Negative conclusion from affirmative premises is asyllogistic fallacy committed when acategorical syllogism has a negativeconclusion yet bothpremises are affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing avalid categoricalsyllogism.
Statements in syllogisms can be identified as the following forms:
The rule states that a syllogism in which both premises are of forma ori (affirmative) cannot reach a conclusion of forme oro (negative). Exactly one of the premises must be negative to construct a valid syllogism with a negative conclusion. (A syllogism with two negative premises commits the relatedfallacy of exclusive premises.)
Example (invalid aae form):
The aao-4 form is perhaps more subtle as it follows many of the rules governing valid syllogisms, except it reaches a negative conclusion from affirmative premises.
Invalid aao-4 form:
This is valid only if A is aproper subset of B and/or B is a proper subset of C. However, this argument reaches a faulty conclusion if A, B, and C areequivalent.[1][2] In the case that A = B = C, the conclusion of the following simple aaa-1 syllogism would contradict the aao-4 argument above:
