Also known as the illicit negative, drawing an affirmative conclusion from negative premises, fallacy of negative premises

This is a formal logical fallacy. Formal fallacies can be confusing and are not as common in everyday situations. They can take some time to fully understand them and to pick them out in day to day life.

Terminology:

Syllogism: an argument typically consisting of three parts: a major premise, a minor premise, and a conclusion.

Categorical Term: usually expressed grammatically as a noun or noun phrase, each categorical term designates a class of things.

Categorical Proposition: joins exactly two categorical terms and asserts that some relationship holds between the classes they designate.

Categorical Syllogism: an argument consisting of exactly three categorical propositions: a major premise, a minor premise, and a conclusion, in which there appears a total of exactly three categorical terms, each of which is used exactly twice.

Description: The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative. Any valid forms of categorical syllogisms that assert a negative premise must have a negative conclusion.

Logical Form:

Any form of categorical syllogism with an affirmative conclusion and at least one negative premise.

Example A

No people under the age of 66 are senior citizens.

No senior citizens are children.

Therefore, all people under the age of 66 are children.

Explanation: In this case, the conclusion is obviously counterfactual although both premises are true.  Why?  Because this is a categorical syllogism where we have one or more negative premises (i.e., “no people…” and “no senior citizens…”), and we are attempting to draw a positive (affirmative) conclusion (i.e., “all people…”). 

Example B

No donkeys are fish.

Some asses are donkeys.

Therefore, some asses are fish.

Explanation: This is a categorical syllogism where we have a single negative premise (i.e., “no donkeys”), and we are attempting to draw a positive (affirmative) conclusion (i.e., “some asses”).

Tip: Syllogisms and identifying formal fallacies, at least by form, are common on intelligence tests. Learn them and become more intelligent! (at least on paper).

References:

Schuyler, A. (1859). The principles of logic: for high schools and colleges. Wilson, Hinkle & co.