The first thing you're ever taught about the contrapositive, generally at the same time the name is taught, is that a statement is exactly equivalent to its contrapositive.
For one thing, the law of the excluded middle holds here just as it holds everywhere else. You've got two options:
- Smoking pot makes you cool.
- Smoking pot does not make you cool.
Those cover all cases.
But, the point I'm making is that you are incorrect to label "being cool helps you access pot" as "the contrapositive" of "smoking pot makes you cool". The concept of a contrapositive does not apply to "smoking pot makes you cool", because it is not a conditional statement.
If you want to cast the idea you're supporting as a conditional statement, you have "if you're not cool, you don't smoke pot". This actually has a contrapositive, "if you smoke pot, you're cool", and it is the same idea.
I don't believe that innovative misuse of specialized technical terms is actually a good idea. When the word you'd really like to use doesn't mean what you want it to mean, suck it up and use some different words.
The symbols above? They're English sentences, and they're perfectly clear in context. You're making a category error by trying to treat them as logical propositions, and it's leading you to waste your time on pedantry.
All right. Why do you choose to call "being cool gets you access to pot" the "contrapositive" of "smoking pot makes you cool"? What is the benefit of using a term from an unrelated area which means something different than what you mean? Why is it a category error for me to treat you as talking about logic when you use a term which is restricted to formal logic?
> No, the contrapositive.
The first thing you're ever taught about the contrapositive, generally at the same time the name is taught, is that a statement is exactly equivalent to its contrapositive.