2. The Existential Fallacy

The existential fallacyis committed when an argument is invalid merely because the premise or premises are interpreted as lacking existential import. With regard specifically to the Aristotelian standpoint and the traditional square of opposition, the existential fallacyoccurs whenever the contrary relation, the subcontrary relation, or the subalternation relation is used with a proposition about nonexistent things (as long as the relation is used properly otherwise).

The existential fallacy cannot be committed in a correct use of the contradictory relation (even if the subject term does not denote anything that actually exists) because the contradictory relation does not depend on the assumption of existential import. This is why the contradictory relation is the only relation that appears both on the traditional square of opposition and on the modern square of opposition.

Use the selection lists to indicate whether each of the following immediate inferences commits the existential fallacy. Also indicate which relation is being used to link the premise with the conclusion in an otherwise correct way.

Argument 1

	It is false that some meteorites are iron-nickel metal fragments.
	Therefore, it is false that all meteorites are iron-nickel metal fragments.

In Argument 1, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 1 commit the existential fallacy.

Argument 2

	It is false that some forms of unleaded gasoline are high-octane fuels.
	Therefore, some forms of unleaded gasoline are not high-octane fuels.

In Argument 2, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 2 commit the existential fallacy.

Argument 3

	All gnomes are creatures who wear pointy hats.
	Therefore, it is false that some gnomes are not creatures who wear pointy hats.

In Argument 3, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 3 commit the existential fallacy.

Argument 4

	All African elephants are large mammals.
	Therefore, it is false that no African elephants are large mammals.

In Argument 4, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 4 commit the existential fallacy.

Argument 5

	It is false that some harpies are not furies.
	Therefore, some harpies are furies.

In Argument 5, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 5 commit the existential fallacy.

Argument 6

	It is false that some unicorns are racehorses for elves.
	Therefore, it is false that all unicorns are racehorses for elves.

In Argument 6, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 6 commit the existential fallacy.

Argument 7

	Some college presidents are accomplished academicians.
	Therefore, it is false that no college presidents are accomplished academicians.

In Argument 7, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 7 commit the existential fallacy.

Argument 8

	All mythical nymphs are spirits who live in groves.
	Therefore, it is false that no mythical nymphs are spirits who live in groves.

In Argument 8, the immediate inference makes use of the relation.

The subject term in these categorical propositions denote something that actually exists.

Therefore, Argument 8 commit the existential fallacy.