Fallacy of four terms

Fallacy of four terms

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Fallacy of four terms

The fallacy of four terms () is the logical fallacy that occurs when a categorical syllogism has four terms.

Explanation

Categorical syllogisms always have three terms:

Major premise: All fish have fins.

Minor premise: All goldfish are fish.

Conclusion: All goldfish have fins.

Here, the three terms are: "goldfish," "fish," and "fins."

Using four terms invalidates the syllogism:

Major premise: All fish have fins.

Minor premise: All goldfish are fish.

Conclusion: All humans have fins.

The premises don't connect "humans" with "fins", so the reasoning is invalid. Notice that there are four terms: "fish", "fins", "goldfish" and "humans". Two premises aren't enough to connect four different terms, since in order to establish connection, there must be one term common to both premises.

In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation: using the same word or phrase but with a different meaning each time, creating a fourth term even though only three distinct words are used:

Major premise: Nothing is better than eternal happiness.

Minor premise: A ham sandwich is better than nothing.

Conclusion: A ham sandwich is better than eternal happiness.

The word "nothing" in the example above has two meanings, as presented: "nothing is better" means the thing being named has the highest value possible; "better than nothing" means the thing being described has only marginal value. Therefore, "nothing" acts as two different words in this example, thus creating the fallacy of four terms.

Another example of equivocation, a more tricky one:

Major premise: The hand touches the pen.

Minor premise: The pen touches the paper.

Conclusion: The hand touches the paper.

This is more clear if you use "is touching" instead of "touches." It then becomes clear that "touching the pen" is not the same as "the pen," thus creating four terms: "the hand" "touching the pen", "the pen", "touching the paper." A correct form of this statement would be:

Major premise: The hand touches the pen.

Minor premise: All that touches the pen, touches the paper.

Conclusion: The hand touches the paper.

Now the term "the pen" has been eliminated, leaving three terms.

The fallacy of four terms is a syllogistic fallacy. Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms.