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His logic is sound, but you're misreading him: he's saying that (quantity of app titles all that matters) => (we're all using windows). We're not all using wind
by necubi 16y ago
His logic is sound, but you're misreading him: he's saying that (quantity of app titles all that matters) => (we're all using windows). We're not all using windows, so by contradiction quantity of apps is not all that matters. He's not saying that everybody is using OS X, just that not everybody is using windows.
- DeusExMachina 16y agoExactly. 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).