# Syllogistic Fallacy

**Taxonomy:** Logical Fallacy > Formal Fallacy > Syllogistic Fallacy

### Subfallacies:

- Affirmative Conclusion from a Negative Premiss
- Exclusive Premisses
- Four-Term Fallacy
- Illicit Process
- Negative Conclusion from Affirmative Premisses
- Undistributed Middle

### History:

The categorical syllogism is part of the oldest system of formal logic, invented by the first formal logician, Aristotle. Several techniques have been devised over the centuries to test syllogistic forms for validation―that is, whether the form is such that its every instance is valid―including sets of rules, diagrams, and even mnemonic poems. More importantly for us, there are sets of fallacies based upon the rules which can be used to test a form. Any syllogistic form which does not commit any of the fallacies is validating. The subfallacies of Syllogistic Fallacy are fallacies of this rule-breaking type. If a categorical syllogism commits none of the subfallacies below, then it has a validating form. To understand these subfallacies, it is necessary to understand some basic terminology about categorical syllogisms:

### An Introduction to the Terminology of Categorical Syllogisms^{*}:

"Categorical syllogisms" are so called because they are made up of categorical statements. A *statement* is a sentence that is either true or false, and a categorical one is a statement that relates two types or *categories* of thing. There are four types of categorical statement:

Type | Form | Example |
---|---|---|

A |
All S are P. |
All whales are mammals. |

E |
No S are P. |
No whales are fish. |

I |
Some S are P. |
Some logicians are philosophers. |

O |
Some S are not P. |
Some philosophers are not logicians. |

A *syllogism* is a type of argument, that is, a type of reasoning with statements, specifically, one that has two premisses and one conclusion. Thus, a *categorical syllogism* is a type of two-premissed argument constructed from categorical statements.

These four types of statement are called **A**, **E**, **I**, and **O** type statements, as indicated. The variables, **S** and **P**, are place-holders for terms which pick out a category of thing. As you can see, each type of categorical statement asserts a different logical relation between two categories.

Additionally, in a categorical syllogism there are three terms, two in each premiss, and two occurrences of each term in the entire argument, for a total of six occurrences. The **S** and **P** which occur in its conclusion—the **S**ubject and **P**redicate terms—are also called the "minor" and "major" terms, respectively. The major term occurs once in one of the premisses, which is therefore called the "major" premiss. The minor term also occurs once in the other premiss, which is thus called the "minor" premiss. The third term occurs once in each premiss, but not in the conclusion, and is called the "middle" term.

The notion of *distribution* plays a role in some of the syllogistic fallacies: the terms in a categorical statement are said to be "distributed" or "undistributed" in that statement, depending on what type of statement it is, and whether the term is the subject or predicate term. Specifically, the subject term is distributed in the **A** and **E** type statements, and the predicate term is distributed in the **E** and **O** type statements. The other terms are undistributed. In the table above, the distributed terms are in **bold**, and the undistributed ones are in *italic*.

Finally, the **A** and **I** type statements are called "affirmative", while the **E** and **O** type are "negative", for reasons which should be obvious. Now, you should be equiped to understand the syllogistic subfallacies listed above.

^{*}**Note:** For introductions to categorical syllogisms and how to evaluate them, see:

- Irving Copi & Carl Cohen, Introduction to Logic (Tenth Edition) (Prentice Hall, 1998), Chapter 8. The standard textbook account.
- Garth Kemerling, "Categorical Syllogisms", Philosophy Pages (2011). A short introduction to categorical syllogisms that explains the use of logical analogy―also called "counter-examples"― and Venn diagrams to evaluate them.
- William Poland, The Laws of Thought, or Formal Logic (1896), Chapter 4.
- William Angus Sinclair, The Traditional Formal Logic: A Short Account for Students (5th edition, 1963), Chapter 4.