Existential fallacy
Encyclopedia
The existential fallacy, or existential instantiation, is a logical fallacy in Boolean logic
while it is not in Aristotelian logic. In an existential fallacy, we presuppose that a class has members even when we are not explicitly told so; that is, we assume that the class has existential import.
An existential fallacy committed in a categorical syllogism is invalid
because it has two universal premises and a particular conclusion. In other words, for the conclusion to be true, at least one member of the class must exist, but the premises do not establish this.
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 enthymeme
s, where hidden premises required to make the syllogism valid assume the existence of at least one member of the class.
This is an existential fallacy of subalternation. However, in Aristotelian logic, this mode of reasoning is perfectly permissible. Let S=soldiers and P=heroes. We then have:
That is, if all soldiers are heroes, then at least one of them must be a hero. Nevertheless, Boole came around with his objection. He said that it is impermissible to presuppose that that "All S are P".
> All S1 (inhabitants of other planets) are P (friendly beings).
> All S2 (Martians) are S1.
Therefore, all Martians are friendly beings.> All S2 are P.
>Some S2 are P.
"Some Martians are friendly beings" implies that there is at least one Martian. This conclusion is an existential fallacy. The absurdity of the result becomes especially evident whenever we use imaginary objects such as Martians or fairies.
In Boolean logic, the universal proposition is not assumed to have members. Here, the universal propositions would be (1) and (2). However, classes in particular propositions like (3) are assumed to have members. We cannot go from the proposition (2) to its subaltern (3).
The existential fallacy is a syllogistic fallacy
. Modern logical constructs, however, allow for conditional logic ("If Martians existed...").
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...
while it is not in Aristotelian logic. In an existential fallacy, we presuppose that a class has members even when we are not explicitly told so; that is, we assume that the class has existential import.
An existential fallacy committed in a categorical syllogism is invalid
Validity
In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....
because it has two universal premises and a particular conclusion. In other words, for the conclusion to be true, at least one member of the class must exist, but the premises do not establish this.
Boolean logic
In modern times, presupposition that a class has members is seen as unacceptable. In 1905, Bertrand RussellBertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
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 enthymeme
Enthymeme
An enthymeme , in its modern sense, is an informally stated syllogism with an unstated assumption that must be true for the premises to lead to the conclusion. In an enthymeme, part of the argument is missing because it is assumed...
s, where hidden premises required to make the syllogism valid assume the existence of at least one member of the class.
First example
Let S=subject and P=predicate. Consider the following two propositions:- A proposition says, "All S is P."
- I proposition says, "Some S is P."
This is an existential fallacy of subalternation. However, in Aristotelian logic, this mode of reasoning is perfectly permissible. Let S=soldiers and P=heroes. We then have:
- All S (soldiers) are P (heroes).
- Some S is P.
That is, if all soldiers are heroes, then at least one of them must be a hero. Nevertheless, Boole came around with his objection. He said that it is impermissible to presuppose that that "All S are P".
Second example
(1) All inhabitants of other planets are friendly beings> All S1 (inhabitants of other planets) are P (friendly beings).
(2) All Martians are inhabitants of another planet.
> All S2 (Martians) are S1.Therefore, all Martians are friendly beings.
> All S2 are P.
(3) Some Martians are friendly beings.
>Some S2 are P."Some Martians are friendly beings" implies that there is at least one Martian. This conclusion is an existential fallacy. The absurdity of the result becomes especially evident whenever we use imaginary objects such as Martians or fairies.
In Boolean logic, the universal proposition is not assumed to have members. Here, the universal propositions would be (1) and (2). However, classes in particular propositions like (3) are assumed to have members. We cannot go from the proposition (2) to its subaltern (3).
The existential fallacy is a syllogistic fallacy
Syllogistic fallacy
Syllogistic fallacies are logical fallacies that occur in syllogisms. They include:Any syllogism type :*fallacy of four termsOccurring in categorical syllogisms:*related to affirmative or negative premises:...
. Modern logical constructs, however, allow for conditional logic ("If Martians existed...").