Why is modus tollens valid

Therefore, it is not a car. It has wheels. Therefore, it is a car. Comment: why is this incorrect? Well, the thing might have wheels but that doesn't mean it has to be a car. It might be a cart, or rollerblades, or a moped. It doesn't have to be a car. It is not a car. Therefore, it does not have wheels.

Consider the argument for the "affirming the consequent" example. Rollerblades are not cars, but they DO have wheels. Here are less sensible examples. Can you determine whether these are examples of Modus Ponens, Modus Tollens, or one of the incorrect constructions? The inference says: if you have proven that if b is an even number then b is a number, and further you have proven that b is a number, then you have in fact proven that b is an even number.

This is clearly fallacious. If we have proved Q then we know that 3 is a number, which is great to verify. A lot of philosophical logical literature has been devoted to discussing the pros and cons of MT and similar basic inference rules and their different forms, and the principles we commit to when we accept them.

I can't go into those because. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Asked 7 years, 8 months ago. Active 5 years, 1 month ago. Viewed 1k times. Improve this question. Often Right Often Right 2 2 silver badges 7 7 bronze badges. Add a comment. Active Oldest Votes. Don't be misled by the second way of presenting Modus Tollens MT. For example, the hard and fast absolute statement: If you have a current password, then you can log into the network According to this statement, a current password is sufficient for you to be able to log in.

So, if we assume this to be true, as we do in the argument below, and we assume that you can't log into the network, then we can definitely conclude: you don't have a current password. So here it is again: You can't log into the network If you have a current password, then you can log into the network Therefore You don't have a current password.

All fish have scales. This salmon is a fish. Therefore, this salmon has scales. All surfers are hot. Conrad is not hot.