# Logic question **URL:** \ **Category:** Factual Questions\ **Created:** [July 17, 2018, 2:32am UTC](https://boards.straightdope.com/t/logic-question/818057 "2018-07-17T02:32:29Z")\ **Posts on this page:** 3\ **Page:** 2
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [July 17, 2018, 3:11pm UTC](https://boards.straightdope.com/t/logic-question/818057/21 "2018-07-17T15:11:39Z")
> [@septimus](#): > > I think the actual definition of logic implication is used routinely by mathematicians reading or writing math, even math unrelated to logic puzzles. I just saw an example of a logical conditional in [another current thread](https://boards.straightdope.com/sdmb/showthread.php?t=858860). > [@Moral hypothetical: the dark knight](https://boards.straightdope.com/t/moral-hypothetical-the-dark-knight/818075/1): > > Joker appears in Gotham. He says “batman: if you don’t reveal your identity, I will kill people”. Batman doesn’t reveal his identity, joker kills people. > [@Moral hypothetical: the dark knight](https://boards.straightdope.com/t/moral-hypothetical-the-dark-knight/818075/6): > > Of course, this example is somewhat muddied by the established and predictable pattern. > > - Batman refuses to reveal his identity. Joker kills people. > - Batman reveals his identity. Joker kills people. > - Batman patrols Gotham City even more thoroughly than usual searching for the Joker. Joker kills people. > - Batman runs off to the ass end of nowhere searching for Ra’s al Ghul or somebody. Joker kills people. > - Batman adds nipples to his Batsuit. Joker kills people. > - etc The Joker wasn’t lying; he just conveniently neglected to mention what he would do if Batman did reveal his identity. The only way “if you don’t reveal your identity, I will kill people” would logically be considered a false statement is if Batman didn’t reveal his identity and the Joker didn’t kill people. This is something that inexperienced math students have to be taught to be careful about: just because a theorem is true doesn’t mean that its converse (or inverse) is true. Mathematical theorems often have the form of conditional statements: “If A then B.” For a simple example: “If a (whole) number ends in a 5 then it is divisible by 5.” This is a true statement, because it’s possible for A to be true and B to be true (e.g. 35); it’s possible for A to be false and B to be false (e.g. 27); and it’s possible for A to be false and B to be true (e.g. 10). It just isn’t possible for A to be true and B to be false. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [July 17, 2018, 5:22pm UTC](https://boards.straightdope.com/t/logic-question/818057/22 "2018-07-17T17:22:56Z")
I think the stumbling block for many here is the concept of [vacuous truth](https://en.wikipedia.org/wiki/Vacuous_truth). “A statement S is “vacuously true” if it resembles the statement P ⇒ Q, where P is known to be false.” ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [July 17, 2018, 5:57pm UTC](https://boards.straightdope.com/t/logic-question/818057/23 "2018-07-17T17:57:56Z")
Just addressing the OP only: The first two points about ruling out vampires are true. For a human the statement “If I am a vampire, then I am normal.” is true. (You can put anything in the “then” part. 2+2 = 4 or 2+2 =5. It’s irrelevant under this condition.) Therefore an abnormal (always lying) human cannot make such a statement. So only a normal human can say this. [Previous page](https://boards.straightdope.com/t/logic-question/818057.md?page=1)