Why is modus ponens a valid form?

Question

Why is modus ponens in prepositional logic considered a valid form?

I can think of an example where a true premise leads to a false conclusion:

If the kid is wet in the winter, then it was raining on him

The kid is wet in the winter

Conclusion: it was raining on him

Where, in fact,

The kid is wet in the winter

A passing car splashed water on him

Therefore, it is not the case that it was raining on him.

Answer 1

Maybe writing it formally helps. To deduce $q$ through modus ponens, we need:

$(p \implies q) \wedge p$

i.e. the premise p and the implication itself must be true. Remember that $(p \implies q)$ is itself a proposition, either true or false. In your case, $p \implies q$ is NOT true, since a kid being wet does not imply that it has rained.

Modus ponens is the inference rule itself, but it doesn't tell you about whether the premises are true or not.