Affirmative conclusion from a negative premise is a logical 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.
This could be illustrated mathematically as
- If A ⊄ B and B ⊄ C then A ⊂ C.
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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