Modus Tollens
Modus tollens is a valid argument form that denies the consequent of a conditional statement to infer the negation of the antecedent. It is the logical pattern: If A then B; Not B; Therefore, not A.
THE IDEA
This valid argument form is similar to modus ponens. However, where modus ponens affirms the antecedent of the conditional statement, modus tollens denies the consequent of the conditional statement. This is why it is translated from the Latin as the “mode of removing.” For example:
If the candle is lit, then there is a flame. There is no flame. Therefore, the candle is not lit.
Here, the consequent of the conditional statement is denied (or negated) in the second premise. And from this, it logically follows that the conclusion is true. Modus tollens takes the following symbolic form:
If A then B. Not B. Therefore, not A.
Here are some more examples of modus tollens. Treat each conditional as a premise for the exercise; the citizenship example is not a complete statement of citizenship law:
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If Steven was born in the United States, then he is a citizen of the United States. Steven is not a citizen of the United States. Therefore, Steven was not born in the United States.
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If Sally has a cat, then she is a pet owner. Sally is not a pet owner. Therefore, Sally does not have a cat.
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If the magician’s assistant had been decapitated, then she would be dead. The magician’s assistant is not dead. Therefore, the magician’s assistant was not decapitated.
In these examples we see clearly the modus tollens pattern. Modus tollens, like modus ponens, is a valid and coherent logical form that should be remembered and employed.
When to use it
Testing a hypothesis: if it necessarily predicts an observation under the test conditions, failure to observe it challenges the hypothesis or the supporting assumptions.
Debugging: if a correct function with valid inputs must produce a particular output, an incorrect output shows that at least one of those assumptions has failed.
Evaluating an alibi: clean shoes rule out presence at a scene only if being there necessarily would have left the shoes muddy and nothing could have removed the mud.
FROM THEORY TO EVERYDAY LIFE
In practice
Candle and flame
If the candle is lit, then there is a flame. There is no flame. Therefore, the candle is not lit.
US Citizenship
Assume for this exercise: if Steven was born in the United States, then he is a citizen of the United States. Steven is not a citizen of the United States. Therefore, Steven was not born in the United States.
Pet owner
If Sally has a cat, then she is a pet owner. Sally is not a pet owner. Therefore, Sally does not have a cat.
Magician's assistant
If the magician’s assistant had been decapitated, then she would be dead. The magician’s assistant is not dead. Therefore, the magician’s assistant was not decapitated.
A MOMENT TO REFLECT
Put it to work.
Can you think of a real-life situation where you used modus tollens to draw a conclusion?
How does modus tollens differ from affirming the consequent, which is a logical fallacy?
Why is it important to understand valid argument forms like modus tollens in everyday reasoning?
CONTINUE THE CONVERSATION
Source texts
- Informal Logical Fallacies A Brief Guide