I'm learning about modus ponens in propositional logic but it doesn't makes sense to me
I can think of an examples where a true premises leads to a false conclusion:
p -> q
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 it was raining on him.
Another example: If the kid is smiling then he is happy the kid is smiling therefore he is happy (No,the kid just faked the smile it doesn't necessarily fellows that he is happy)
It's the same as saying: if it have 4 legs then it is a dog, it have 4 legs,therefore it is a dog. (no it's a cat)
Meaning: Q is just a possible outcome and there is not enuff information for us to deduce q as the true cause or the conclusion by applying modus ponens in natural language. For modus ponens to be correct according To its form, we need to see it as a necessary connection like the connection between fire and heat.
But as the examples shows And as far as i know modus ponens is not considered as a necessary connection, Rather it's considered as implication. p imply q or if p then q (some kind of a weak connection but not a necessary one).