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Existential Fallacy

A standard form categorical syllogism with two universal premises has a particular conclusion. The idea is that some universal properties need not be instantiated. It may be true that ‘all trespassers will be shot’ even if there are no trespassers. It may be true that ‘all brakeless trains are dangerous’ even though there are no brakeless trains. That is the point of this fallacy.


  1. All mice are animals, and all animals are dangerous, so some mice are dangerous.
  2. No honest people steal, and all honest people pay taxes, so some homest people pay taxes.


Assume that the premises are true, but that there are no instances of the category described. For example, in (i) above, assume there are no mice, and in (ii) above, assume there are no honest people. This shows that the conclusion is false.