quaternio terminorum

(also known as: ambiguous middle term)

**Description:** This fallacy occurs in a categorical syllogism when the syllogism has four terms rather than the requisite three (in a sense, it cannot be a categorical syllogism to begin with!) If it takes on this form, it is invalid. The *equivocation fallacy* can also fit this fallacy because the same term is used in two different ways, making four distinct terms, although only appearing to be three.

**Logical Form: **There are many possible forms, this is one example:

All X are Y.

All A are B.

Therefore, all X are B.

**Example #1:**

All cats are felines.

All dogs are canines.

Therefore, all cats are canines.

**Explanation:** When you add in a fourth term to a categorical syllogism that can only have three terms to be logically valid, we get nonsense -- or at least an invalid argument.

**Example #2:**

All Greek gods are mythical.

All modern day gods are real.

Therefore, all Greek gods are real.

**Explanation:** Again, nonsense. If we take away one of the terms, we end up with a valid syllogism:

All Greek gods are mythical.

All mythical gods don’t really exist.

Therefore, all Greek gods don’t really exist.

**References:** {apa}

Bunnin, N., & Yu, J. (2008). *The Blackwell Dictionary of Western Philosophy*. John Wiley & Sons.

{/apa}