In order to write arguments in the forms of modus ponens and modus tollens, it's important to understand the formal differences between the modes. The modus ponens "affirms by affirming". In other words, it claims: "If P, then Q." It then asserts P, and concludes Q. An example would be:
- If the pond is frozen, it is winter. The pond is frozen. Therefore it is winter.
The modus tollens works by denying the consequent. In other words, if P implies Q and Q is not the case, then P could not have been the case.
- If the pond is frozen, it is winter. It is not winter. Therefore the pond is not frozen.