Fallacy of exclusive premises

Formal fallacies → Syllogistic / quantification

The fallacy of exclusive premises is when both of your starting facts are negative ("no X are Y"). Two "no"s don't link the terms in a way that supports any conclusion about how they relate. You need at least one positive premise to connect the categories. With only negative premises, the argument has no valid conclusion.

Examples

  • No dogs are cats. No cats are birds. So no dogs are birds.

  • No reptiles are mammals. No fish are reptiles. So no fish are mammals.

  • No students were absent. No teachers were absent. So no students are teachers.

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