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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

p

Therefore 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).

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    "If the kid is wet in the winter, then it was raining on him" In your example this premise is false, since the antecedent is true and the consequent is false. But if all your premises were true, the conclusion would have to be true as well, that's all it means for an argument to be logically valid (on the other hand, a "sound" argument is logically valid and it has true premises, so your example is logically valid but unsound).
    – Hypnosifl
    Jun 25 at 18:20
  • As many have already said (1, 2, your conditional hypothesis is not true in the situations you describe so modus ponens can't be applied there. I don't know what else you expect to hear at this point. "P->Q" means exactly that as soon as you know that P is true, you can immediately be absolutely certain that Q is true. This isn't the case in your "examples." Maybe you're mixing up necessary and sufficient conditions (e.g. it is true that "If the kid gets rained on then he is wet")? Jun 25 at 18:35
  • @Hypnosifl thanks for your comment i think i understand what you are saying, but i don't see how this inference rule can help us in the real world rather then emphasizing the obvious.. if i walk on the street in winter outside, and i see a wet kid, and i have a general assumption(a Premise) that if the kid is wet then it was raining on him, how can i conclude correctly the cause?
    – Dasem
    Jun 25 at 18:38
  • If i can't what's the point of modus ponens except stating the obvious.
    – Dasem
    Jun 25 at 18:40
  • Real world inferences usually involve inductive reasoning which is fundamentally different than purely deductive reasoning, and formal logic (including modus ponens) is just about deductive reasoning. The most common application of pure deductive reasoning is probably in mathematical proofs; it may help to think of logic problems as basically like word-problems in math.
    – Hypnosifl
    Jun 25 at 18:42
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"If the kid is wet in the winter, then it was raining on him" In your example this premise is false, since the antecedent is true and the consequent is false. But if all your premises were true, the conclusion would have to be true as well, that's all it means for an argument to be logically valid (on the other hand, a "sound" argument is logically valid and it has true premises, so your example is logically valid but unsound).

Real world inferences usually involve inductive reasoning which is fundamentally different than purely deductive reasoning, and formal logic (including modus ponens) is just about deductive reasoning. The most common application of pure deductive reasoning is probably in mathematical proofs; it may help to think of logic problems as basically like word-problems in math.

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