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Exactly. This is a logical error that I keep seeing being made from people, and having a logics background I can't help to notice. A implies B does not imply t
by DeusExMachina 16y ago
Exactly. This is a logical error that I keep seeing being made from people, and having a logics background I can't help to notice.
A implies B does not imply that not B implies not A.
- ddlatham 16y agoActually, (A implies B) does imply (!B implies !A). It's the contrapositive. For example, from Wikipedia, "All birds are animals" does imply "All non-animals are non-birds". http://en.wikipedia.org/wiki/Contraposition http://en.wikipedia.org/wiki/Contraposition
- StavrosK 16y agoApparently he meant "(A implies B) does not imply (B implies A)". Affirming the consequent and all that.
- RyanMcGreal 16y ago>A implies B does not imply that not B implies not A. Wait, what? Every time I eat a hard candy, I get a toothache. I don't have a toothache, therefore I didn't eat a hard candy.
- DeusExMachina 16y agoActually I made a mistake there. Going on mere memory and without checking, I put the double negation, which comes from an axiom. So yes, what I meant is "If I eat hard candy, I get toothache" does not imply "I have a toothache, so I ate hard candies". Which is the form I was commenting on. I should have provided an example (and double checked!).
- othermaciej 16y agoActually, it does mean that. If you write out the truth table, A -> B is equivalent to ~A \/ B, which means ~B -> ~A. This is called the contrapositive and is a valid inference. The two classical invalid inferences from A -> B are ~A -> ~B (the inverse) and B -> A (the converse).