Negative conclusion from affirmative premises

Formal fallacies → Syllogistic / quantification

Negative conclusion from affirmative premises is when both of your starting facts are positive ("all … are …" or "some … are …") but you conclude something negative ("no … are …" or "some … are not …"). In classical syllogistic logic, you can't validly get a negative conclusion from two affirmative premises. The two positives don't license that negative step.

Examples

  • All birds have wings. All sparrows are birds. So no sparrows are flightless.

  • All mammals are warm-blooded. All whales are mammals. So no whales are cold-blooded.

  • All employees are trained. All managers are employees. So no managers are untrained.

  • All metals conduct electricity. Copper is a metal. So no non-metals conduct electricity.

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