Fallacy of Four Terms

Brad Pitt is a star, and stars are giant balls of gas, so Brad Pitt is a giant ball of gas.

The fallacy of four terms looks like a valid argument form called “Barbara”:
A is B.
B is C.
Therefore, A is C.

For example:
Frogs are amphibians.
Amphibians are cold-blooded.
Therefore, frogs are cold-blooded. (valid)

This argument has three terms:
A: frogs
B: amphibians
C: cold-blooded

How many terms does the following argument have?

Brad Pitt is a star.
Stars are giant balls of gas.
Therefore, Brad Pitt is a giant ball of gas.

It looks like it has three, but it really has four:
A: Brad Pitt
B: star (celebrity)
C: star (celestial object)
D: giant ball of gas

Therefore, it commits the fallacy of four terms:
A is B.
C is D.
Therefore, A is D.

Here, the extra term sneaks in through equivocation (i.e., using the same word to mean two different things in the same argument).

Here’s an example of the fallacy of four terms without equivocation:

Frogs are amphibians.
Dogs are mammals.
Therefore, frogs are mammals.

This mistake is obvious. The fallacy of four terms is more likely to fool us when combined with equivocation.

Here's a more realistic example of the fallacy of four terms:

Gravity is a theory.
A theory is a hunch.
Therefore, gravity is a hunch.

While it looks like there are three terms, there are actually four:
A: gravity
B: theory (scientific meaning)
C: theory (colloquial meaning)
D: hunch

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