From diarrhea, on the misuse of logical implication

When we have diarrhea, people around us sometimes guess, "It must be something you are eating that is not fresh" or "It must be that you run around without clothes and get your stomach cold." But it was actually because I drank cold water after eating a plate of dried plums.
The first two are often misused: "Because you have diarrhea because you are not eating fresh". Whether from the perspective of logical implication or semantic implication, it is essentially a misuse of the implication symbol "→".

classical logic

modus ponens: A, A→B⊢B, the derivation process is interpreted as: now there is an A, if A then B, so B.
The substitution event is, if I have a parent who thinks that "without clothes, my stomach will be cold and I will have diarrhea", but he does not know the fact that I have eaten dried plums and drank cold water, and when he sees my diarrhea without clothes Next, the modus ponens inference will be offered: Look, if you don't wear clothes (A), if you don't wear clothes, you will be so cold that you will have diarrhea (A→B), how about you have diarrhea (B). But in fact, I didn't wear clothes yesterday, but I didn't have diarrhea, which means that today's A and B just happened to happen together, and there is no direct logical relationship.

linguistics

A,A→B⊨B, which is similar to the classical logical form, but expresses a completely different meaning, when expressing semantic implication, the meaning behind it is that if B is true, the antecedents are all true (generally expressed as a set Γ) . Also substitute the above event. In the case of my diarrhea (B) becoming a fact, according to the statement A, A→B⊨B derivation, A and A→B are both facts. A is indeed a fact, but it is not a fact that A semantically contains the form of B. Even in the intuitive semantics, "don't wear clothes" cannot contain the semantics of "diarrhea".

Misuse of A→B

A implies B, generally read as if A then B. But "if then" here does not mean "cause and consequence" in our traditional sense, but means that A contains B, B is a part of A, and B does not exist any part more than A.
For example, the sentence that misuses implication as causation "If you drive fast every day, there will be a car accident one day". The original meaning of this sentence is good, but since it is impossible to rule out special cases such as "one person drives an express train for two days and died at home due to a heart attack on the third day", which is not included in the previous sentence, this implication relationship cannot be established. . That is to say, under normal logic, a person must meet all the conditions for encountering that car accident at the same time (the "set Γ" mentioned earlier) in order to determine that the car accident occurred. Rather than a single cause "driving fast every day" will inevitably lead to a definite "car accident" outcome.

The correct concept of A→B

Logical derivation and intuitive judgment based on experience are two different things. The former is a rigorous argument, and the latter is that the more experience you have, the greater the probability that the intuition will match the facts, but after all, it is only an empirical judgment, and cannot be the premise of any complex derivation process.
For example, through the fact that I have diarrhea, it can semantically contain guesses such as "I may have a cold stomach", "I may have eaten expired food", or "I may have eaten dried plums and drank cold water"; In places other than the toilet, I must squat in the toilet", which further implies the logical result of "then I will squat in the toilet".

Conceptually, the form in which A implies B can be used only if the complete B is a part of A, such as "now there is a living cat sleeping on my pillow", then "the heart of this cat is Must be dancing" without implying "this cat is really cheap," despite the fact that he is.