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Fallacy of Four Terms

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:

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



Registered User Comments

Krista Neckles
Thursday, November 28, 2019 - 09:02:10 PM
Hello again Sir,

From the following excerpt I would like to know if it is possible to reduce the number of terms to three, or if the four-term fallacy would still occur:
"Autistic children are occasionally helped by aversion therapy. But aversion therapy is sometimes inhumane.Thus, autistic children are sometimes helped by inhumane therapy".

Thank you Sir(By the way I am not endorsing any point of view).

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Bo Bennett, PhD
Friday, November 29, 2019 - 09:39:49 AM
We can make this non-fallacious by combining terms, but do note that this DOES change the claim being made. This is also becomes a tautology.

Autistic children are sometimes helped by inhumane aversion therapy.
Thus, autistic children are sometimes helped by inhumane therapy.

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