Affirmative conclusion from a negative premise

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Affirmative conclusion from a negative premise (illicit negative) is a formal fallacy that is committed when a categorical syllogism has a positive conclusion, but one or two negative premises.

For example:

No fish are dogs, and no dogs can fly, therefore all fish can fly.

The only thing that can be properly inferred from these premises is that some things that are not fish cannot fly, provided that dogs exist.

Or:

We don't read that trash. People who read that trash don't appreciate real literature. Therefore, we appreciate real literature.

This could be illustrated mathematically as

If A \cap B = \emptyset and B \cap C = \emptyset then AC.

It is a fallacy because any valid forms of categorical syllogism that assert a negative premise must have a negative conclusion.

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