Definition:Fallacy of Four Terms

Definition

Consider a categorical syllogism $S$ of the form:

Major Premise:	$\map {\mathbf \Phi_1} {A, B}$
Minor Premise:	$\map {\mathbf \Phi_2} {C, D}$
Conclusion:	$\map {\mathbf \Phi_3} {x, y}$

where:

$A$, $B$, $C$ and $D$ are terms of the categorical syllogism

each of $\mathbf \Phi_1$, $\mathbf \Phi_2$ and $\mathbf \Phi_3$ is one of the categorical statements $\mathbf A$, $\mathbf E$, $\mathbf I$ or $\mathbf O$

$x$ and $y$ are each one of $A$, $B$, $C$ and $D$.

Then $S$ commits the fallacy of four terms.

Examples

Arbitrary Example

The following is an example of the fallacy of four terms:

$(1): \quad$ All metals are elements.

$(2): \quad$ Brass is a metal.

$(3): \quad$ Therefore, brass is an element.

Also see

• Definition:Equivocation

• Results about the fallacy of four terms can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fallacy