Logic question

[Thudlow_Boink]

@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.

@HowSoonIsThen

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.

@Steve_MB

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.

[Lance_Turbo]

I think the stumbling block for many here is the concept of vacuous truth.

“A statement S is “vacuously true” if it resembles the statement P ⇒ Q, where P is known to be false.”

[ftg]

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.