Syllogism facts for kids

A syllogism is a special kind of logical argument. It's like a mini-puzzle where you start with two or more statements (called premises) and then figure out a new statement (the conclusion) that must be true if the first ones are true. It's a way of using logic to reach a certain answer.

The ancient Greek thinker Aristotle came up with the idea of the syllogism. He described it as "a discussion where, if certain things are assumed to be true, something different from those things must naturally follow because of them."

Each part of a syllogism usually includes a form of the verb 'to be' (like 'is' or 'are'). Think of a syllogism as a small machine with three main parts:

• The major premise (a general statement).
• The minor premise (a more specific statement).
• The conclusion (what you figure out from the first two).

If the first two parts are true, then the conclusion must also be true.

How Syllogisms Work

Let's look at some examples to see how these parts fit together.

Example 1: All Greeks are mortal

• Major premise: All men are mortal.
• Minor premise: All Greeks are men.
• Conclusion: All Greeks are mortal.

In this example, we have three different ideas or categories: "men," "mortal," and "Greeks."

• "Mortal" is the major term (it's the bigger, more general idea).
• "Greeks" is the minor term (it's the smaller, more specific idea).
• "Men" is the middle term. It's the idea that connects the major and minor terms in the two premises.

Both of the starting statements (premises) in this example are universal, meaning they apply to "all" of something. The conclusion is also universal.

Example 2: Some men die

• Major premise: All mortals die.
• Minor premise: Some men are mortals.
• Conclusion: Some men die.

Here, the major term is "die," the minor term is "men," and the middle term is "mortals." The major premise is universal ("All mortals"). But the minor premise and the conclusion are particular, meaning they apply to "some" of something.

Aristotle studied many different syllogisms. He found out which ones were valid. A syllogism is valid if its conclusion must be true whenever its premises are true. The examples above are both valid syllogisms.

Logic Today

Over time, new ways of thinking about logic developed. The syllogism was eventually replaced by a system called first-order logic. This newer logic was created by Gottlob Frege in 1879.

First-order logic is very useful for things like mathematics, computer science, and linguistics (the study of language). This is because it uses numbers and symbols (called quantified variables) instead of just sentences. This makes it more precise and powerful for solving complex problems.

See also

In Spanish: Silogismo para niños