in other words, why are statements of the form “If A then B” always true if A is false?
In: 8
That statement only sounds weird if you already know Bob didn’t drink. What if you don’t know whether Bob drink or not?
In general, there are 4 reasons:
A) To ensure that statement about unknown possibilities, does not fail for stupid reasons.
Let’s say you make a statement “Bob is so alcohol-shy that he’s always the last one to drink; if Bob drinks, then everyone drink” as you make your way to the bar. Once you’re at the bar, you notice Bob did not drink. That shouldn’t make the statement false.
B) For “for all” statement – statement that quantify over unknown object – the statement actually focus only on specific kind of object you described.
I consider this a slam dunk example: “if something is edible, you can eat it”. This statement is obviously true. It should not be false just because there are things that are not edible, so by making sure that the statement is automatically true whenever “something” is not edible you ensure that the content of the statement is focused only on the case where “something” is edible.
C) To ensure that whenever you proved something, it is actually true.
To prove “If A then B”, you assume A is true, then prove B is true. Since your proof ignore what happen when A is false, to ensure that the proof never prove a wrong claim, the statement must be automatically true when A is false.
D) To allow argument by absurdity to work.
Imagine you’re looking at the sky with your child and they say “hey look, it’s a star” and you reply “if it’s a star, it’s moving awfully fast”. Well, the whole purpose of the statement is to show that it’s not a star, so it should be true even when it’s not a star.
Latest Answers