Quaternio terminorum

Quaternio terminorum is a fallacious syllogism with four terms instead of three, because one term changes meaning.

Example

“Men are free.”
“Women are not men.”
“Therefore, women are not free.”
(“Men” shifts meaning.)

Applied example (political)

“Citizens are free. Immigrants are not citizens. Therefore immigrants are not free.” (The term shifts meaning.)

Applied example (mystical)

“Light is good. This lamp is not light. Therefore this lamp is not good.” (“Light” is used in two senses.)

Why it is fallacious

• An equivocal term introduces a hidden fourth term.
• The conclusion depends on the shift in meaning.
• The form looks valid but is not.

How to spot it

• A key word has two senses.
• The syllogism hinges on that ambiguity.
• Terms are left undefined.

How to respond

• Define terms consistently.
• Rebuild the syllogism with a single meaning.
• Show that without ambiguity the conclusion fails.