# A brief introduction to syllogisms

July 23, 2013

Arguments can be very productive. If you and I have a framework to argue without making personal attacks, the argument can be something like a science experiment for ideas. I might propose a theory, and you might test it, eventually disproving it. The syllogism is one framework for arguments which I often find useful.

# What is a syllogism?

A syllogism consists of two or more statements, connected by a logical argument, which imply a conclusion. If

• The definitions of the terms are clear, and
• The premises are true, and
• The logic is valid

Then we must agree on the conclusion.

Socratic Logic is an excellent book by Peter Kreeft on the subject.

# The canonical syllogism

To demonstrate the rules described above, let’s look at a simple example.

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.


This syllogism has three terms.

• Man/men: a male human person (middle term)
• Mortal: a state of existence in which one will die (major term)
• Socrates: the Greek philosopher (minor term)

This syllogism has two premises.

• Major, universal premise: All men are mortal.
• Minor, specific premise: Socrates is a man.

Here the universal premise is connected to the specific premise via a shared term, (called the middle term). The logic implies that the subject of the minor premise (called the minor term) is a specific member of the group of all items described by the predicate of the major premise (called the major term). The conclusion then uses the minor term as its subject and the major term as its predicate.

# How to disagree

If you don’t believe the conclusion is true, then you must argue that either

• At least one term is not properly defined, or
• At least one premise is not true, or
• The logic is fallacious

These three items present the entire useful space of argument, which allows us to productively explore the correctness of the conclusion.

In this canonical syllogism, the definition of these three terms are rather simple (this won’t often be the case). But suppose that you argued about the definition of the term man. If you feel that man should be defined instead as a male human person or a male vampire, then you may feel the major premise is false, since vampires are not mortal.

You could instead accept the definition of man, and argue that the major premise is false, citing that Jesus is an immortal male human. If so, then there is a chance Socrates was also an immortal male human, rendering the conclusion uncertain.

You could also disagree with the minor premise, stating that Socrates was not an actual human, but instead he was a figment of Plato’s imagination. In that sense, he is immortal, living on in our minds just as he did in Plato’s.

# Why do syllogisms matter?

It is often difficult to be certain about a conclusion, since the space of possible arguments against the conclusion may be vast.

Syllogisms rather nicely limit that seemingly infinite space of arguments to a relevant finite space. Often all of the arguments in that finite space can be examined, which may then provide us with more confidence about the conclusion.

When the conclusion will be become the foundation for other decisions, confidence in its correctness is of paramount importance.