Negative Conclusion from Affirmative Premises
A logical fallacy where a categorical syllogism has a negative conclusion yet both premises are affirmative, violating the rule that any valid syllogism with a negative conclusion must have at least one negative premise.
THE IDEA
Negative Conclusion from Affirmative Premises
(also known as: illicit affirmative)
Description: The conclusion of a standard form categorical syllogism is negative, but both of the premises are positive. Any valid forms of categorical syllogisms that assert a negative conclusion must have at least one negative premise.
Logical Form: Both premises of a categorical syllogism are affirmative, but its conclusion denies a relationship.
Example #1:
- All cats are animals.
- Some pets are cats.
- Therefore, some pets are not animals.
Explanation: The conclusion might be true – I had a pet rock growing up, but the argument still does not logically support that. Think of sets and subsets. All cats are animals: we have a set of animals and a subset of cats. “Some” pets are cats: so all we know is that there is a part of our set, “pets” that intersects with the subset, “cats”, but we don’t have the information we need to logically conclude that some pets are not animals. This argument is invalid, thus as a formal argument, it is fallacious.
Example #2:
- All dogs are mammals.
- All poodles are dogs.
- Therefore, some poodles are not mammals.
Explanation: The premises place every poodle among dogs and every dog among mammals. The conclusion that some poodles are not mammals conflicts with those premises.
Exception: None.
When to use it
When analyzing a standard categorical syllogism, checking whether a negative conclusion has at least one negative premise.
In a logic exercise, using sets to see which relationships affirmative premises establish.
In education, teaching students to avoid this fallacy when constructing syllogisms.
When evaluating a categorical syllogism in a legal or scientific discussion, checking its form before assessing whether its premises are true.
FROM THEORY TO EVERYDAY LIFE
In practice
Example #1: All cats are animals, some pets are cats, therefore some pets are not animals.
The conclusion might be true – I had a pet rock growing up, but the argument still does not logically support that. Think of sets and subsets. All cats are animals: we have a set of animals and a subset of cats. “Some” pets are cats: so all we know is that there is a part of our set, “pets” that intersects with the subset, “cats”, but we don’t have the information we need to logically conclude that some pets are not animals. This argument is invalid, thus as a formal argument, it is fallacious.
Example #2: All dogs are mammals, all poodles are dogs, therefore some poodles are not mammals.
The premises place every poodle among dogs and every dog among mammals. The conclusion that some poodles are not mammals conflicts with those premises.
A MOMENT TO REFLECT
Put it to work.
How can you spot a negative conclusion from affirmative premises in an argument?
Can you construct an example of a valid categorical syllogism with a negative conclusion?
Why is it necessary to have at least one negative premise to support a negative conclusion?
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies