The Existential Fallacy

“It is a curious feature of logic that statements which refer to the whole of a class do not actually tell us whether there are any members of that class.”

Madsen Pirie

This sentence introduces the principle of logic according to which statements that refer to the whole of a class, known as universal statements, do not necessarily provide information about the existence or non-existence of members of that class. For example, the statement “All dogs are mammals” is a universal statement that refers to the class of dogs and the class of mammals. While this statement tells us that all dogs belong to the class of mammals, it does not tell us whether or not there are any dogs in existence.

Universal statements can be either true or false, depending on whether they accurately describe the relationship between the classes they refer to. In the case of the statement “All dogs are mammals,” the statement is true because all dogs belong to the class of mammals. However, if the statement were “All dogs are reptiles,” it would be false because dogs do not belong to the class of reptiles.

It is important to understand that universal statements do not provide information about the existence or non-existence of members of the class they refer to. Instead, they describe the relationship between the classes they refer to, and they can be evaluated based on whether they accurately describe this relationship or not.

“Statements which tell us about some of a class, however, do imply the existence of member of the class”.

It is a principle of logic that statements that refer to some members of a class, known as particular statements, do imply the existence of members of that class. For example, the statement “Some dogs are golden retrievers” is a particular statement that refers to the class of dogs and the subcategory of golden retrievers. This statement tells us that at least one dog belongs to the subcategory of golden retrievers, and therefore implies the existence of at least one dog.

Particular statements can also be either true or false, depending on whether they accurately describe the relationship between the classes they refer to. In the case of the statement “Some dogs are golden retrievers,” the statement is true because there are indeed some dogs that belong to the subcategory of golden retrievers. However, if the statement were “Some dogs are unicorns,” it would be false because there are no dogs that belong to the class of unicorns.

So, particular statements do imply the existence of members of the class they refer to, as they describe a relationship between two classes where at least one member of the first class belongs to the second class. This is in contrast to universal statements, which do not necessarily provide information about the existence or non-existence of members of the class they refer to.

“If we have premises which do not imply existence and we draw from them a conclusion which implies existence, then we are committing a fallacy”

If you are starting with premises that do not imply the existence of any members of a class, and you are drawing a conclusion that implies the existence of at least one member of that class, you may be committing a logical fallacy known as the existential fallacy. This fallacy occurs when you infer the existence of something from a premise that does not provide any information about the existence or non-existence of that thing.

For example, consider the following argument:

Premise 1: All dogs are mammals.

Premise 2: Some mammals are carnivorous.

Conclusion: Some dogs are carnivorous.

In this argument, the first premise is a universal statement that does not imply the existence of any dogs. The second premise is a particular statement that implies the existence of at least one mammal. However, the conclusion is a particular statement that implies the existence of at least one dog. Because the conclusion implies the existence of something that was not implied by the premises, the argument commits the existential fallacy. It is important to be aware of the existential fallacy, as it can lead to invalid or unsound arguments. When constructing an argument, it is important to make sure that your conclusion is properly supported by your premises, and that you are not inferring the existence of something from a premise that does not provide any information about the existence or non-existence of that thing.