Existential fallacy
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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.
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[edit] Boolean logic
In modern times, 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.
[edit] Examples
[edit] 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".
[edit] 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. Modern logical constructs, however, allow for conditional logic ("If Martians existed...").
[edit] See also
[edit] References
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This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.
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