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The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, one presupposes that a class has members when one is not supposed to do so; i.e., when one should not assume existential import.
One example would be: "Every unicorn definitely has a horn on its forehead". It does not imply that there are any unicorns at all in the world, and thus it cannot be assumed that, if the statement were true, somewhere there is a unicorn in the world (with a horn on its forehead). The statement, if assumed true, implies only that if there were any unicorns, each would definitely have a horn on its forehead.
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, an assumption 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".
In the following syllogism, it is incorrectly concluded that dinosaurs exist.
- All dinosaurs are reptiles
- All reptiles lay eggs
- Some dinosaurs lay eggs
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