Negative Conclusion from Affirmative Premisses

Alias: Negative Conclusion with No Negative Premiss*

Taxonomy: Logical Fallacy > Formal Fallacy > Syllogistic Fallacy > Negative Conclusion from Affirmative Premisses

Sibling Fallacy: Affirmative Conclusion from a Negative Premiss


Any form of categorical syllogism with a negative conclusion and affirmative premisses.

Example Counter-Example
All pets are tame animals.
Some birds are pets.
Therefore, some birds are not tame.
All dogs are animals.
Some pets are dogs.
Therefore, some pets are not animals.
Venn diagram

Venn Diagram:

This diagram shows that both the Example and Counter-Example are invalid, since it fails to show that there is anything in the area with the question mark.

Syllogistic Rule Violated:

Any validating form of categorical syllogism with both premisses affirmative has an affirmative conclusion.


Inferring a negative conclusion in a syllogistic argument that has no negative premisses is a formal fallacy of categorical syllogisms. This is a type of rule-breaking fallacy, and the rule broken by an argument of this form is that shown just above. All validating forms of categorical syllogism that have a negative conclusion also have exactly one negative premiss, which can be shown by inspection of the 256 different forms of categorical syllogism. However, it's intuitive that if a negation appears in the conclusion then at least one premiss should be negative. However, this does not necessarily generalize to other systems of logic, so one should not assume that just any argument with a negative conclusion and no negative premisses commits this fallacy, that is, the fallacy applies only to categorical syllogisms.


*Note: J. L. Mackie, "Fallacies", The Encyclopedia of Philosophy, Paul Edwards, Editor in Chief, (1972), p. 171