Paradox as a counter-example to logic, part 1
One of the most popular ways to try to disprove logic is by bringing up paradoxes. A paradox is where a statement or scenario which appears to be meaningful actually gives absurd results. Take the liar paradox, for example. There are two ways of stating the liar paradox. One way is to say, “A: Statement B is true. B: Statement A is false.” Another way is to say, “This statement is false.” If you assume the statement is true, then it’s false, but if you assume it’s false, then it’s true. So is the statement true or false? According to the law of excluded-middle, it’s one or the other, but this statement appears to be both or neither. So it is often used as an argument against logic.
There are a couple of problems with using paradoxes as an argument against logic. The first problem is that it assumes logic while trying to disprove it, so it’s self-refuting. Whenever a person uses a paradox as an argument against logic, they are forming a syllogism.
1. If the laws of logic are true, they cannot be violated.
2. A paradox violates the laws of logic.
3. Therefore, the laws of logic are not true.
But if the laws of logic are not true, then the conclusion doesn’t follow from the premises since it requires logic to do so.
[There's another way to say the same thing. A paradox is usually brought up as a counter-example to logic. In other words the existence of a paradox is supposed to contradict the laws of logic, and the laws of logic are deemed invalid for that reason. The problem here should be obvious. If the laws of logic are invalid, then you can't dismiss them on the basis that a paradox contradicts them. You need the law of non-contradiction to do that.]