Modus Tollens
Modus tollens (MT) arguments have the same first premise as with modus ponens, but the denial of the second premise leads to the conclusion that the first part of the premise should be denied as well.
Its logical form is as follows.
- If A, then B
- Not B
- Therefore, not A.
In common language, the argument can be expressed as following.
- If you have a PhD, then you are a graduate
- You are not a graduate
- Therefore, you don’t have a PhD.
While denying the consequent implies denial of the antecedent, the reverse is not true. Hence, the following argument shall be invalid.
- If A, then B
- Not A
- Therefore, not B.
In common language
- If you have a PhD, then you are a graduate
- You don’t have a PhD
- Therefore, you are not a graduate.
This argument is clearly wrong because you first become a graduate and then go for a PhD. Hence, not having PhD does not mean that you are not a graduate. The argument hardly appears convincing to anyone. Therefore, it can’t be said to be a fallacy.
Now consider another argument,
- If you have a PhD in Indian philosophy, you possess good knowledge of Indian philosophy.
- You don’t have a PhD in Indian philosophy.
- Therefore, you don’t have good knowledge of Indian philosophy.
This argument is a logical fallacy since a person can have excellent knowledge of Indian philosophy by self-learning even without formally getting PhD degree in the subject. However, this argument is commonly used in most academic institutions to deny a non-PhD applicant the opportunity to teach. In reality, some of the greatest philosophers in the world never had a PhD degree in philosophy.
