Existential Fallacy

The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, we presuppose that a class has members when we are not supposed to do so; that is, when we should not assume existential import.

An existential fallacy is committed in a medieval categorical syllogism because it has two universal premises and a particular conclusion with no assumption that at least one member of the class exists, which is not established by the premises.

In modern logic, the presupposition that a class has members is seen as unacceptable. In 1905, Bertrand Russell wrote an essay entitled "The Existential Import of Proposition", in which he called this Boolean approach "Peano's interpretation".

The fallacy does not occur in enthymemes, where hidden premises required to make the syllogism valid assume the existence of at least one member of the class.

One central concern of the Aristotelian tradition in logic is the theory of the categorical syllogism. This is the theory of two-premised arguments in which the premises and conclusion share three terms among them, with each proposition containing two of them. It is distinctive of this enterprise that everybody agrees on which syllogisms are valid. The theory of the syllogism partly constrains the interpretation of the forms. For example, it determines that the A form has existential import, at least if the I form does. For one of the valid patterns (Darapti) is:

Every C is B

Every C is A

So, some A is B

This is invalid if the A form lacks existential import, and valid if it has existential import. It is held to be valid, and so we know how the A form is to be interpreted. One then naturally asks about the O form; what do the syllogisms tell us about it? The answer is that they tell us nothing. This is because Aristotle did not discuss weakened forms of syllogisms, in which one concludes a particular proposition when one could already conclude the coresponding universal. For example, he does not mention the form:

No C is B

Every A is C

So, some A is not B

If people had thoughtfully taken sides for or against the validity of this form, that would clearly be relevant to the understanding of the O form. But the weakened forms were typically ignored. —Terence Parsons, The Stanford Encyclopedia of Philosophy