Negative conclusion from affirmative premises
Encyclopedia
Negative conclusion from affirmative premises is a syllogistic fallacy
committed when a categorical syllogism has a negative conclusion yet both premise
s 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:
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):
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 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:
Syllogistic fallacy
Syllogistic fallacies are logical fallacies that occur in syllogisms. They include:Any syllogism type :*fallacy of four termsOccurring in categorical syllogisms:*related to affirmative or negative premises:...
committed when a categorical syllogism has a negative conclusion yet both premise
Premise
Premise can refer to:* Premise, a claim that is a reason for, or an objection against, some other claim as part of an argument...
s 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
Validity
In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is 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
Fallacy of exclusive premises
The fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.Example of an EOO-4 invalid proposition:...
.)
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
Equivalence relation
In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell...
. 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
- affirmative conclusion from a negative premiseAffirmative conclusion from a negative premiseAffirmative 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:...
, in which a syllogism is invalid because an affirmative conclusion is reached from a negative premise - fallacy of exclusive premisesFallacy of exclusive premisesThe fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.Example of an EOO-4 invalid proposition:...
, in which a syllogism is invalid because both premises are negative