Negative conclusion from affirmative premises
Negative conclusion from affirmative premisesis asyllogistic fallacycommitted when acategorical syllogismhas a negativeconclusionyet bothpremisesare affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing avalidcategorical syllogism.
Statements in syllogisms can be identified as the following forms:
- a:All A is B. (affirmative)
- e:No A is B. (negative)
- i:Some A is B. (affirmative)
- o:Some A is not B. (negative)
The rule states that a syllogism in which both premises are of formaori(affirmative) cannot reach a conclusion of formeoro(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):
- Premise: All colonels are officers.
- Premise: All officers are soldiers.
- Conclusion: Therefore, no colonels are soldiers.
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:
- All A is B.
- All B is C.
- Therefore, some C is not A.
This is valid only if A is aproper subsetof 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:
- All B is A.
- All C is B.
- Therefore, all C is A.
See also[edit]
- Affirmative conclusion from a negative premise,in which a syllogism is invalid because an affirmative conclusion is reached from a negative premise
- Fallacy of exclusive premises,in which a syllogism is invalid because both premises are negative
References[edit]
- ^Alfred Sidgwick (1901).The use of words in reasoning.A. & C. Black. pp.297–300.
- ^Fred Richman (July 26, 2003)."Equivalence of syllogisms"(PDF).Florida Atlantic University. p. 16. Archived fromthe original(PDF)on June 19, 2010.
External links[edit]
- Gary N. Curtis."Negative Conclusion from Affirmative Premisses".Fallacy Files.RetrievedDecember 20,2010.