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An existential assumption (or existential fallacy) occurs whenever the conclusion of a syllogism requires that a class has at least one member, but one or more of the premises do not.
- P1: All X, if they existed, would be Y. (valid)
- P2: All Y that exist are Z. (valid)
- C1: All X are Z. (invalid)
Universally true premises need not be instantiated. The truth value of the statement "all trespassers will be shot" does not depend on the existence of trespassers. People can still vow to shoot at any and all trespassers, even if none currently exist on their plot of land.
The fallacy occurs when there is a mismatch between the necessity of existence for the first and second premises. For example:
- P1: All unicorns are animals. (does not require existence; valid)
- P2: Animals are dangerous. (requires existence; valid)
- C1: Therefore, unicorns are dangerous. (invalid)
The problem with this argument is that the premises don't imply that conclusion is true, because a unicorn doesn't need to exist for it to be classed as an animal, yet it does need to exist to be dangerous.
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