Errors of necessary and sufficient conditions

Take the following statement: “All nerds are smart”  N –> S

If I find a nerd, then I’ve found a smart person.  But if I find a smart person, have I found a nerd?  Careful. You can only read “If….then” statements from left to right. “N” lets us conclude “S”.

But knowing the necessary condition, “S” doesn’t let us conclude anything. You can be smart and not nerdy. It is also wrong to conclude that because someone is not a nerd “N” then then are not smart “S

If you want names for them, the two major errors are:

1. Incorrect reversal: Assuming that all smart people are nerds. (S –> N)

2. Incorrect Negation: Assuming that anyone who isn’t a nerd is not smart. (N –> S)

They’re really the same error.

Next: Contrapositive

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