The Existential Fallacy

Taxonomy: Logical Fallacy > Formal Fallacy > Quantificational Fallacy > The Existential Fallacy

Alias: The Fallacy of Existential Assumption

History:

In the traditional formal logic of categorical syllogisms developed by Aristotle and subsequent logicians through the Middle Ages and up to the middle of the nineteenth century, it was assumed that the classes of things referred to by the subject and predicate terms of categorical propositions were non-empty. For this reason, certain arguments were considered valid that would not be valid if some class were empty: in particular, it was thought that an A-type proposition implied an I-type with the same subject and predicate terms, and an E-type implied an O-type, again with the same subject and predicate terms:

Subalternation
All Catholics are christians. No atheists are christians.
Therefore, some christians are Catholics. Therefore, some christians are not atheists.

This type of inference, which is called "subalternation", is a non-validating form of argument if one of the terms refers to an empty class, such as "unicorns"; see the Counter-Example, below.

For reasons explained in the Exposure, below, logicians of the later nineteenth century dropped the traditional assumption of non-emptiness, and adopted what is called the "Boolean interpretation"—after logician George Boole—of universal quantifiers. Under the Boolean interpretation, I- and O-type propositions have existential import―see the Exposition, below―whereas both A- and E-types lack it. This has the consequence that some immediate inferences—such as subalternation—and categorical syllogisms which were valid under the traditional interpretation become instances of the existential fallacy.

Form:

Any argument whose conclusion implies that a class has at least one member, but whose premisses do not so imply. Usually, this involves arguing from a universal premiss or premisses to a particular conclusion.

Example Counter-Example
All trespassers will be prosecuted. All unicorns are animals.
Therefore, some of those prosecuted will have trespassed. Therefore, some animals are unicorns.
Venn diagram

Venn Diagram:

This diagram represents both the Example and Counter-Example, which it shows to be invalid, since the area with the question mark would be empty if the class S were empty.

Exposition:

A proposition has existential import if it implies that some class is not empty, that is, that there is at least one member of the class. For example:

Existential Import No Existential Import
There are black swans. There are no ghosts.

"There are black swans" implies that the class of black swans is not empty, whereas "There are no ghosts" implies that the class of ghosts is empty. To reason from premisses that lack existential import for a certain class to a conclusion that has it is to commit the Existential Fallacy.

Exposure:

Source:

Irving Copi & Carl Cohen, Introduction to Logic (Tenth Edition) (Prentice Hall, 1998), pp. 181-184.