Modus Tollens
Modus Tollens (MT), “the way that denies by denying”, is also a very common valid argument form. It follows the form of negating the consequent of a given implication and concluding the negated antecedent of that implication.
a → b
¬b
¬a
Note: MT is based on the implication: You can review it here.
Although its description can sound scary, MT is very straightforward. One way to think of this form is by using the geography analogy given in the implication lesson:
“If you are in Los Angeles (L), then you are in California (C). You are not in California (¬C), so you are not in Los Angeles (¬L)”
- L → C
- ¬C
- ¬L MT 1, 2
Using this example, it becomes clear that because “something” that is necessary is negated, whatever depends on that “something” must also be negated. That is the gist of MT. In the example above, being in Los Angeles depends on being in California, so if you are not in California, you cannot be in Los Angeles.
The most common pitfall when using MT is again mistaking what is sufficient for what is necessary, but in this case, because the statements are negated, it would produce the fallacy of the inverse, which was touched upon in Implication.
Briefly restated, the fallacy of the inverse follows this form:
a → b
¬a
¬b
Note: The fallacy of the inverse “denies” (or negates) the sufficient condition of the given implication and concludes the negation of its necessary condition. That is like saying, “If you are in Los Angeles, you must be in California. You are not in Los Angeles, so you are not in California”–that is not right because you can potentially be anywhere else in California, so long as you are outside of Los Angeles.
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Modus Tollens (MT), “the way that denies by denying”, is also a very common valid argument form. It follows the form of negating the consequent of a given implication and concluding the negated antecedent of that implication.
a → b
¬b
¬a
Note: MT is based on the implication: You can review it here.
Although its description can sound scary, MT is very straightforward. One way to think of this form is by using the geography analogy given in the implication lesson:
“If you are in Los Angeles (L), then you are in California (C). You are not in California (¬C), so you are not in Los Angeles (¬L)”
- L → C
- ¬C
- ¬L MT 1, 2
Using this example, it becomes clear that because “something” that is necessary is negated, whatever depends on that “something” must also be negated. That is the gist of MT. In the example above, being in Los Angeles depends on being in California, so if you are not in California, you cannot be in Los Angeles.
The most common pitfall when using MT is again mistaking what is sufficient for what is necessary, but in this case, because the statements are negated, it would produce the fallacy of the inverse, which was touched upon in Implication.
Briefly restated, the fallacy of the inverse follows this form:
a → b
¬a
¬b
Note: The fallacy of the inverse “denies” (or negates) the sufficient condition of the given implication and concludes the negation of its necessary condition. That is like saying, “If you are in Los Angeles, you must be in California. You are not in Los Angeles, so you are not in California”–that is not right because you can potentially be anywhere else in California, so long as you are outside of Los Angeles.
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to the first studycard and the first level of all activities for free. Get the app now: