Fallacy of Four Terms - Explanation

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 do not connect "humans" with "fins", so the reasoning is invalid. Notice that there are four terms: "fish", "fins", "goldfish" and "humans". Two premises are not 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" only means that the thing being described has some 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 pen touches the paper.

Minor premise: The hand touches the pen.

Conclusion: The hand touches the paper.

This is more clear if one uses "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: All that touches the pen, touches the paper.

Minor premise: The hand touches the pen.

Conclusion: The hand touches the paper.

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

The fallacy of four terms also applies to syllogisms that contain five or six terms.