Marble head of Aristotle (384-322 B.C.)

Syllogistic Fallacy

Type: Formal Fallacy

Form:

Any non-validating form of categorical syllogism.

Exposition:

The categorical syllogism is part of the oldest system of formal logic, invented by the first formal logician, Aristotle. There are several techniques devised to test syllogistic forms for validation, including sets of rules, diagrams, and even mnemonic poems.

More importantly for us, there are sets of fallacies based upon the rules such that any syllogism which does not commit any of the fallacies will have a validating form. 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:

A Short Introduction to Categorical Syllogisms:

A categorical syllogism is a type of argument with two premisses—that is, a syllogism—and one conclusion. Each of these three propositions is one of four forms of categorical proposition:

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.

These four types of proposition are called A, E, I, and O type propositions, as indicated. The variables, S and P, are place-holders for terms which pick out a class—or category—of thing; hence the name "categorical" proposition.

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 Subject and Predicate 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 for this reason 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 proposition are said to be "distributed" or "undistributed" in that proposition, depending upon what type of proposition it is, and whether the term is the subject or predicate term. Specifically, the subject term is distributed in the A and E type propositions, and the predicate term is distributed in the E and O type propositions. 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 propositions are called "affirmative" propositions, while the E and O type are "negative", for reasons which should be obvious. Now, you should be equiped to understand the following types of syllogistic fallacy.

Subfallacies:

Source:

Irving Copi & Carl Cohen, Introduction to Logic (Tenth Edition) (Prentice Hall, 1998), Chapter 8.

Acknowledgment: The print of the bust of Aristotle is available from AllPosters.


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