Illicit Contraposition
A formal fallacy that occurs when switching the subject and predicate of a categorical proposition and negating each results in an invalid argument form, specifically for type E ('no') and type I ('some') propositions.
THE IDEA
Illicit Contraposition
New Terminology: A formal fallacy where switching the subject and predicate terms of a categorical proposition, then negating each, results in an invalid argument form. The examples below make this more clear. This is a fallacy only for type “E” and type “I” forms, or forms using the words “no” and “some”, respectively.
Logical Form:
- Type E ("No S are P") → Contraposition: "No non-P are non-S" – invalid.
- Type I ("Some S are P") → Contraposition: "Some non-P are non-S" – invalid.
Example #1:
- Premise: No Catholics are Jews. (assumed for this logical example)
- Conclusion (contraposition): No non-Jews are non-Catholics. (false – e.g., a non-Jew and non-Catholic person exists)
- Explanation: Treating the premise as given does not rule out people in neither category. Such a case makes the proposed conclusion false.
Example #2:
- Premise: Some dogs bark. (true)
- Conclusion (contraposition): Some non-barking things are non-dogs. (also true, but does not logically follow)
- Explanation: The argument is invalid because the form is flawed. For a countermodel, consider a nonempty universe in which every object is both S and P. The original particular claim is true, but there are no non-P objects to satisfy the proposed conclusion.
Exception:
Type A ("All S are P") and type O ("Some S are not P") are valid when contraposed: e.g., "All humans are mortals" contraposes to "All immortals are non-human" – valid.
Tip:
Check a proposed transformation by looking for a case in which the original statement is true and the transformed statement is false.
When to use it
Analyzing arguments in political speeches or debates to detect flawed reasoning based on categorical statements.
Evaluating logical reasoning in academic papers, especially in fields like philosophy or mathematics.
Avoiding errors in everyday reasoning when converting statements like 'No X are Y' into 'No non-Y are non-X'.
Teaching introductory logic courses to help students understand the difference between valid and invalid argument forms.
FROM THEORY TO EVERYDAY LIFE
In practice
Example with 'No' (Type E)
Premise: No Catholics are Jews, assumed for this example. Proposed conclusion: No non-Jews are non-Catholics. The premise does not exclude people who belong to neither category, so it does not establish the conclusion.
Example with 'Some' (Type I)
Premise: Some dogs bark. (true) Conclusion (contraposition): Some non-barking things are non-dogs. (also true, but the argument is invalid because the logical form is flawed; truth does not guarantee validity.)
A MOMENT TO REFLECT
Put it to work.
Can you identify a real-world argument that mistakenly uses illicit contraposition?
Why is it important to focus on the form of an argument rather than the truth of its premises?
How does illicit contraposition differ from the valid contraposition of type A and type O propositions?
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies