Existential fallacy

Formal fallacies → Syllogistic / quantification

The existential fallacy is when you reason from "all X are Y" to "some X are Y" when X might not exist. You can't get "some" from "all" if nothing is there. In classical logic, "all unicorns have horns" doesn't imply that there are any unicorns, so "some unicorns have horns" doesn't follow. The argument assumes existence when the premises don't guarantee it.

Examples

  • All unicorns have horns. So some unicorns have horns.

  • All dragons breathe fire. So some dragons breathe fire.

  • All perfect numbers are even. So some perfect numbers are even.

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