Negative conclusion from affirmative premises is a
syllogistic fallacy
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
...
committed when a
categorical syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...
has a negative
conclusion yet both
premise
A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agre ...
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:
* 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
In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ...
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 or Equivalent may refer to:
Arts and entertainment
*Album-equivalent unit, a measurement unit in the music industry
* Equivalence class (music)
*'' Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre
*''Equiva ...
.
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 premise
Affirmative conclusion from a negative premise (illicit negative) is a formal fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid b ...
, 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
External links
*
{{Formal fallacy
Syllogistic fallacies