finding out the truth of the premises (the matter). In many cases, this will require defining the terms (definition) or distinguishing the different meanings of a term (divisions).
Let us take an example of an argument where the matter is defective:
Only the things that I can see exist.
I cannot see God.
Therefore, God does not exist.
Regarding the truth of the first premise, we must object that there are many things we cannot see but whose existence we accept, e.g., love, justice, and other people’s brains.
Here is an example of a defective form:
Man is an animal.
The donkey is an animal.
Therefore, man is a donkey.
What’s wrong with this logic? What makes its form defective? What are the rules for correct reasoning anyway? There are eight basic rules for the simple syllogism. And we will study them next time.