Philosophy:Negative conclusion from affirmative premises
Negative conclusion from affirmative premises is a syllogistic fallacy committed when a categorical syllogism has a negative conclusion yet both premises are affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing a valid categorical 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 form a or i (affirmative) cannot reach a conclusion of form e or o (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 related fallacy 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 a proper subset of B and/or B is a proper subset of C. However, this argument reaches a faulty conclusion if A, B, and C are equivalent. 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.
- 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
- Alfred Sidgwick (1901). The use of words in reasoning. A. & C. Black. pp. 297–300. https://archive.org/details/useofwordsinreas00sidgiala.
- Fred Richman (July 26, 2003). Equivalence of syllogisms. Florida Atlantic University. p. 16. http://www.math.fau.edu/richman/docs/syllog-4.pdf.
- Gary N. Curtis. "Negative Conclusion from Affirmative Premisses". Fallacy Files. http://www.fallacyfiles.org/negfroma.html.
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