Part I: Lesson

You may have heard something along the lines of the following argument in the past: 

1. All men are mortal. 
2. Socrates is a man. 
3. Therefore, Socrates is mortal.

These lines are an example of a type of deductive reasoning that is known as a syllogism. We defined “syllogism” earlier, but we can also describe them as follows: 

• Syllogism: a type of argument that deduces a conclusion on the basis of two premises which share three distinct terms. These terms are known as the minor term, the middle term, and the major term

You may have seen syllogisms used before in everyday life, but never known how to describe how they work or been able to distinguish their features from those of other types of arguments. In this lesson, we aim to give you the terminology to do exactly that. Today’s lesson will focus on the components of a syllogism.

In any syllogism, there are three distinct terms: the minor term, the major term, and the middle term.

• Minor Term: the subject of the conclusion. In the above example, the minor term is ‘Socrates’.
• Major Term: the predicate of the conclusion. In the above example, the major term is ‘mortal’.

These terms constitute the conclusion of the syllogism; they are the terms in the premises about which we are making the inference.

A note on the terminology: the adjectives of ‘minor’ and ‘major’ do not describe any relative significance of the terms or their roles in the argument. The major term is not more significant than the minor term in any manner — they are distinguished only by their placements in the conclusion.

• Middle Term: the shared term that connects the two premises and enables us to draw the conclusion. In the above example, the middle term is ‘man’.

The middle term is the term that does the bulk of the inferential work in the syllogism. If the middle term was not shared between the two premises in the above syllogism, then the argument would not produce any valid conclusion relating the minor term to the major term. For example, consider replacing ‘men’ in the first premise with ‘cats’: 

1. All cats are mortal
2. Socrates is a man.
3. Therefore, Socrates is mortal.

Although, certainly, the conclusion is actually true — Socrates was mortal! — the argument used to deduce the conclusion is far from valid. Without a shared middle term to connect the two premises, the two premises are irrelevant to each other.

In any syllogism, there are three statements which are composed of the above terms. We have referred to them above as the premises and the conclusion, but some of them have specific titles as well. These three statements are called the minor premise, major premise, and conclusion.

• Minor Premise: the premise that contains the minor term. It can be the first or second premise. In the above example, the minor premise is “Socrates is a man” (although we could have equivalently written it in the first place)

• Major Premise: the premise that contains the major term. It can also be the first or second premise. In the above example, the major premise is “All men are mortal” (although, like with the minor premise, we could have equivalently written in the second place)

• Conclusion (this stays the same): the final statement of the syllogism. The conclusion combines the term that is unique to the minor premise to the term that is unique to the major premise. The middle term is never present in the conclusion. In the above example, the conclusion is “Socrates is mortal”.

Therefore, we can conclude that the middle term can be shared in one of four ways. These ways determine what logicians call the figure of a syllogism.   

(1) it can be the subject of the major premise and the predicate of the minor premise (called “first figure”) 

(2) it can be the predicate of both premises (called “second figure”) 

(3) it can be the subject of both premises (called “third figure”), or

(4)  it can be the predicate of the major premise and the subject of the minor premise (called “fourth figure”) Understanding the figure of a syllogism and how to determine it is important, because through it we can realize that switching the order of the premises of a syllogism will not change its figure. Neither will it change the content of each premise. Thus, we can conclude that the premises of a syllogism have no required order. We can switch them around and still have a syllogism with all the same relevant properties: validity/invalidity, types of categorical propositions, soundness/unsoundness, term clarity/vagueness, etc.