Syllogism

I. Definition

A syllogism is a systematic representation of a single logical inference. It has three parts: a major premise, a minor premise, and a conclusion. The parts are defined this way:

• The major premise contains a term from the predicate of the conclusion
• The minor premise contains a term from the subject of the conclusion
• The conclusion combines major and minor premise with a “therefore” symbol (∴)

When all the premises are true and the syllogism is correctly constructed, a syllogism is an ironclad logical argument.

II. Examples and Explanation

1. The most famous syllogism in philosophy is this:
   • All men are mortal (major premise)
   • Socrates is a man (minor premise)
   • ∴Socrates is mortal (conclusion)

Notice that the major premise provides the predicate, while the minor premise provides the subject. As long as both premises are true, the conclusion must be true as well.

2. That first syllogism was pretty easy, since no one would ever argue with its premises. But syllogisms become more difficult when the premises are more complicated or debatable. For example:
   • Cats make good pets (major premise)
   • Dogs and cats are equally good as pets (minor premise)
   • ∴ dogs make good pets (conclusion)

Is this argument true? It depends! Some people might disagree with the premises, or with the conclusion. It’s a matter of opinion. However, the logical validity of the syllogism is not a matter of opinion, because the conclusion really does follow from the premises. That is, if the premises are true, then the conclusion must be true as well. That makes it a logically valid syllogism regardless of whether or not you agree with the premises or the conclusion!

3. You can also have cases where a syllogism is logically sound, but factually incorrect. For example:
   • This car is expensive (minor premise)
   • All expensive cars are Ferraris. (major premise)
   • ∴ this car is a Ferrari. (conclusion)

The major premise in this syllogism, of course, is wrong. In terms of its logical structure, there’s nothing wrong with the syllogism. But it’s based on a faulty assumption, and therefore the argument doesn’t work. If the major premise were true, then the conclusion would follow, which means the syllogism is perfectly logical. It just so happens that the premise isn’t true.

III. The Importance of Syllogisms

Syllogisms represent the strongest form of logical argument, so if you could build an argument entirely out of syllogisms it would probably be very persuasive! Like triangles in architecture, the syllogism is the strongest logical structure. When formed correctly, they are indisputable in terms of their logical validity.

However, it’s important to remember what syllogisms don’t do: they don’t prove their own premises. So you could build an argument out of very strong syllogisms, but it wouldn’t work if its original premises weren’t correct. Thus, you have to ensure that the starting point of your argument is solid, or no amount of syllogisms will make the argument successful as a whole.

IV. How to Write a Syllogism

1. Start with the conclusion. Most of the time, you’re writing a syllogism as a way of laying out the steps in your argument – steps you’ve already worked out in your head. So you can easily start with the conclusion. That’s the most important part of the syllogism, the part that you’re trying to prove through logic.

Example: Although most have live young, some mammals lay eggs.

2. Break the conclusion down into subject and predicate. The grammar of your conclusion will dictate the logical structure of the syllogism you use to support it. So you have to be able to recognize subject and predicate in the sentence.

Although most have live young, some mammals (subject)

lay eggs (predicate)

3. Locate the key terms. Take the subject and predicate, and boil them down to their key terms. Get rid of unnecessary adjectives and other extraneous words, and just focus on the word or words that carry the weight of the sentence.

mammals | lay eggs

4. Craft your premises. Remember that the major premise will contain the key terms of the predicate, while the minor premise contains the key terms of the subject. Craft separate sentences around these key terms such that they fit together into a syllogism.

Echidnas are mammals (minor premise)

Echidnas lay eggs (major premise)

5. Check whether the conclusion follows from the premises. Can you make a persuasive “if…then” statement using your premises to prove your conclusion? If not, the syllogism is not logically structured and will not work in your argument.

If echidnas are mammals AND echidnas lay eggs, then of course it follows that some mammals must lay eggs.

6. Check whether the premises are persuasive. If you think the reader will accept both premises, and the syllogism is logically sound, then this step in your argument will be beyond criticism. However, bear in mind that a skeptical reader will often find ways to doubt your premises, so don’t take them for granted!

Echidnas are mammals (persuasive because of scientific consensus)

Echidnas lay eggs (persuasive because of empirical observation)

V. When to Use a Syllogism

Syllogisms are very abstract representations, and you rarely see them outside of formal logic and analytic philosophy. In other fields, it’s probably best not to write the syllogism out as part of your paper. However, it can still be very useful as a mental exercise! Even if you don’t end up showing the whole syllogism to your reader, you can write it out on scratch paper as a way of evaluating your own argument. If you can write your argument out in syllogism form, then you know it’s logical. If not, then there may be more work for you to do before the argument is ready for submission.

VII. Examples in Philosophy and Literature

1. Ambrose Bierce famously satirized the syllogism form in his Devil’s Dictionary:
   • 60 men together can work 60 times as quickly as one man alone.
   • One man alone can dig a whole in one minute.
   • Therefore, 60 men can dig a whole in one second.

Each step in this syllogism seems to make sense, and the syllogism itself is logically sound. But the conclusion is clearly wrong! That’s because premise #1 is deceptive: in theory it’s true that 60 men can work 60 times as fast as one. But in practice things are not so simple, as Bierce’s clever example shows.

2. Aristotle invented the example in §2, the one about Socrates being mortal. But he also used another example to demonstrate how a valid syllogism could produce a false conclusion if based on faulty premises (despite the syllogism itself being logically valid).
   • Everything white is sweet
   • Salt is white
   • ∴ salt is sweet.

Clearly, premise #2 is wrong, and the conclusion is wrong as well. But if premise #2 were correct, then the conclusion would be correct as well. That means the syllogism is logically valid though factually incorrect

VIII. Examples in Popular Culture

1. It can be fun to locate (and critique) the hidden syllogisms in the world around us. In advertising, for example, there is always a hidden syllogism with “therefore, you should buy our product” as its conclusion. For example, many liquor ads are based on the following syllogism:
   • Women like men who buy [this brand of alcohol].
   • You are a man and you want women to like you.
   • Therefore, you should buy [this brand].

There are many potential problems with this argument, but the most obvious one is that it (probably) has at least one false premise: women probably don’t truly prefer men who purchase that particular brand. In addition, the viewer may well be a woman or a gay man, in which case the other premise is also false.

2. “That’s a faulty syllogism. Just because you call Bill a dog doesn’t mean he is a dog.” (Dr. House, House)

In one episode of House, the title character refers to a “faulty syllogism” in a way that’s not entirely clear. But the syllogism he’s referring to looks like this:

• I call Bill a dog.
• Things are whatever I call them.
• ∴ Bill is a dog.

The syllogism is clearly faulty because premise #2 is false.