Syllogistic Fallacy

Taxonomy: Logical Fallacy > Formal Fallacy > Syllogistic Fallacy

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:

A Short Introduction to Categorical Syllogisms:

A categorical syllogism is a type of argument constructed from categorical propositions, which come in four types:

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. Each type of categorical proposition asserts a logical relation between two categories of thing.

A categorical syllogism is an argument with two premisses—that is, a syllogism—and one conclusion. Each of these three propositions is a 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.

Resource:

Garth Kemerling, "Categorical Syllogisms", Philosophy Pages (2011). A somewhat longer, more detailed introduction to categorical syllogisms, which explains the use of logical analogy―also called "counter-examples"― and Venn diagrams to evaluate them.